Browse Algebra problems Studdy Solved!

Problem 19901

Use $f(x)=x^{2}-9$ and $g(x)=x^{2}+9$ to find a formula for each expression. Identify its domain. (a) $(f+g)(x)$ (c) $(\mathrm{fg})(\mathrm{x})$ (b) $(f-g)(x)$ (d) $(f / g)(x)$ (a) $(f+g)(x)=$ $\square$ (Simplify your answer. Do not factor.)

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Problem 19902

A cubic function $g(x)$ with integral coefficients has the following properties: $g(3)=0, g\left(-\frac{3}{4}\right)=0,(x+2)$ is a factor of $g(x), g(1)=-84$ . Determine $g(x)$ .

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Problem 19903

Use properties of logarithms to express each logarithm as a sum or difference logarithms. Assume that all variables represent positive real numbers. $\frac{\log _{3} \frac{\sqrt[4]{x} \cdot \sqrt[5]{y}}{r^{4}}}{\log _{3} \frac{\sqrt[4]{x} \cdot \sqrt[5]{y}}{r^{4}}=\square}$ $\square$

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Problem 19904

Write the following using the log base change rule, and change to either log base 10 (write log) or log base e (write it as In) $\log _{2}(7)$

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Problem 19905

11. Jika $f(x)=\frac{(5 x-3)^{4}-1}{3}$ , maka nilai dari $f^{-1}(5)$ adalah...

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Problem 19906

7. $\begin{array}{r}3 w+x+y+z=2 \\ x+2 y+3 z=1 \\ -2 z=2 \\ 3 w \quad 2 x+4 y+7 z=1\end{array}$

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Problem 19907

Write an equation of the line. Vertical; through $(2,-3)$

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Problem 19908

ills Check Quiz (Integrated Question 1 of 17 This question $1 \leftarrow$
Use properties of rational exponents to simplify the expression. Assume that all variables represent positive numbers. $\begin{array}{l} \frac{x^{1 / 5}}{x^{2 / 5}} \\ \frac{x^{1 / 5}}{x^{2 / 5}}= \end{array}$ $\square$ (Use positive exponents only.)

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Problem 19909

Rewrite the expression with rational exponents. $\sqrt[3]{9}$

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Problem 19910

Question 4
A factor of $x^{3}+12 x^{2}+41 x+42$ is $x-3$ $x+3$ $x-2$ $x-7$

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Problem 19911

Question 4 of 17
Factor the polynomial if it is a perfect square trinomial, or state that the polynomial is prime. $x^{2}-20 x y+100 y^{2}$
Select the correct choice below and fill in any answer boxes within your choice. A. $x^{2}-20 x y+100 y^{2}=$ $\square$ B. The polynomial is prime.

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Problem 19912

Given the function $y=x^{3}$ , what are the parameters of the transformed function $y=\frac{1}{5}(x+2)^{3}+9$ and what is the effect of each parameter on the graph of the original function? $a=\frac{1}{5}$ , vertical stretch about the $x$ -axis by a factor of $\frac{1}{5}$ $h=-2$ , horizontal translation 2 units left $k=9$ , vertical translation 9 units up $a=5$ , vertical stretch about the $x$ -axis by a factor of 5 $h=-2$ , horizontal translation 2 units left $k=9$ , vertical translation 9 units right $a=5$ , vertical stretch about the $x$ -axis by a factor of 5 $h=-2$ , horizontal translation 2 units right $k=9$ , vertical translation 9 units down $a=\frac{1}{5}$ , vertical stretch about the $x$ -axis by a factor of $\frac{1}{5}$ $h=9$ , horizontal translation 9 units left $k=-2$ , vertical translation 2 units down

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Problem 19913

Find the zeros of $f(x)=(x-2)^{5}(x+5)^{3}$ and state the multiplicity. 2 , multiplicity $5 ;-5$ , multiplicity 3 5 , multiplicity $2 ;-5$ , multiplicity 3 5 , multiplicity $2 ; 3$ , multiplicity -5 2 , multiplicity $5 ; 3$ , multiplicity -5

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Problem 19914

Simplify the expression. $\left(\frac{1}{16}\right)^{1 / 2}$ $\left(\frac{1}{16}\right)^{1 / 2}=$ $\square$ (Type an integer or a simplified fraction.)

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Problem 19915

Solve the following exponential equation. Express your answer as both an exact expression and a decimal approximation rounded to two decimal places. $7^{2 x-8}=1009$

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Problem 19916

4 Skills Check Quiz (Integrated Question 8 of 1
Perform the addition. $\begin{array}{l} \frac{x-5}{x+4}+\frac{x+4}{x-5} \\ \frac{x-5}{x+4}+\frac{x+4}{x-5}= \end{array}$ $\square$ (Simplify your answer. Type your answer in factored form.)

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Problem 19917

If $x-1$ is a factor of $x^{3}-k x^{2}+2 x$ , what is the value of $k$ ?

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Problem 19918

10. The sum of the squares of two consecutive integers is 365 . Find the integers.

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Problem 19919

Factor the given polynomial. $x^{2}-13 x+40$
Select the correct choice below and, if necessary, fill in the answer box within your choice. A. $x^{2}-13 x+40=$ $\square$

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Problem 19920

Question 13
Factor the trinomial, or state that the trinomial is prime. $x^{2}-4 x-45$
Select the correct choice below and fill in any answer boxes within your choice A. $x^{2}-4 x-45=$ $\square$ B. The polynomial is prime.

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Problem 19921

7 Mark for Review
A model predicts that the population of Springfield was 15,000 in 2005. The model also predicts that each year for the next 5 years, the population $p$ increased by $4 \%$ of the previous year's population. Which equation best represents this model, where $x$ is the number of years after 2005 , for $x \leq 5$ ? (A) $p=0.96(15,000)^{x}$ (B) $p=1.04(15,000)^{x}$ (C) $p=15,000(0.96)^{x}$ (D) $p=15,000(1.04)^{x}$ Question 7 of 22

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Problem 19922

Identify a and b for the hyperbola with equation $-\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ . $\begin{array}{l} a=\square \\ b=\text { Enter an interer or decinal rumber frove.d } \end{array}$ Submit Question

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Problem 19923

Factoring and Applications Lesson \#4: Factori Factor. a) $4(3 x+1)^{2}-5(3 x+1)+1$

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Problem 19924

Find all zeros of $f(x)=x^{3}-3 x^{2}-3 x+1$ . Enter the zeros separated by commas. Enter exact value, not decimal approximations.

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Problem 19925

Lovis organise un spectade musical, ses dépences sélevent à 3800\ $-Les billels pour acultes se vendront 25\$, Jand que les billets pour enfant seront$ 12 \$$-Louis prévoit qu'il y aura deux fois plus adultes que enfants. écrits une inequation qui petmeltra à $L$ uis de vérifier s'il couvira qu moins ses dépenges à láide de ses revenus.

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Problem 19926

Slope As a Rate of Change Slope is often referred to as a rate of change because it compares the change in one variable (the rise) to the change in another variable (the run). Chris runs each day as part of his daily exercise. The graph shows his distance from home as he runs his route.
Calculate his rate of change (speed) for each segment of the graph and describe what is happening in each segment. Don't forget to include units in your calculations! \begin{tabular}{|c|c|c|} \hline Segment & \begin{tabular}{c} Slope (Rate of \\ Change) \end{tabular} & \\ \hline AB & & \\ \hline BC & & \\ \hline CD & & \\ \hline DE & & \\ \hline \end{tabular} 17

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Problem 19927

Use common logarithms or natural logarithms and a calculator to evaluate the expression. $\log _{19} 11$
Evaluate the expression. $\log _{19} 11 \approx \square$ (Type an integer or a decimal. Do not round until the final answer. Then round to four dec

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Problem 19928

breath, which is the limiting reactant? (4 $180.18 \mathrm{~g} / \mathrm{mol} 32^{2} \cdot \mathrm{ciog} / \mathrm{mal} \sim \infty 60_{2}(0.008125 \mathrm{mul})$ is the $\frac{2.94 \mathrm{~g}}{180.18 \mathrm{~g} \mathrm{hol}}=0.0163 \mathrm{~mol} \quad \frac{0.26 \mathrm{~g}}{32.00 \mathrm{~g} / \mathrm{mol}}=0.008125 \mathrm{~mol}$ (d) How much carbon dioxide will be produced in grams? (3 marks)

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Problem 19929

13. Jika $f(x)=2 x^{2}-5$ dan $g(x): \sqrt{3 x+22}$ maka $(f \circ g)^{-1}(-3)$ adaiah...

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Problem 19930

Write the equation in logarithmic form. $e^{z}=u$ $\square$ Hint 5 (1) Submit Question

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Problem 19931

Without graphing, determine whether system has one solution, no solution, or an infinite number of solutions. $\left\{\begin{array}{c} x+y=6 \\ 4 x+4 y=24 \end{array}\right.$

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Problem 19932

Using the change of base formula, the expression $\frac{\log _{5} 22}{\log _{5} 23}$ can also be written as $\log _{22} 23$ $\frac{\log _{23} 22}{5}$ $\log _{23} 22$ $\frac{\log _{5} 22}{23}$

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Problem 19933

Given the function $C(r)=2 r^{4}-10 r^{3}-12 r^{2}$ its $C$ -intercept is $\square$ its $r$ -intercepts are $\square$

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Problem 19934

Use the product rule to simplify the expression. $\begin{array}{c} (7 p y)(-8 p) \\ (7 p y)(-8 p)= \end{array}$ (Type your answer using exponential notation.)

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Problem 19935

Question 5 of 18, Step 1 of 1 4/19 Correct
Simplify the following complex fraction. $\frac{5 x^{-2}+y^{-2}}{5 x^{-3}-y^{-2}}$
Answer

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Problem 19936

Use the quotient rule to simplify. $\frac{x^{4} y^{7}}{x^{2} y^{7}}$

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Problem 19937

\begin{tabular}{|c|} \hline Compound Interest Applications \\ \hline Solve the following compound interest problems. Round your results to the nearest cent as needed. \\ \hline \begin{tabular}{l} Michael invests $\$ 3000$ for 3 years at an interest rate of $6 \%$ compounded quarterly. Determine the interest he will earn at the end of 3 years. \\ Michael will earn $\$ 184.09 \times$ in interest on his investment. \\ dollars \end{tabular} \\ \hline \begin{tabular}{l} Maureen takes out a loan with a compound interest rate of $14 \%$ . If Maureen borrows $\$ 4000$ for 11 years compounded monthly, how much interest will she pay at the end of 11 years? \\ Maureen will pay back \\square$ in interest on her loan. \\ dollars \end{tabular} \\ \hline \end{tabular}

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Problem 19938

x-1 2x-1 3(2x-1)=56-1) 2x-176+ +1 2x #1 х- box-3=5x-5 Бос- +3 +3 pc+1/2 6x=5x-5+3 6x=5x-2 -6xx -5xc x=-2 x-1 5x+20 b. x+3 x²-16 (-1)(x²-16)=(5c+20) (7 (pc-1) (x+4) (c-4)=5 (ac-1) (3c-41) = $lact. (c2-पा(-120+14) = 8 (DC-11) (OC+1)=0 OC ж

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Problem 19939

Unit 4: Rational Expressions and Equations Assignment Booklet 4
10. Consider each scenario: a. A high-speed passenger train in Europe completes an 800 km trip in 3 hours. The train travels the first 600 km at an average speed that was $100 \mathrm{~km} / \mathrm{h}$ faster than the last 200 km of the trip. If $x$ represents the average speed of the train on the second part of the trip, then an equation to represent this situation is: $\frac{600}{x+100}+\frac{200}{x}=3$
Identify all restrictions on the variable $x$ in this context. (2 marks)

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Problem 19940

Find the horizontal asymptote of $f(x)=\frac{-4 x+4 x^{3}-5}{x^{3}+2 x^{2}+3}$ $y=$

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Problem 19941

Simplify. Use positive exponents for any variables. $(6 x)^{0}+6 x^{0}$

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Problem 19942

If $\|\mathbf{v}\|=2.4$ and $\|\mathbf{w}\|=4$ and the angle between $\mathbf{v}$ and $\mathbf{w}$ is $60^{\circ}$ , find $\mathbf{v} \cdot \mathbf{w}$ . Give an exact answer. $\mathbf{v} \cdot \mathbf{w}=$ $\square$ $\sqrt{\square}$

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Problem 19943

$y=x^{2}+4 x-12$

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Problem 19944

Factor completely. $u^{2}-9 u+14=$

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Problem 19945

11. Algebra, STD2 A4 2014 HSC 26d
Draw each graph on the grid below and hence solve the simultaneous equations. (3 marks) $\begin{array}{l} y=2 x+1 \\ x-2 y-4=0 \end{array}$ (3 marks)

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Problem 19946

$f(x)=x^{2}+4-12$
Entrada...

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Problem 19947

Simplify. Write the answer using positive exponents only. $\left(\frac{x^{-8}}{x^{-3}}\right)^{-9}$

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Problem 19948

Simplify. Write the answer using positive exponents only. $\left(\frac{x^{-3} y^{-5}}{a^{-3}}\right)^{-5}$

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Problem 19949

Answer all of the following questions. (1) What is the domain of $f(x)=\frac{3}{x+4}$ ? Explain how you reached your conclusion. (2) Consider the graph of $f(x)=\frac{3}{x+4}$ shown below. What do you think is the range of $f(x)$ ?

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Problem 19950

Calculate the slope and enter it below to aim the X Wing and destroy all TIE-Fighters. \begin{tabular}{|l|l|} \hline Slope & Aim Left or Right \\ \hline & \\ \hline \end{tabular}
Fire

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Problem 19951

Simplify. $\left(\frac{4 x^{2}}{y^{3}}\right)^{3}\left(\frac{4 x^{8}}{y}\right)^{-2}$

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Problem 19952

$\sqrt{2 x}+3=9$

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Problem 19953

Add. $\left(6 x^{3} y-6 x y+5\right)+\left(8 x^{3} y+6 x y+5 x\right)$

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Problem 19954

If 28600 dollars is invested at an interest rate of 7 percent per year, find the value of the investment at the end of 5 years for the following compounding methods. (a) Annual:
Your answer is $\square$ (b) Semiannual:
Your answer is $\square$ (c) Monthly:
Your answer is $\square$ (d) Daily:
Your answer is $\square$ (e) Continuously:
Your answer is $\square$

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Problem 19955

Word Problems: Problem 14 (1 point) In 2010, the population of a country was $1 million and growing at a rate of 1.5% per year. Assuming the percentage growth rate remains constant express the population P. in millions, as a function of t the number of years after 2010. P= f(t)= million people help (formulas) Preview My Answers Submit Answers

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Problem 19956

14 Mark for Review
The function $f(t)=60,000(2)^{\frac{t}{40}}$ gives the number of bacteria in a population $t$ minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?
Answer Preview:

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Problem 19957

Solve the equation. Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. $10^{5+2 y}+8500=94,000$ There is no solution, $\}$ . The exact solution set is $\square$
$\log$ $\square{ }^{\circ l o g}$

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Problem 19958

Question 7
Evaluate the following expressions.
1 (a) $\log _{3} 3^{13}=$ $\square$ (b) $\log _{3} 81=$ $\square$ (c) $\log _{4} 256=$ $\square$ (d) $\log _{5} 5^{10}=$ $\square$

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Problem 19959

In 2010, the population of a country was 81 million and growing at a rate of $1.5 \%$ per year. Assuming the percentage growth rate remains constant, express the population, $P$ , in millions, as a function of $t$ , the number of years after 2010. $P=f(t)=$ $\square$ million people help (formulas)

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Problem 19960

a) $\log _{5} x=3$

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Problem 19961

If 28600 dollars is invested at an interest rate of 7 percent per year, find the value of the investment at the end of 5 years for the following compounding methods. (a) Annual:
Your answer is $\square$ (b) Semiannual:
Your answer is $\square$ (c) Monthly:
Your answer is $\square$ (d) Daily:
Your answer is $\square$ (e) Continuously:
Your answer is $\square$

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Problem 19962

- For $f(x)=\frac{9}{x-8}$ and $g(x)=\frac{1}{x}$ , find the following composite functions and state the domain of each. (a) $f \circ g$ (b) $g \circ f$ (c) $f \circ f$ (d) $\mathrm{g} \circ \mathrm{g}$ (a) $(f \circ g)(x)=$ $\square$ (Simplify your answer.)

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Problem 19963

Kristen invests \ $5,000 in a bank. The bank pays$ 6 \%$ interest compounded monthly. To the nearest tenth of a year, how long mus she leave the money in the bank for it to double?

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Problem 19964

Consider the following. line: passes through $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right): x=x_{1}+t\left(x_{2}-x_{1}\right), y=y_{1}+t\left(y_{2}-y_{1}\right)$ Find a set of parametric equations to represent the graph of the line. (Enter your answers as a comma-separated list of equations.) line: passes through $(1,3)$ and $(-7,4)$

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Problem 19965

B. Assume that one-year interest rate is $11 \%$ in the USA while the one. year interest rate in Ghana is $34 \%$ . A USA bank is prepared to buy tho Ghana Cedi at a discount of $13 \%$ one year from now. An investor wity $\$ 1,000,000$ in USA is considering whether it is worthwhile to take advantage of covered interest arbitrage. Assume a spot rate of $\$ 1$ to GHe1.4.
Required: i Determine whether covered interest arbitrage is worthwhile. (12 marks) ii. Give two reasons why the investor should not attempt covent

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Problem 19966

Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: $x=h+r \cos (\theta), \quad y=k+r \sin (\theta)$

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Problem 19967

A factor of $x^{3}+15 x^{2}+71 x+105$ is $x+5$ $x-5$ $x-7$ $x-3$

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Problem 19968

$x+x=$

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Problem 19969

project initially costs $\$ 100,000$ to get stairted and has a discount rate of $9 \%$ . It has a useful life of five years. You expect the project to have a NPV of $\$ 15,000$ . nat would be the equal yearly cashflow generated by the project need to be to reach the target NPV
Multiple Choice \ $30,785.59 \$29,565.63 \$29,006.36 \$28,693.57$ \ $28,075.47$

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Problem 19970

Solve the equation by using the square root property. $(3 p+2)^{2}=8$
The solution set is $\square$ (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.

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Problem 19971

Determine all values of $a$ for which the following set of vectors is dependent or independent. You can select 'always', 'never', ' $a=$ ', or ' $a \neq$ ', then specify a value or comma-separated list of values. $\left\{\left[\begin{array}{c} 1 \\ 3 \\ -1 \\ a \end{array}\right],\left[\begin{array}{l} 1 \\ 3 \\ 0 \\ 1 \end{array}\right],\left[\begin{array}{l} 2 \\ 6 \\ 1 \\ 2 \end{array}\right]\right\}$
Dependent: Always
Independent: Always SUBMIT AND MARK SAVE AND CLOS

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Problem 19972

Question 4 [10 points] Determine all values of $a$ for which the following set of vectors is dependent or independent. You can select 'always', 'never', ' $a=$ ', or ' $a \neq$ ', then specify a value or comma-separated list of values. $\left\{\left[\begin{array}{c} a \\ 1 \\ -2 \\ -3 \end{array}\right],\left[\begin{array}{c} 2 \\ 6 \\ 1 \\ -5 \end{array}\right],\left[\begin{array}{c} 4 \\ -8 \\ -10 \\ -2 \end{array}\right]\right\}$
Dependent: Always Independent: Always

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Problem 19973

Suppose that $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{4}$ is such that its action on a vector $\left[\begin{array}{c}x \\ y \\ z\end{array}\right]$ is given below: $T\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} x+3 y+3 z \\ -x-2 y-4 z \\ 2 x+5 y+6 z \\ 3 x+8 y+9 z \end{array}\right]$
Find the matrix $M_{D B}(T)$ that represents $T$ relative to the bases $B$ and $D$ shown below: $\begin{array}{l} \left.B=\left\{\begin{array}{l} 1 \\ 2 \\ 2 \end{array}\right],\left[\begin{array}{c} 1 \\ 3 \\ 1 \end{array}\right],\left[\begin{array}{c} 0 \\ 2 \\ -3 \end{array}\right]\right\} D=\left\{\left[\begin{array}{c} 1 \\ 1 \\ -2 \\ 0 \end{array}\right],\left[\begin{array}{c} -1 \\ 0 \\ 1 \\ -1 \end{array}\right],\left[\begin{array}{c} 1 \\ 1 \\ -3 \\ 1 \end{array}\right],\left[\begin{array}{c} 0 \\ 1 \\ 0 \\ -1 \end{array}\right]\right\} \\ M_{D B}(T)=\left[\begin{array}{lll} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right] \end{array}$

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Problem 19974

$\frac{y}{21}=4$

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Problem 19975

Example 4: a 3.34 g sample of a hydrate has the formula $\mathrm{SrS}_{2} \mathrm{O}_{3} \cdot \times \mathrm{H}_{2} \mathrm{O}$ , and contains 2.30 g of $\mathrm{SrS}_{2} \mathrm{O}_{3}$ . Find the value of $x$

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Problem 19976

$y=6 x+3$ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 1 & $\square$ \\ \hline 3 & $\square$ \\ \hline 6 & $\square$ \\ \hline 8 & $\square$ \\ \hline \end{tabular}

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Problem 19977

5. $T_{1}, T_{2}$ dan $T_{3}$ adalah tiga sebutan berturatan suatu janjang $T_{1}=7$ dan $T_{n=1}=T_{n}+4$ bagi $n \geqslant 1$ . Cari sebutan Ke-17. (3 markah) $T_{1}=7$

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Problem 19978

b) selesaikan persamaan $\sqrt{x-2}=\sqrt{x}-1$ [3 markah]

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Problem 19979

2. If $x=-3, y=4$ and $z=-5$ , then verify each of the following: (a) $|x+z| \leq|x|+|z|$ (b) ly- (c) $|x y z|=|x| \cdot|y| \cdot|z|$ (d) $\left|\frac{\mathrm{x}}{\mathrm{z}}\right|=$

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Problem 19980

LG 1 P3-10 Statement of retained earnings Hayes Enterprises began 2015 with a retained earnings balance of $\$ 1,151,000$ . During 2015 , the firm earned $\$ 528,000$ after taxes. From this amount, preferred stockholders were paid $\$ 98,000$ in dividends. At yearend 2015 , the firm's retained earnings totaled $\$ 1,324,000$ . The firm had 100,000 shares of common stock outstanding during 2015. a. Prepare a statement of retained earnings for the year ended December 31, 2015, for Hayes Enterprises. (Note: Be sure to calculate and include the amount of cash dividends paid in 2015.) b. Calculate the firm's 2015 earnings per share (EPS). c. How large a per-share cash dividend did the firm pay on common stock during 2015?

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Problem 19981

parent punction: $y=x^{3}$ find the equation with $(-4,-1),(-5,-2),(-6,-3)$ Descrive the trans formation that were applied to the parent function

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Problem 19982

23. In the figure, the line $k x+4 y-12=0$ cuts the $\mathrm{x}-\mathrm{axis}$ at A and the $\mathrm{y}-\mathrm{axis}$ at B . If the area of $\triangle \mathrm{OAB}$ is 6 square units, then $k=$ Av) 1 B. 3 C. 5 D. 7

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Problem 19983

The length of a rectangle is 3 ft more than twice the width, and the area of the rectangle is $54 \mathrm{ft}^{2}$ . Find the dimensions of the rectangle.

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Problem 19984

105 Campo elettrico di due piani paralleli Due piani infiniti di carica disposti parallelamente uno all'altro hanno densità superficiale di carica rispettivamente pari a $2,0 \mu \mathrm{C} / \mathrm{m}^{2} \mathrm{e} 4,0 \mu \mathrm{C} / \mathrm{m}^{2}$ . Determina il campo elettrico all'interno e all'esterno delle piastre. $\left[3,4 \cdot 10^{5} \mathrm{~N} / \mathrm{C} ; 1,1 \cdot 10^{5} \mathrm{~N} / \mathrm{C}\right]$

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Problem 19985

\begin{tabular}{|c|c|c|c|} \hline Q1 & \begin{tabular}{l} The curve of $\frac{y^{2}}{y+x}=1$ is symmetric about: \\ A) Origin \\ B) $x$ -axis \end{tabular} & C) y-axis & D) Not symmetric \\ \hline Q2 & \begin{tabular}{l} $\lim _{x \rightarrow+\infty} \frac{\sqrt{1+2 x^{2}}}{x+2}=$ \\ A) $-\sqrt{2}$ \\ B) 2 \end{tabular} & C) $\sqrt{2}$ & D) -2 \\ \hline Q3 & \begin{tabular}{l} The function $f(x)=x^{2} \sin (x)$ is: \\ A) even \\ B) odd \end{tabular} & C) even and odd & D) neither \\ \hline Q4 & \begin{tabular}{l} If $f(x)=4+\frac{x}{x-1}$ , then $f^{-1}(x)=$ \\ A) $\frac{2-x}{3-x}$ \\ B) $\frac{3-x}{4-x}$ \end{tabular} & C) $\frac{4-x}{5-x}$ & D) $\frac{5-x}{6-x}$ \\ \hline Q5 & \begin{tabular}{l} For all real numbers $x$ , a function $f(x)$ satis \\ A) 5 \\ B) -5 \end{tabular} & \begin{tabular}{l} $|f(x)+1| \leq \mid x$ \\ C) -1 \end{tabular} & \begin{tabular}{l} 5, then $\lim _{x \rightarrow-5} f(x)$ \\ D) 1 \end{tabular} \\ \hline \end{tabular}

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Problem 19986

Dr. Abdullah Shukri
Let the orthogonal matrix $Q$ be: $Q=\left(\begin{array}{cc} 0 & -1 \\ 1 & 0 \end{array}\right)$ p 1: Verify Orthogonality 2: Find the eigenvalues p 3: Find the eigenvectors

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Problem 19987

Simplify and express the answer using only positive exponents. a) $\frac{10^{6}}{10}$ b) $\frac{5^{3}}{5^{7}}$ c) $\frac{7^{5}}{7^{3}}$ d) $\frac{3}{3^{5}}$

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Problem 19988

$15 \sqrt{3}=$

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Problem 19989

Solve the system by the method of substitution. Check your solution(s) graphically. $\left\{\begin{array}{l} x-3 y=-9 \\ x+2 y=1 \end{array}\right.$ $(x, y)=(\square)$

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Problem 19990

16) If $f(x)=2-(x-1)^{3}$ , then the graph that represents the function $f$ is (a) (b) (c) (d) 17) The rule of the function represented in the opposite figure is $f(x)=$ $\qquad$ (a) $(x-2)^{2}+1$ (b) $-(x-2)^{2}+1$ (c) $-(x-1)^{2}+2$ (d) $(-x+1)^{2}+2$ 18) The symmetric point of the function $f: f(x)=x^{3}-2$ is $\qquad$ (a) $(0,2)$ (b) $(0,-2)$ (c) $(2,0)$ (d) $(-2,0)$ 19) The vertex of the curve of the function $f$ where $f(x)=(1+x)^{2}-3$ is $\qquad$ (a) $(1,3)$ (b) $(1,-3)$ (c) $(-1,3)$ (d) $(-1,-3)$ 20) If $y=f(x)$ is a real function, then its image by translation 3 units vertically upwards is $g(x)=$ $\qquad$ (a) $f(x-3)$ (b) $f(x+3)$ (c) $f(x)+3$ (d) $(x)-3$

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Problem 19991

43. $\begin{array}{l} 7 x+3 y=16 \\ y=4 x-1\end{array}$

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Problem 19992

$\begin{array}{l}2 x+y=8 \\ 4 x+3 y=16\end{array}$

See Solution

Problem 19993

1. $f(x)=\frac{1}{x-5} \Rightarrow$
Undefined value(s): $\qquad$ Domain: $\qquad$ $x \neq 5$ Vertical asymptote(s): $\qquad$ $x=5$
Removable discontinuity points(s): $\qquad$ none
Horizontal asymptote(s): $\qquad$

See Solution

Problem 19994

6. What is the coefficient of $1 / x^{6}$ in the expression $\left(x^{5}+1 / x^{3}\right)^{10}$ .
ANS:

See Solution

Problem 19995

2. Sketch the following graphs on separate diagrams. (a) $y=(x+a)^{3}, a>0$ (b) $y=x^{3}-b, b>0$

See Solution

Problem 19996

Solve X raise to power $1+\mathrm{x}$ raise to power 2 = 1

See Solution

Problem 19997

Solve the equation. $\frac{1}{27}=b^{-3}$

See Solution

Problem 19998

$f(t) = \sqrt[3]{t^{11}} - 4 \sqrt{t^{3}}$

See Solution

Problem 19999

PROBLĖMES AVEC LA MULTIPLICATION ET DIVIIION DES POLYNÔMES $\frac{\left(-4,5 x^{2}+3,6 x\right)}{0,5 x}$

See Solution

Problem 20000

If $f(x)=5^{x}$ , find $f(3)$ . $f(3)=$ $\square$ (Simplify your answer. Type an integer or a fraction.)

See Solution

Algebra

Problem 19901

Problem 19902

A cubic function g(x)g(x)g(x) with integral coefficients has the following properties: g(3)=0,g(−34)=0,(x+2)g(3)=0, g\left(-\frac{3}{4}\right)=0,(x+2)g(3)=0,g(−43​)=0,(x+2) is a factor of g(x),g(1)=−84g(x), g(1)=-84g(x),g(1)=−84. Determine g(x)g(x)g(x).

Problem 19903

Problem 19904

Write the following using the log base change rule, and change to either log base 10 (write log) or log base e (write it as In) log⁡2(7)\log _{2}(7)log2​(7)

Problem 19905

11. Jika f(x)=(5x−3)4−13f(x)=\frac{(5 x-3)^{4}-1}{3}f(x)=3(5x−3)4−1​, maka nilai dari f−1(5)f^{-1}(5)f−1(5) adalah...

Problem 19906

7. 3w+x+y+z=2x+2y+3z=1−2z=23w2x+4y+7z=1\begin{array}{r}3 w+x+y+z=2 \\ x+2 y+3 z=1 \\ -2 z=2 \\ 3 w \quad 2 x+4 y+7 z=1\end{array}3w+x+y+z=2x+2y+3z=1−2z=23w2x+4y+7z=1​

Problem 19907

Write an equation of the line. Vertical; through (2,−3)(2,-3)(2,−3)

Problem 19908

Problem 19909

Rewrite the expression with rational exponents. 93\sqrt[3]{9}39​

Problem 19910

Question 4A factor of x3+12x2+41x+42x^{3}+12 x^{2}+41 x+42x3+12x2+41x+42 is x−3x-3x−3 x+3x+3x+3 x−2x-2x−2 x−7x-7x−7

Problem 19911

Problem 19912

Problem 19913

Problem 19914

Simplify the expression. (116)1/2\left(\frac{1}{16}\right)^{1 / 2}(161​)1/2 (116)1/2=\left(\frac{1}{16}\right)^{1 / 2}=(161​)1/2= □\square□ (Type an integer or a simplified fraction.)

Problem 19915

Solve the following exponential equation. Express your answer as both an exact expression and a decimal approximation rounded to two decimal places. 72x−8=10097^{2 x-8}=100972x−8=1009

Problem 19916

Problem 19917

If x−1x-1x−1 is a factor of x3−kx2+2xx^{3}-k x^{2}+2 xx3−kx2+2x, what is the value of kkk ?

Problem 19918

10. The sum of the squares of two consecutive integers is 365 . Find the integers.

Problem 19919

Factor the given polynomial. x2−13x+40x^{2}-13 x+40x2−13x+40Select the correct choice below and, if necessary, fill in the answer box within your choice. A. x2−13x+40=x^{2}-13 x+40=x2−13x+40= □\square□

Problem 19920

Question 13Factor the trinomial, or state that the trinomial is prime. x2−4x−45x^{2}-4 x-45x2−4x−45Select the correct choice below and fill in any answer boxes within your choice A. x2−4x−45=x^{2}-4 x-45=x2−4x−45= □\square□ B. The polynomial is prime.

Problem 19921

Problem 19922

Problem 19923

Factoring and Applications Lesson \#4: Factori Factor. a) 4(3x+1)2−5(3x+1)+14(3 x+1)^{2}-5(3 x+1)+14(3x+1)2−5(3x+1)+1

Problem 19924

Find all zeros of f(x)=x3−3x2−3x+1f(x)=x^{3}-3 x^{2}-3 x+1f(x)=x3−3x2−3x+1. Enter the zeros separated by commas. Enter exact value, not decimal approximations.

Problem 19925

Problem 19926

Problem 19927

Use common logarithms or natural logarithms and a calculator to evaluate the expression. log⁡1911\log _{19} 11log19​11Evaluate the expression. log⁡1911≈□\log _{19} 11 \approx \squarelog19​11≈□ (Type an integer or a decimal. Do not round until the final answer. Then round to four dec

Problem 19928

Problem 19929

13. Jika f(x)=2x2−5f(x)=2 x^{2}-5f(x)=2x2−5 dan g(x):3x+22g(x): \sqrt{3 x+22}g(x):3x+22​ maka (f∘g)−1(−3)(f \circ g)^{-1}(-3)(f∘g)−1(−3) adaiah...

Problem 19930

Write the equation in logarithmic form. ez=ue^{z}=uez=u □\square□ Hint 5 (1) Submit Question

Problem 19931

Without graphing, determine whether system has one solution, no solution, or an infinite number of solutions. {x+y=64x+4y=24\left\{\begin{array}{c} x+y=6 \\ 4 x+4 y=24 \end{array}\right.{x+y=64x+4y=24​

Problem 19932

Problem 19933

Given the function C(r)=2r4−10r3−12r2C(r)=2 r^{4}-10 r^{3}-12 r^{2}C(r)=2r4−10r3−12r2 its CCC-intercept is □\square□ its rrr-intercepts are □\square□

Problem 19934

Use the product rule to simplify the expression. (7py)(−8p)(7py)(−8p)=\begin{array}{c} (7 p y)(-8 p) \\ (7 p y)(-8 p)= \end{array}(7py)(−8p)(7py)(−8p)=​ (Type your answer using exponential notation.)

Problem 19935

Question 5 of 18, Step 1 of 1 4/19 CorrectSimplify the following complex fraction. 5x−2+y−25x−3−y−2\frac{5 x^{-2}+y^{-2}}{5 x^{-3}-y^{-2}}5x−3−y−25x−2+y−2​Answer

Problem 19936

Use the quotient rule to simplify. x4y7x2y7\frac{x^{4} y^{7}}{x^{2} y^{7}}x2y7x4y7​

Problem 19937

Problem 19938

x-1 2x-1 3(2x-1)=56-1) 2x-176+ +1 2x #1 х- box-3=5x-5 Бос- +3 +3 pc+1/2 6x=5x-5+3 6x=5x-2 -6xx -5xc x=-2 x-1 5x+20 b. x+3 x²-16 (-1)(x²-16)=(5c+20) (7 (pc-1) (x+4) (c-4)=5 (ac-1) (3c-41) = $lact. (c2-पा(-120+14) = 8 (DC-11) (OC+1)=0 OC ж

Problem 19939

Problem 19940

Find the horizontal asymptote of f(x)=−4x+4x3−5x3+2x2+3f(x)=\frac{-4 x+4 x^{3}-5}{x^{3}+2 x^{2}+3}f(x)=x3+2x2+3−4x+4x3−5​ y=y=y=

Problem 19941

Simplify. Use positive exponents for any variables. (6x)0+6x0(6 x)^{0}+6 x^{0}(6x)0+6x0

Problem 19942

Problem 19943

y=x2+4x−12y=x^{2}+4 x-12y=x2+4x−12

Problem 19944

Factor completely. u2−9u+14=u^{2}-9 u+14=u2−9u+14=

Problem 19945

11. Algebra, STD2 A4 2014 HSC 26dDraw each graph on the grid below and hence solve the simultaneous equations. (3 marks) y=2x+1x−2y−4=0\begin{array}{l} y=2 x+1 \\ x-2 y-4=0 \end{array}y=2x+1x−2y−4=0​ (3 marks)

Problem 19946

f(x)=x2+4−12f(x)=x^{2}+4-12f(x)=x2+4−12Entrada...

Problem 19947

Simplify. Write the answer using positive exponents only. (x−8x−3)−9\left(\frac{x^{-8}}{x^{-3}}\right)^{-9}(x−3x−8​)−9

Problem 19948

A cubic function $g(x)$ with integral coefficients has the following properties: $g(3)=0, g\left(-\frac{3}{4}\right)=0,(x+2)$ is a factor of $g(x), g(1)=-84$ . Determine $g(x)$ .

Write the following using the log base change rule, and change to either log base 10 (write log) or log base e (write it as In) $\log _{2}(7)$

11. Jika $f(x)=\frac{(5 x-3)^{4}-1}{3}$ , maka nilai dari $f^{-1}(5)$ adalah...

7. $\begin{array}{r}3 w+x+y+z=2 \\ x+2 y+3 z=1 \\ -2 z=2 \\ 3 w \quad 2 x+4 y+7 z=1\end{array}$

Write an equation of the line. Vertical; through $(2,-3)$

Rewrite the expression with rational exponents. $\sqrt[3]{9}$

Question 4
A factor of $x^{3}+12 x^{2}+41 x+42$ is $x-3$ $x+3$ $x-2$ $x-7$

Simplify the expression. $\left(\frac{1}{16}\right)^{1 / 2}$ $\left(\frac{1}{16}\right)^{1 / 2}=$ $\square$ (Type an integer or a simplified fraction.)

Solve the following exponential equation. Express your answer as both an exact expression and a decimal approximation rounded to two decimal places. $7^{2 x-8}=1009$

If $x-1$ is a factor of $x^{3}-k x^{2}+2 x$ , what is the value of $k$ ?

Factor the given polynomial. $x^{2}-13 x+40$
Select the correct choice below and, if necessary, fill in the answer box within your choice. A. $x^{2}-13 x+40=$ $\square$

Question 13
Factor the trinomial, or state that the trinomial is prime. $x^{2}-4 x-45$
Select the correct choice below and fill in any answer boxes within your choice A. $x^{2}-4 x-45=$ $\square$ B. The polynomial is prime.

Factoring and Applications Lesson \#4: Factori Factor. a) $4(3 x+1)^{2}-5(3 x+1)+1$

Find all zeros of $f(x)=x^{3}-3 x^{2}-3 x+1$ . Enter the zeros separated by commas. Enter exact value, not decimal approximations.

Use common logarithms or natural logarithms and a calculator to evaluate the expression. $\log _{19} 11$
Evaluate the expression. $\log _{19} 11 \approx \square$ (Type an integer or a decimal. Do not round until the final answer. Then round to four dec

13. Jika $f(x)=2 x^{2}-5$ dan $g(x): \sqrt{3 x+22}$ maka $(f \circ g)^{-1}(-3)$ adaiah...

Write the equation in logarithmic form. $e^{z}=u$ $\square$ Hint 5 (1) Submit Question

Without graphing, determine whether system has one solution, no solution, or an infinite number of solutions. $\left\{\begin{array}{c} x+y=6 \\ 4 x+4 y=24 \end{array}\right.$

Given the function $C(r)=2 r^{4}-10 r^{3}-12 r^{2}$ its $C$ -intercept is $\square$ its $r$ -intercepts are $\square$

Use the product rule to simplify the expression. $\begin{array}{c} (7 p y)(-8 p) \\ (7 p y)(-8 p)= \end{array}$ (Type your answer using exponential notation.)

Question 5 of 18, Step 1 of 1 4/19 Correct
Simplify the following complex fraction. $\frac{5 x^{-2}+y^{-2}}{5 x^{-3}-y^{-2}}$
Answer

Use the quotient rule to simplify. $\frac{x^{4} y^{7}}{x^{2} y^{7}}$

Find the horizontal asymptote of $f(x)=\frac{-4 x+4 x^{3}-5}{x^{3}+2 x^{2}+3}$ $y=$

Simplify. Use positive exponents for any variables. $(6 x)^{0}+6 x^{0}$

$y=x^{2}+4 x-12$

Factor completely. $u^{2}-9 u+14=$

11. Algebra, STD2 A4 2014 HSC 26d
Draw each graph on the grid below and hence solve the simultaneous equations. (3 marks) $\begin{array}{l} y=2 x+1 \\ x-2 y-4=0 \end{array}$ (3 marks)

$f(x)=x^{2}+4-12$
Entrada...

Simplify. Write the answer using positive exponents only. $\left(\frac{x^{-8}}{x^{-3}}\right)^{-9}$

Simplify. Write the answer using positive exponents only. $\left(\frac{x^{-3} y^{-5}}{a^{-3}}\right)^{-5}$

Answer all of the following questions. (1) What is the domain of $f(x)=\frac{3}{x+4}$ ? Explain how you reached your conclusion. (2) Consider the graph of $f(x)=\frac{3}{x+4}$ shown below. What do you think is the range of $f(x)$ ?

Calculate the slope and enter it below to aim the X Wing and destroy all TIE-Fighters. \begin{tabular}{|l|l|} \hline Slope & Aim Left or Right \\ \hline & \\ \hline \end{tabular}
Fire

Simplify. $\left(\frac{4 x^{2}}{y^{3}}\right)^{3}\left(\frac{4 x^{8}}{y}\right)^{-2}$

$\sqrt{2 x}+3=9$

Add. $\left(6 x^{3} y-6 x y+5\right)+\left(8 x^{3} y+6 x y+5 x\right)$

14 Mark for Review
The function $f(t)=60,000(2)^{\frac{t}{40}}$ gives the number of bacteria in a population $t$ minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?
Answer Preview:

Question 7
Evaluate the following expressions.
1 (a) $\log _{3} 3^{13}=$ $\square$ (b) $\log _{3} 81=$ $\square$ (c) $\log _{4} 256=$ $\square$ (d) $\log _{5} 5^{10}=$ $\square$

a) $\log _{5} x=3$

Kristen invests \ $5,000 in a bank. The bank pays$ 6 \%$ interest compounded monthly. To the nearest tenth of a year, how long mus she leave the money in the bank for it to double?

Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: $x=h+r \cos (\theta), \quad y=k+r \sin (\theta)$

A factor of $x^{3}+15 x^{2}+71 x+105$ is $x+5$ $x-5$ $x-7$ $x-3$

$x+x=$

Solve the equation by using the square root property. $(3 p+2)^{2}=8$
The solution set is $\square$ (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.

$\frac{y}{21}=4$