Browse Algebra problems Studdy Solved!

Problem 23901

Simplify each of the expressions below. Your final simplification should not contain negative exponents. Homework Help a. $\left(5 x^{3}\right)\left(-3 x^{-2}\right)$ b. $\left(4 p^{2} q\right)^{3}$ c. $\frac{3 m^{t}}{m^{-1}}$

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Problem 23902

$008 \quad 10.0$ points A woman of mass 49 a 68 kg canoe that is in If her velocity is 2 m / the velocity of the canoe
Unit 4) 24-25-tejeda - (PerezKPHY1_1) The acceleration of gravity is $9.8 \mathrm{~m} / \mathrm{s}^{2}$ .
Initially, the 6 kg block and 2 kg block rest on a horizontal surface with the 6 kg block in contact with the spring (but not compressing it) and with the 2 kg block in contact with the 6 kg block. The 6 kg block is then moved to the left, compressing the spring a distance of 0.2 m , and held in place while the 2 kg block remains at rest as shown below.
Determine the elastic energy $U$ stored in the compressed spring.
Answer in units of $J$ . 013 (part 2 of 4 ) 10.0 points The 6 kg block is then released and accelerates to the right, toward the 2 kg block. The surface is rough and the coefficient of friction between each block and the surface is 0.3 . The two blocks collide, stick together, and move to the right. Remember that the spring is not attached to the 6 kg block.
Find the speed of the 6 kg block just before it collides with the 2 kg block.
Answer in units of $\mathrm{m} / \mathrm{s}$ .

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Problem 23903

If using the method of completing the square to solve the quadratic equation $x^{2}+15 x+4=0$ , which number would have to be added to "complete the square"?

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Problem 23904

Simplify exch of the expressions below. Y A. $\left(5 e^{6}\right)\left(-9 \pi^{-2}\right)$

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Problem 23905

The functions $f$ and $g$ are defined as follows. $\begin{array}{l} f(x)=\frac{x^{2}}{x-6} \\ g(x)=\frac{x+9}{x^{2}+17 x+72} \end{array}$
For each function, find the domain. Write each answer as an interval or union of intervals.
Domain of $f$ : $\square$
Domain of $g$ : $\square$

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Problem 23906

4. Factorize: $a^{2}-7 a$ $\qquad$
Level 2: Slightly Challenging
5. Factorize: $3 x^{2}-12 x+12$
6. Factorize: $x^{2}+2 x-8$
7. Factorize: $4 y^{2}-16$
8. Factorize: $5 x^{3}-10 x^{2}+15 x$ $\qquad$
Level 3: Medium Difficulty
9. Factorize: $x^{3}+2 x^{2}-x-2$
10. Factorize: $2 a^{2}-3 a-9$
11. Factorize: $6 x^{2}+13 x+5$
12. Factorize: $9 x^{3}-27 x^{2}+12 x$

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Problem 23907

Given an arithmetic progression with $u_{21}=65$ and $d=-2$ , find the value of the first term.

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Problem 23908

Solve: $\frac{x}{11}-\frac{x}{2}=7+\frac{7 x}{22}$ Select one: a. $x=-\frac{77}{8}$ b. $x=\frac{77}{3}$ c. $x=-\frac{9}{22}$ d. $x=-\frac{22}{9}$ e. $x=-22$

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Problem 23909

Factor $y^{3}-5 y^{2}+6 y-30$ completely. $y^{3}-5 y^{2}+6 y-30=$ $\square$

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Problem 23910

1. Factor. $h^{2}+11 h+24$

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Problem 23911

Solve the system by the addition method. $\begin{array}{l} x^{2}+y^{2}=13 \\ x^{2}-y^{2}=5 \end{array}$

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Problem 23912

b) $2 x^{2}-5 x=7 \quad \rightarrow \quad 2 x$

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Problem 23913

2. $x\left(x^{2}-3 x+3\right)(4 x-7)=0$
3. $\left(4 a^{2}-16\right)\left(a^{2}+9\right)=0$
4. $0=\left(p^{2}-5 p+6\right)(p+1)(p-2)$
5. $\left(x^{2}+2 x+2\right)(2 x-3) x=0$

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Problem 23914

10) Explain the difference between "and" \& "or" in a compound inequality. ( 3 points)
The difference between "and" \& "or" is ...

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Problem 23915

Graph the function. $y=\ln x$
Use a graph icon to plot the asymptote and two points.

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Problem 23916

Find the inverse of the function $f(x)=\sqrt{x}+4$ . $f^{-1}(x)=(x+4)^{2}, x \geq 4$ $f^{-1}(x)=(x-4)^{2}, x \geq 0$ $f^{-1}(x)=(x-4)^{2}, x \geq 4$ $f^{-1}(x)=(x+4)^{2}, x \geq 0$ Clear my selection

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Problem 23917

investment services company experienced dramatic growth in the last two decades. The following models for the compar and expenses or costs $C$ (both in millions of dollars) are functions of the years past 1990. $R(t)=21.4 e^{0.131 t} \text { and } C(t)=18.6 e^{0.131 t}$ (a). Use the models to predict the company's profit in 2030. (Round your answer to one decimal place.) $\square$ million Enter a number. (b) How long before the profit found in part (a) is predicted to double? (Round your answer to the nearest whole nun 45 $\square$ years after 1990

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Problem 23918

The population (in thousands) of people of a city is approximated by the function $\mathrm{P}(\mathrm{t})=1400(2)^{0.1048 t}$ , where t is the number of years since 2010. a. Find the population of this group in 2018. b. Predict the population in 2026. a. The population of this group in 2018 is $\square$ (Round to the nearest thousand as needed.)

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Problem 23919

Question
What is an equation of the line that passes through the point $(-1,0)$ and is parallel to the line $5 x+y=6$ ?

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Problem 23920

$2 x-1=2 \sin x+\cos x$

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Problem 23921

4) $\begin{array}{l}14 x-2 y=6 \\ 7 x-4 y=12\end{array}$

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Problem 23922

Use the function below to answer the following questions. $y=\log _{2}(x+6)$ (a) Use transformations of the graph of $y=\log _{2} x$ to graph the given function. (b) Write the domain and range in interval notation. (c) Write an equation of the asymptote.
Part: $0 / 3$
Part 1 of 3 (a) Use transformations of the graph of $y=\log _{2} x$ to graph the given function.

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Problem 23923

State what this comparison operator means: >
Type your answer here (max 400 chars.)

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Problem 23924

Write an expression for the perimeter of this shape. Simplify your answer fully.

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Problem 23925

For help with questions 5 to 8, refer to Investigate 2.
5. a) Copy the graph. b) $\square$ b) Write an equation for this exponential function. c) c) Graph the line $y=x$ on the same grid. d) Sketch a graph of the inverse of the function by reflecting its graph in the line $y=x$ .

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Problem 23926

10. The half-life of the radioactive element plutonium-239 is 25,000 years. If 11 kilograms of plutonium-239 are initially present (between the size of a softball and shotput), how many years will it take for it to decay to less than 1 kilogram?

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Problem 23927

Using the rational root theorem, list out all possible/candidate rational roots of $f(x)=-5 x^{5}+19 x+25 x^{2}-2 x^{4}+17 x^{3}-10$ . Express your answer as inte or as fractions in simplest form. Use commas to separate.

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Problem 23928

Divide. $\left(4 x^{3}-17 x-8\right) \div\left(2 x^{2}-5\right)$
Write your answer in the following form: Quotient $+\frac{\text { Remainder }}{2 x^{2}-5}$ . $\frac{4 x^{3}-17 x-8}{2 x^{2}-5}=\square+\frac{\square}{2 x^{2}-5}$

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Problem 23929

Question 3
Find the vertex of the graph of $g(x)=-2 x^{2}+20 x-44$ . $(-5,-194)$ $(5,106)$ $(5,6)$ $(0,-44)$ $(-5,-94)$

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Problem 23930

$y=6+2$ R. The serpe is $\square$
$\square$ 1

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Problem 23931

6.
Function 1 Function 2
The population of a bacteria colony grows at a rate of $1.5 \%$ per day. The $y=50(1.017)^{2}$ initial population is 70 , and the population is represented by a function, where $x$ is the number of days.
If the constant prevent of change for the function with the larger percent of change is written as $r \%$ , what is the value of $r$ ?

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Problem 23932

$10(x+4)+1$

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Problem 23933

Solve for $x$ : $\log _{2}(x+5)=5$ 5 20 27 0

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Problem 23934

implify. $11 x^{2} y^{3}\left(16 x^{2} y^{3}\right)$ Attempt 1 out of 2

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Problem 23935

Write the equation for the function $g(x)$ that has a graph with the shape of $y=\sqrt{x}$ but is shifted right 7 units. $g(x)=\sqrt{x-7}$ $g(x)=\sqrt{x}+7$ $g(x)=\sqrt{x+7}$ $g(x)=\sqrt{x}-7$

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Problem 23936

Determine the zeros of the quadratic function $f(x)=6 x^{2}+13 x+5$ . $-\frac{1}{2},-\frac{5}{3}$ $\frac{1}{2}, \frac{5}{3}$ $-\frac{1}{3},-\frac{5}{2}$ $\frac{1}{3}, \frac{5}{2}$

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Problem 23937

Look at the algebra grids below. What expressions should replace $A, B$ and $C$ ?

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Problem 23938

Determine all solutions of the equation $-2 w^{2}+14=0$ . $-2,7$ $-7,7$ $-\sqrt{7}, \sqrt{7}$ $-2,-\sqrt{7}, \sqrt{7}$

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Problem 23939

Check your answer: What is $(3 x-2)\left(x^{3}+2 x^{2}+4 x-1\right){ }^{2}$ Use your work from the previous slide to answer. $3 x^{4}+4 x^{3}+8 x^{2}-11 x-2$ $3 x^{4}+4 x^{3}+8 x^{2}-11 x+2$ $3 x^{3}+4 x^{2}+8 x-11 x+2$ $3 x^{4}+8 x^{3}+16 x^{2}$

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Problem 23940

Evaluate the function at the given values of $x$ . Round to 4 decimal places, if necessary. $g(x)=3^{x}$
Part: $0 / 4$
Part 1 of 4 $g(-2)=$ $\square$

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Problem 23941

Evaluate the following expression without using a calculator. $\begin{array}{c} 3^{\log _{3} 2} \\ 3^{\log _{3} 2}= \end{array}$

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Problem 23942

(15 points) Solve the equation below, finding all real solutions. Write your final answer(s) in the box provided. $\log _{6}(2 x-1)+\log _{6}(x)=1$

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Problem 23943

Evaluate the function at the given values of $x$ . Round to 4 decimal places, if necessary. $g(x)=3^{x}$
Part 1 of 4 $g(-2)=0.1111$
Part: 1 / 4
Part 2 of 4 $g(5.7)=$ $\square$

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Problem 23944

Use synthetic division to find the quotient and remainder for $\frac{-2 x^{3}-5 x^{2}-3 x^{2}+3}{x+1}$

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Problem 23945

Find the inverse of the function. $\begin{array}{l} f(x)=\sqrt[3]{13 x+10} \\ f^{-1}(x)= \end{array}$ $\square$
Calculator
Check Answer

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Problem 23946

Solve the quadratic equation by completing the square: $x^{2}+14 x+7=18$ Give the equation after completing the square, but before taking the square root. Your answer should look like: $(x-a)^{2}=b$ The equation is: $\square$ Give all solutions to the equation. The solutions are: $x=$ $\square$ Calculator

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Problem 23947

Find the solution of the system of equations. $\left\{\begin{array}{l} x-5 y=-20 \\ -4 x-5 y=5 \end{array}\right.$
Show your work here $\begin{array}{l} x= \\ y= \end{array}$

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Problem 23948

The population of a small town in Alabama has shown a linear decline in the years 2000 to 2015. The population in 2000 was 8608 , and in 2015 the population was 7798.
Write a linear equation expressing the population of this town, $P$ , as a function of $t$ , the number of years since 2000. $P(t)=$ $\square$ Be sure to use $t$ as your variable!
If the town is still experiencing the same rate of population decline, what will the population be in 2022? $\square$

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Problem 23949

$\$ 18,000$ is invested in an account paying 3.1\% interest compounded continuously. The amount $A(t)$ in the account after $t$ years is given by the exponential function $A(t)=18,000 e^{0.031 t}$ .
1. Determine the amount in the account after 8 years. (Round to two decimal places) $\square$
2. How many years will it take for the account to grow to $\$ 24,000$ ? (Round to 3 decimal places) $\square$

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Problem 23950

stion 15 yet wered rked out of 0 Flag estion
Decide whether the function is even, odd, or neither. $g(x)=x^{3}-5 x$
Select one: a. Even b. Odd c. Neither odd nor even
Clear my choice

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Problem 23951

Find the domain of the following rational function. $H(x)=\frac{-3 x^{2}}{(x-3)(x+3)}$

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Problem 23952

Use properties of logarithms to condense the logarithmic expression. logarithmic expressions. $\begin{array}{l} \ln x+\ln 17 \\ \ln x+\ln 17= \end{array}$ $\square$

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Problem 23953

12
Find the solution of the system of equations. $\left\{\begin{array}{l} 5 x+2 y=4 \\ 2 x-2 y=10 \end{array}\right.$
Show your work here $\begin{array}{l} x= \\ y= \end{array}$

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Problem 23954

Solve the equation: $\log _{6}(x)+\log _{6}(x+16)=2$ The solution(s) is (are) $x=$ $\square$
Calculator

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Problem 23955

Use properties of logarithms to condense the logarithmic expression. expressions if possible. $\begin{array}{l} 2 \ln (x+9)-3 \ln x \\ 2 \ln (x+9)-3 \ln x= \end{array}$ $\square$

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Problem 23956

(a) Graph $f(x)=x^{2}-4 ; x \leq 0$ .

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Problem 23957

Bookwork code: 2C Calculator not allowed
Write an equation to represent the function machine below.
Input Output $x \rightarrow \times 6+4 \rightarrow 7$

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Problem 23958

Alexandra thinks of a number, $t$ . She multiplies it by 4 , then she subtracts 7 and gets an answer of 18 . Write an equation to describe this.

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Problem 23959

Use your calculator to find the real zero(s) and the relative minimum of the function $f(x)=3 x^{3}-3 x^{2}-6 x-4$
The real zero(s) is (are) $\square$ Round to 4 decimal places The relative minimum is $\square$ Round to 4 decimal places
Calculator

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Problem 23960

(18) Solve for $x: a+b(x-c)=0$ (A) $\frac{a+b c}{b}$ (B) $\frac{b c-a}{b}$ (C) $c-a$ (19) Solve for $x: x^{2}-x+3=0$ (A) $x=$ (C) $x=-\frac{3}{2}, x=\frac{5}{2}$ (D) $x=3, x=-$ (20) Solve for $x: 2 x^{2}-9 x+3=0$ (C) $x=1, x=3$ (A) $x=$ (D) $x=4, x=9$ (21) Solve the inequality: $-3 a+7>19$ (A) $a<-4$ (B) $a<12$ (C) $a>-4$ 2) Find the interval solution for $x$ : (A) $(-2,+2]$ (B) $\left[-\frac{9}{4}, 2\right)$ $-6<4 x+3$ (C) $(-6$

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Problem 23961

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution. $11^{x}=67$
The solution set expressed in terms of logarithms is $\square$ \}. (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the expression. Use In for natural logarithm and log for common logarithm.)

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Problem 23962

(19) Solve for $x: x^{2}-x+3=0$ (C) $x=-\frac{3}{2}, x=\frac{5}{2}$ (D) $x=$

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Problem 23963

expand $g(x)=(x-3)^{4}$

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Problem 23964

Polynomials and Factoring Factoring out a monomial from a polynomlal: Univariate
Factor $16 w+20 w^{2}$ . $\square$

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Problem 23965

Solve the following polynomial using synthetic division. $\begin{array}{l} x^{3}+8 x^{2}+11 x-20=0 \\ x=\square \\ x=\square \\ x=\square \end{array}$

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Problem 23966

A good radiograph is taken with 20 mAs using tabletop with an $\mathrm{EI}=200$ . Find the EI value using 40 mAs and 10:1 grid.

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Problem 23967

Which graph represents a proportional relationship?
A
B
C
D

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Problem 23968

Use the definition of a one-to-one function to determine if the function is one-to-one. $k(x)=x^{3}-16$ The function is one-to-one. The function is not one-to-one.

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Problem 23969

$3-4$ . State the answer as an ordered pair $(x, y)$ , if possible.
3. Solve $\left\{\begin{array}{c}y=4 x-1 \\ y=-\frac{1}{2} x+8\end{array}\right.$ by graphing.

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Problem 23970

Use the properties of logarithms to rewrite the expression $\log _{5}\left(x^{9}\right)$ . Write your answer without any powers. $\log _{5}\left(x^{9}\right)=$
Enter your next step here $\square$

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Problem 23971

Solve the following quadratic equation for all values of $x$ in simplest form. $6+3 x^{2}=18$
Answer Attempt 1 out of 2 † Additional Solution No Solution $x=$ $\square$ Submit Answer

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Problem 23972

38) A cyclist bikes at a constant speed for 17 miles. He then returns home at the same speed but takes a different route. His return trip takes one hour longer and is 22 miles. Find his speed.

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Problem 23973

THIW - Ch 5 Linear Google Slides Equations from a Table of Value what is the slope of $y=m x+b$ - itybuilder/instance/674efbba6950e871bcac89db/student/674f475712e503d27285c524\#screenld=26479922-20fd-4c48-86a9-348b257edc3a
Iues and Graph \begin{tabular}{|l|l|l|l|} \hline & 1 & TT & $\sqrt{ \pm}$ \\ \hline \end{tabular} n
Write the equation of a line in slope intercept form GIVEN A GRAPH. Enter all three into the answer box.
Find the slope by: Change in $y$ Slope: $\qquad$ Y-intercept: $\qquad$ Change in $x$
Equation: $\qquad$ Search ENG US

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Problem 23974

3. $f(x)=\frac{1}{\sqrt{1-x^{2}}}$

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Problem 23975

Find a formula for the inverse of the function. $\begin{array}{l} f(x)=\sqrt{x^{2}+2 x}, x>0 . \\ f^{-1}(x)= \end{array}$

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Problem 23976

What is the leading coefficient? $2 x^{6}-3 x^{5}+15 x^{4}$
15 1 Answer $\triangle 15$ 20
6 2 Dowe G kahoot.it Game PIN: 7617209

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Problem 23977

- Des que le revenu est d'au moins 20000 \ $, on doit payer un minimum de$ 25 \% $d'impôt. - Le taux d'imposition augmente de$ 5 \% $pour chaque tranche de$ 15000 \$$ de salaire supplémentaire. - Le taux d'imposition maximal est de $45 \%$. a) Représentez cette situation dans le plan cartésien ci-contre. b) Déterminez la règle qui permet de calculer le taux d'imposition pour un salaire variant de 20000 \$ à 80000 \$. onse:

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Problem 23978

1. Solve each equation. Use a double number line if it is helpful. a. $-3 x-5=20$ $-25 / 3$ b. $\frac{4}{5} x+2=14$
15 $\{3(x-4+13)=36$

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Problem 23979

Solve for $h$ . $h+3>9$

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Problem 23980

Name: Ayda Avila 0.
Writing Systems of Equations Mixed Practice
1. Write a system of equations to represent the following graph. A. $4 x+9 y=36$ C. $4 x+9 y=36$ $y=3 x-2$ $6 x-2 y=-4$ B. $9 x+4 y=36$ D. $y=3 x-2$ $y=-3 x-2$ $y=-\frac{9}{4} x+4$

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Problem 23981

Question 6
Reputable scientists know that the average surface temperature of the world has been rising steadily. One model found using sets of temperature data is: $T=0.02 t+15.0$
Where T is temperature in ${ }^{\circ} C$ and t is years since 1950. (a) Describe what the slope and T-intercept represent. (b) Use the equation to predict the average globle surface temperature in 2050. $\square$ ${ }^{\circ} \mathrm{C}$
Question Help: Message instructor Post to forum Submit Question

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Problem 23982

The base ticket price for a football game is modeled by the function $p(x)=15 x+10$ , where $x$ is the years since the team started playing football. Not included in each base ticket price is a service charge modeled by the function $c(x)=5 x+2$ . To find the total cost of a ticket, a fan should use what operation on the polynomials? Addition Subtraction Multiplication It cannot be determined

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Problem 23983

7 Si $f(x)=x^{2}$ , ¿qué función es el resultado de desplazar $f(x) 3$ unidades hacia la izquierda y 2 unidades hacia abajo? (1) $g(x)=(x+2)^{2}-3$ (3) $j(x)=(x+3)^{2}-2$ (2) $h(x)=(x-2)^{2}+3$ (4) $k(x)=(x-3)^{2}+2$
8 La ecuación utilizada para calcular la velocidad de un objeto es la siguiente: $v^{2}=u^{2}+2 a s$ , donde $u$ es la velocidad inicial, $v$ es la velocidad final, $a$ es la aceleración del objeto y $s$ es la distancia recorrida. Cuando se resuelve esta ecuación para $a$ , el resultado es (1) $a=\frac{v^{2} u^{2}}{2 s}$ (3) $a=v^{2}-u^{2}-2 s$ (2) $a=\frac{v^{2}-u^{2}}{2 s}$ (4) $a=2 s\left(v^{2}-u^{2}\right)$
9 La clase de Matemáticas de la Sra. Smith hizo una encuestó a los estudiantes para determinar sus sabores favoritos de helado. Los resultados se muestran en la siguiente tabla. \begin{tabular}{|c|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & Chocolate & Vainilla & Combinado \\ \hline 11. $^{\circ}$ grado & 42 & 27 & 45 \\ \hline 12. $^{\circ}$ grado & 67 & 42 & 21 \\ \hline \end{tabular}
De los estudiantes que prefieren chocolate, Aproximadamente, ¿qué porcentaje era de $12 .^{\circ}$ grado? (1) 27.5 (3) 51.5 (2) 44.7 (4) 61.5

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Problem 23984

16. $\sqrt[3]{x-12}=3$
17. $\sqrt[4]{5 x+6}-9=0$
18. $\sqrt{1-3 x}-6=4$
19. $3 x^{\frac{2}{3}}=75$

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Problem 23985

Mathematics 30-2
14. Write $\log _{5} a+\log _{5} b-\left(\log _{5} c+\log _{5} d\right)$ as a single logarithm. A) $\log _{5} \frac{a}{b c d}$ B) $\log _{5} \frac{a b}{c d}$ C) $\log _{5} \frac{a b c}{d}$ D) $\log _{5} a b c d$

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Problem 23986

Factor completely $4 x^{5}-20 x^{4}-36 x^{3}$ . $4\left(x^{5}-5 x^{4}-9 x^{3}\right)$ $x^{3}\left(4 x^{2}-20 x-36\right)$ $x^{2}-5 x-9$ $4 x^{3}\left(x^{2}-5 x-9\right)$

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Problem 23987

n, using a calculator if necessary to evaluate the logarithm. Write your answer as a fraction or ro $\ln \left(\mathrm{e}^{\mathrm{x}}\right)=15.1$ w window) $x=$ $\square$

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Problem 23988

```latex Voici un exemple de démarche possible, 7 A partir de la longueur d'un segment, du paramètre b. $4=\frac{1}{|b|} \cdot d_{\text {onc }}|b|=\frac{1}{4}=0,25$ $2=|a|$
A partir de la distance entre consécutifs, soit 2, absolue du paramètre a.
Puisque chaque segment est de la forme Observez la représentation graphique de chaque segment pour déterminer le signe du paramètre b. , $b>0$ , donc $b=0,25$ .
La fonction est croissante, donc a et b sont même signe. Comme $b>0$ , alors $a>0$ , donc $a$ $1(4,2)$ Analysez la variation (croissance ou décroissance) de la fonction afin de déterminer le signe du paramètre a.
Choisissez un point fermé afin de déterminer les valeurs possibles d'un couple ( $h, k$ ). terminez une règle possible pour la tion représentée de la forme : $a[b(x-h)]+k . \quad \mid f(x)=2[0,25(x-4)]+2$ ez chaque fonction ci-dessous. $50\left[\frac{1}{1000}(x+500)\right]$
exemple ```

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Problem 23989

Warm Up Solve the following radical equation for $x$ . $8 \sqrt{2 x+3}-10=30$

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Problem 23990

10. $f(x)=\frac{2}{x+1}, g(x)=\frac{x}{x+1}$
Find the domain of the function.

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Problem 23991

5 Résolvez les équations suivantes. a) $-5 x^{2}+160 x-1200=0$

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Problem 23992

Consider the quadratic function $y=1.7 x^{2}-9.1 x+2.3$ The graph of this function is a Select an answer Question Help: Message in:
Select an answer straight line that slopes downward Submit Part Jump to Ans parabola that opens downward straight line that slopes upward parabola that opens upward

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Problem 23993

- Ch 5 Linear Google Slides Equations from a Table of Value Ider/instance/674efbba6950e871bcac89db/student/674f475712e503d27285c524\#screenld=01649728-103f-45a5-8ca4-0960cd2619db and Graph n
Write the equation of a line in slope intercept form GIVEN A GRAPH. Enter all three into the answer box. Slope: $\qquad$ Y-intercept: $\qquad$ Equation: $\qquad$ 2 5
4 13 $\square$ 4 $\square$ $\sqrt{ \pm}$ Submit 33 12 45 Search ENG US

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Problem 23994

Part 1 of 4
Consider the quadratic function $y=1.7 x^{2}-9.1 x+2.3$ The graph of this function is a parabola that opens upward $\checkmark^{\checkmark} \sigma^{\Delta}$ $\square$ Part 2 of 4
The vertex of this graph is its lowest $\square$ $\checkmark$ os point, so this function has a $\square$ minimum $\checkmark$ of value. Part 3 of 4
State the vertex $(x, y)$ of this parabola. If necessary, round each value to three decimal places. $\square$ , $\square$ )

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Problem 23995

onsider the quadratic function $y=1.7 x^{2}-9.1 x+2.3$ The graph of this function is a parabola that opens upward $\checkmark^{\checkmark} 0^{s}$ $\square$ 0
The vertex of this graph is its lowest $\checkmark \checkmark$ point, so this function has a minimum $0^{8}$ value. $\square$ Part 2 of 4 $\qquad$ State the vertex $(x, y)$ of this parabola. If necessary, round each value to three decimal places. $\begin{array}{l} 2.676 \\ 0^{s} \\ \text { - }) \end{array}$ $-9.878$ Part 4 of 4
Fill in the blanks to interpret the vertex. If necessary, round each value to three decimal places. The minimum value of this function is $\square$ , which occurs at an $x$ value of $\square$ .

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Problem 23996

/activitybuilder/instance/674efbba6950e871bcac89db/student/674f475712e503d27285c524\#screenld=b41ae290-cc56-429e-810e-07bd955554a2 f Values and Graph ${ }^{\pi}$ n
Write the equation of a line in slope intercept form GIVEN A GRAPH. Enter all three into the answer box.
Slope: $\qquad$ Y-intercept: $\qquad$ Equation: $\qquad$ $\square$ Submit

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Problem 23997

Are the systems of equations equivalent? Explain. $\begin{array}{rlrl} 2 x+4 y & =3 & 6 x+12 y & =9 \\ 6 x+3 y & =17 & 6 x+3 y & =17 \end{array}$
The first equation in the second system $\square$ in the first system, and the second equation in the second system $\square$ in the first system. Thus, the systems $\square$ equivalent.

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Problem 23998

Find all excluded values for the expression. That is, find all values of $w$ for which the expression is undefined. $\frac{w+6}{w+7}$
If there is more than one value, separate them with commas. $w=$ $\square$

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Problem 23999

Determine whether the ordered pair is a solution to the inequality. $5 x+6 y>30$ (a) $(-1,2)$ (b) $(4,-1)$ (c) $(6,0)$

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Problem 24000

Exercise 16B 1 The profit, $\$ P$ million, made by a business which invests $\$ x$ million in advertising is given by $P=10 x^{2}-10 x^{4} \text { for } x \geqslant 0$
Find the maximum profit the company can make based on this model. 2 A manufacturer produces smartphone covers. They know that if they sell $n$ thousand covers, they will make a profit of $\$ P$ hundred, and they use the model $P=20 n-3 n^{2}-n^{5}$ . Find, to the nearest dollar, the maximum profit they can make according to this model. 3 The fuel consumption of a car, $F$ litres per 100 km , varies with the speed, $v \mathrm{~km} \mathrm{~h}^{-1}$ , according to the equation $F=\left(3 \times 10^{-6}\right) v^{3}-\left(1.2 \times 10^{-4}\right) v^{2}-0.035 v+12$ At what speed should the car be driven in order to minimize fuel consumption? 4 The rate of growth, $R$ , of a population of bacteria, $t$ hours after the start of an experiment, is modelled by $R=\frac{6}{t}-\frac{47}{t^{4}}$ for $t \geqslant 2$ . Find the time when the population growth is the fastest. 5 A rectangle has width $x \mathrm{~cm}$ and length $20-x \mathrm{~cm}$ . a Find the perimeter of the rectangle. b Find the maximum possible area of the rectangle. 6 A rectangle has sides $3 x \mathrm{~cm}$ and $\frac{14}{x} \mathrm{~cm}$ . a Find the area of the rectangle. b Find the smallest possible perimeter of the rectangle. 7 A cuboid is formed by a square base of side length $x \mathrm{~cm}$ . The other side of the cuboid is of length $9-x \mathrm{~cm}$ . Find the maximum possible volume of the cuboid. 8 A rectangle has area $36 \mathrm{~cm}^{2}$ . Let $x \mathrm{~cm}$ be the length of one of the sides. a Express the perimeter of the rectangle in terms of $x$ . b Hence find the smallest possible perimeter.

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Algebra

Problem 23901

Simplify each of the expressions below. Your final simplification should not contain negative exponents. Homework Help a. (5x3)(−3x−2)\left(5 x^{3}\right)\left(-3 x^{-2}\right)(5x3)(−3x−2) b. (4p2q)3\left(4 p^{2} q\right)^{3}(4p2q)3 c. 3mtm−1\frac{3 m^{t}}{m^{-1}}m−13mt​

Problem 23902

Problem 23903

If using the method of completing the square to solve the quadratic equation x2+15x+4=0x^{2}+15 x+4=0x2+15x+4=0, which number would have to be added to "complete the square"?

Problem 23904

Simplify exch of the expressions below. Y A. (5e6)(−9π−2)\left(5 e^{6}\right)\left(-9 \pi^{-2}\right)(5e6)(−9π−2)

Problem 23905

Problem 23906

Problem 23907

Given an arithmetic progression with u21=65u_{21}=65u21​=65 and d=−2d=-2d=−2, find the value of the first term.

Problem 23908

Solve: x11−x2=7+7x22\frac{x}{11}-\frac{x}{2}=7+\frac{7 x}{22}11x​−2x​=7+227x​ Select one: a. x=−778x=-\frac{77}{8}x=−877​ b. x=773x=\frac{77}{3}x=377​ c. x=−922x=-\frac{9}{22}x=−229​ d. x=−229x=-\frac{22}{9}x=−922​ e. x=−22x=-22x=−22

Problem 23909

Factor y3−5y2+6y−30y^{3}-5 y^{2}+6 y-30y3−5y2+6y−30 completely. y3−5y2+6y−30=y^{3}-5 y^{2}+6 y-30=y3−5y2+6y−30= □\square□

Problem 23910

1. Factor. h2+11h+24h^{2}+11 h+24h2+11h+24

Problem 23911

Solve the system by the addition method. x2+y2=13x2−y2=5\begin{array}{l} x^{2}+y^{2}=13 \\ x^{2}-y^{2}=5 \end{array}x2+y2=13x2−y2=5​

Problem 23912

b) 2x2−5x=7→2x2 x^{2}-5 x=7 \quad \rightarrow \quad 2 x2x2−5x=7→2x

Problem 23913

Problem 23914

10) Explain the difference between "and" \& "or" in a compound inequality. ( 3 points)The difference between "and" \& "or" is ...

Problem 23915

Graph the function. y=ln⁡xy=\ln xy=lnxUse a graph icon to plot the asymptote and two points.

Problem 23916

Problem 23917

Problem 23918

Problem 23919

QuestionWhat is an equation of the line that passes through the point (−1,0)(-1,0)(−1,0) and is parallel to the line 5x+y=65 x+y=65x+y=6 ?

Problem 23920

2x−1=2sin⁡x+cos⁡x2 x-1=2 \sin x+\cos x2x−1=2sinx+cosx

Problem 23921

4) 14x−2y=67x−4y=12\begin{array}{l}14 x-2 y=6 \\ 7 x-4 y=12\end{array}14x−2y=67x−4y=12​

Problem 23922

Problem 23923

State what this comparison operator means: >Type your answer here (max 400 chars.)

Problem 23924

Write an expression for the perimeter of this shape. Simplify your answer fully.

Problem 23925

For help with questions 5 to 8, refer to Investigate 2.5. a) Copy the graph. b) □\square□ b) Write an equation for this exponential function. c) c) Graph the line y=xy=xy=x on the same grid. d) Sketch a graph of the inverse of the function by reflecting its graph in the line y=xy=xy=x.

Problem 23926

10. The half-life of the radioactive element plutonium-239 is 25,000 years. If 11 kilograms of plutonium-239 are initially present (between the size of a softball and shotput), how many years will it take for it to decay to less than 1 kilogram?

Problem 23927

Using the rational root theorem, list out all possible/candidate rational roots of f(x)=−5x5+19x+25x2−2x4+17x3−10f(x)=-5 x^{5}+19 x+25 x^{2}-2 x^{4}+17 x^{3}-10f(x)=−5x5+19x+25x2−2x4+17x3−10. Express your answer as inte or as fractions in simplest form. Use commas to separate.

Problem 23928

Problem 23929

Question 3Find the vertex of the graph of g(x)=−2x2+20x−44g(x)=-2 x^{2}+20 x-44g(x)=−2x2+20x−44. (−5,−194)(-5,-194)(−5,−194) (5,106)(5,106)(5,106) (5,6)(5,6)(5,6) (0,−44)(0,-44)(0,−44) (−5,−94)(-5,-94)(−5,−94)

Problem 23930

y=6+2y=6+2y=6+2 R. The serpe is □\square□ □\square□ 1

Problem 23931

Problem 23932

10(x+4)+110(x+4)+110(x+4)+1

Problem 23933

Solve for xxx : log⁡2(x+5)=5\log _{2}(x+5)=5log2​(x+5)=5 5 20 27 0

Problem 23934

implify. 11x2y3(16x2y3)11 x^{2} y^{3}\left(16 x^{2} y^{3}\right)11x2y3(16x2y3) Attempt 1 out of 2

Problem 23935

Write the equation for the function g(x)g(x)g(x) that has a graph with the shape of y=xy=\sqrt{x}y=x​ but is shifted right 7 units. g(x)=x−7g(x)=\sqrt{x-7}g(x)=x−7​ g(x)=x+7g(x)=\sqrt{x}+7g(x)=x​+7 g(x)=x+7g(x)=\sqrt{x+7}g(x)=x+7​ g(x)=x−7g(x)=\sqrt{x}-7g(x)=x​−7

Problem 23936

Determine the zeros of the quadratic function f(x)=6x2+13x+5f(x)=6 x^{2}+13 x+5f(x)=6x2+13x+5. −12,−53-\frac{1}{2},-\frac{5}{3}−21​,−35​ 12,53\frac{1}{2}, \frac{5}{3}21​,35​ −13,−52-\frac{1}{3},-\frac{5}{2}−31​,−25​ 13,52\frac{1}{3}, \frac{5}{2}31​,25​

Problem 23937

Look at the algebra grids below. What expressions should replace A,BA, BA,B and CCC ?

Problem 23938

Determine all solutions of the equation −2w2+14=0-2 w^{2}+14=0−2w2+14=0. −2,7-2,7−2,7 −7,7-7,7−7,7 −7,7-\sqrt{7}, \sqrt{7}−7​,7​ −2,−7,7-2,-\sqrt{7}, \sqrt{7}−2,−7​,7​

Problem 23939

Problem 23940

Evaluate the function at the given values of xxx. Round to 4 decimal places, if necessary. g(x)=3xg(x)=3^{x}g(x)=3xPart: 0/40 / 40/4Part 1 of 4 g(−2)=g(-2)=g(−2)= □\square□

Problem 23941

Evaluate the following expression without using a calculator. 3log⁡323log⁡32=\begin{array}{c} 3^{\log _{3} 2} \\ 3^{\log _{3} 2}= \end{array}3log3​23log3​2=​

Problem 23942

(15 points) Solve the equation below, finding all real solutions. Write your final answer(s) in the box provided. log⁡6(2x−1)+log⁡6(x)=1\log _{6}(2 x-1)+\log _{6}(x)=1log6​(2x−1)+log6​(x)=1

Problem 23943

Evaluate the function at the given values of xxx. Round to 4 decimal places, if necessary. g(x)=3xg(x)=3^{x}g(x)=3xPart 1 of 4 g(−2)=0.1111g(-2)=0.1111g(−2)=0.1111Part: 1 / 4Part 2 of 4 g(5.7)=g(5.7)=g(5.7)= □\square□

Problem 23944

Use synthetic division to find the quotient and remainder for −2x3−5x2−3x2+3x+1\frac{-2 x^{3}-5 x^{2}-3 x^{2}+3}{x+1}x+1−2x3−5x2−3x2+3​

Problem 23945

Find the inverse of the function. f(x)=13x+103f−1(x)=\begin{array}{l} f(x)=\sqrt[3]{13 x+10} \\ f^{-1}(x)= \end{array}f(x)=313x+10​f−1(x)=​ □\square□CalculatorCheck Answer

Simplify each of the expressions below. Your final simplification should not contain negative exponents. Homework Help a. $\left(5 x^{3}\right)\left(-3 x^{-2}\right)$ b. $\left(4 p^{2} q\right)^{3}$ c. $\frac{3 m^{t}}{m^{-1}}$

If using the method of completing the square to solve the quadratic equation $x^{2}+15 x+4=0$ , which number would have to be added to "complete the square"?

Simplify exch of the expressions below. Y A. $\left(5 e^{6}\right)\left(-9 \pi^{-2}\right)$

Given an arithmetic progression with $u_{21}=65$ and $d=-2$ , find the value of the first term.

Solve: $\frac{x}{11}-\frac{x}{2}=7+\frac{7 x}{22}$ Select one: a. $x=-\frac{77}{8}$ b. $x=\frac{77}{3}$ c. $x=-\frac{9}{22}$ d. $x=-\frac{22}{9}$ e. $x=-22$

Factor $y^{3}-5 y^{2}+6 y-30$ completely. $y^{3}-5 y^{2}+6 y-30=$ $\square$

1. Factor. $h^{2}+11 h+24$

Solve the system by the addition method. $\begin{array}{l} x^{2}+y^{2}=13 \\ x^{2}-y^{2}=5 \end{array}$

b) $2 x^{2}-5 x=7 \quad \rightarrow \quad 2 x$

10) Explain the difference between "and" \& "or" in a compound inequality. ( 3 points)
The difference between "and" \& "or" is ...

Graph the function. $y=\ln x$
Use a graph icon to plot the asymptote and two points.

Question
What is an equation of the line that passes through the point $(-1,0)$ and is parallel to the line $5 x+y=6$ ?

$2 x-1=2 \sin x+\cos x$

4) $\begin{array}{l}14 x-2 y=6 \\ 7 x-4 y=12\end{array}$

State what this comparison operator means: >
Type your answer here (max 400 chars.)

For help with questions 5 to 8, refer to Investigate 2.
5. a) Copy the graph. b) $\square$ b) Write an equation for this exponential function. c) c) Graph the line $y=x$ on the same grid. d) Sketch a graph of the inverse of the function by reflecting its graph in the line $y=x$ .

Using the rational root theorem, list out all possible/candidate rational roots of $f(x)=-5 x^{5}+19 x+25 x^{2}-2 x^{4}+17 x^{3}-10$ . Express your answer as inte or as fractions in simplest form. Use commas to separate.

Question 3
Find the vertex of the graph of $g(x)=-2 x^{2}+20 x-44$ . $(-5,-194)$ $(5,106)$ $(5,6)$ $(0,-44)$ $(-5,-94)$

$y=6+2$ R. The serpe is $\square$
$\square$ 1

$10(x+4)+1$

Solve for $x$ : $\log _{2}(x+5)=5$ 5 20 27 0

implify. $11 x^{2} y^{3}\left(16 x^{2} y^{3}\right)$ Attempt 1 out of 2

Write the equation for the function $g(x)$ that has a graph with the shape of $y=\sqrt{x}$ but is shifted right 7 units. $g(x)=\sqrt{x-7}$ $g(x)=\sqrt{x}+7$ $g(x)=\sqrt{x+7}$ $g(x)=\sqrt{x}-7$

Determine the zeros of the quadratic function $f(x)=6 x^{2}+13 x+5$ . $-\frac{1}{2},-\frac{5}{3}$ $\frac{1}{2}, \frac{5}{3}$ $-\frac{1}{3},-\frac{5}{2}$ $\frac{1}{3}, \frac{5}{2}$

Look at the algebra grids below. What expressions should replace $A, B$ and $C$ ?

Determine all solutions of the equation $-2 w^{2}+14=0$ . $-2,7$ $-7,7$ $-\sqrt{7}, \sqrt{7}$ $-2,-\sqrt{7}, \sqrt{7}$

Evaluate the function at the given values of $x$ . Round to 4 decimal places, if necessary. $g(x)=3^{x}$
Part: $0 / 4$
Part 1 of 4 $g(-2)=$ $\square$

Evaluate the following expression without using a calculator. $\begin{array}{c} 3^{\log _{3} 2} \\ 3^{\log _{3} 2}= \end{array}$

(15 points) Solve the equation below, finding all real solutions. Write your final answer(s) in the box provided. $\log _{6}(2 x-1)+\log _{6}(x)=1$

Evaluate the function at the given values of $x$ . Round to 4 decimal places, if necessary. $g(x)=3^{x}$
Part 1 of 4 $g(-2)=0.1111$
Part: 1 / 4
Part 2 of 4 $g(5.7)=$ $\square$

Use synthetic division to find the quotient and remainder for $\frac{-2 x^{3}-5 x^{2}-3 x^{2}+3}{x+1}$

Find the inverse of the function. $\begin{array}{l} f(x)=\sqrt[3]{13 x+10} \\ f^{-1}(x)= \end{array}$ $\square$
Calculator
Check Answer

Find the solution of the system of equations. $\left\{\begin{array}{l} x-5 y=-20 \\ -4 x-5 y=5 \end{array}\right.$
Show your work here $\begin{array}{l} x= \\ y= \end{array}$

stion 15 yet wered rked out of 0 Flag estion
Decide whether the function is even, odd, or neither. $g(x)=x^{3}-5 x$
Select one: a. Even b. Odd c. Neither odd nor even
Clear my choice

Find the domain of the following rational function. $H(x)=\frac{-3 x^{2}}{(x-3)(x+3)}$

Use properties of logarithms to condense the logarithmic expression. logarithmic expressions. $\begin{array}{l} \ln x+\ln 17 \\ \ln x+\ln 17= \end{array}$ $\square$

12
Find the solution of the system of equations. $\left\{\begin{array}{l} 5 x+2 y=4 \\ 2 x-2 y=10 \end{array}\right.$
Show your work here $\begin{array}{l} x= \\ y= \end{array}$

Solve the equation: $\log _{6}(x)+\log _{6}(x+16)=2$ The solution(s) is (are) $x=$ $\square$
Calculator

Use properties of logarithms to condense the logarithmic expression. expressions if possible. $\begin{array}{l} 2 \ln (x+9)-3 \ln x \\ 2 \ln (x+9)-3 \ln x= \end{array}$ $\square$

(a) Graph $f(x)=x^{2}-4 ; x \leq 0$ .

Bookwork code: 2C Calculator not allowed
Write an equation to represent the function machine below.
Input Output $x \rightarrow \times 6+4 \rightarrow 7$

Alexandra thinks of a number, $t$ . She multiplies it by 4 , then she subtracts 7 and gets an answer of 18 . Write an equation to describe this.

Use your calculator to find the real zero(s) and the relative minimum of the function $f(x)=3 x^{3}-3 x^{2}-6 x-4$
The real zero(s) is (are) $\square$ Round to 4 decimal places The relative minimum is $\square$ Round to 4 decimal places
Calculator

(19) Solve for $x: x^{2}-x+3=0$ (C) $x=-\frac{3}{2}, x=\frac{5}{2}$ (D) $x=$

expand $g(x)=(x-3)^{4}$

Polynomials and Factoring Factoring out a monomial from a polynomlal: Univariate
Factor $16 w+20 w^{2}$ . $\square$

Solve the following polynomial using synthetic division. $\begin{array}{l} x^{3}+8 x^{2}+11 x-20=0 \\ x=\square \\ x=\square \\ x=\square \end{array}$

A good radiograph is taken with 20 mAs using tabletop with an $\mathrm{EI}=200$ . Find the EI value using 40 mAs and 10:1 grid.

Which graph represents a proportional relationship?
A
B
C
D

Use the definition of a one-to-one function to determine if the function is one-to-one. $k(x)=x^{3}-16$ The function is one-to-one. The function is not one-to-one.

$3-4$ . State the answer as an ordered pair $(x, y)$ , if possible.
3. Solve $\left\{\begin{array}{c}y=4 x-1 \\ y=-\frac{1}{2} x+8\end{array}\right.$ by graphing.

Use the properties of logarithms to rewrite the expression $\log _{5}\left(x^{9}\right)$ . Write your answer without any powers. $\log _{5}\left(x^{9}\right)=$
Enter your next step here $\square$

Solve the following quadratic equation for all values of $x$ in simplest form. $6+3 x^{2}=18$
Answer Attempt 1 out of 2 † Additional Solution No Solution $x=$ $\square$ Submit Answer

3. $f(x)=\frac{1}{\sqrt{1-x^{2}}}$