Browse Algebra problems Studdy Solved!

Problem 2801

Read the description of a proportional relationship.
Every day after school, Jeremiah and his sister Grace play their favorite video game, Wizarding Legends. The goal of the game is to earn power points by defeating goblins. There is a proportional relationship between the number of goblins defeated, $x$ , and the number of power points earned, $y$ .
Today, Jeremiah earns 42 power points defeating 14 goblins. Write the equation for the relationship between $x$ and $y$ . $y=$ $\square$

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Problem 2802

The polynomial is a Select an answer $\vee$ . $11+15 u^{3}+10 u^{4}$
The degree of this polynomial is $\square$

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Problem 2803

2. Members of the band sold juice and popcorn at a college football game to raise money for an upcoming trip. The band raised $\$ 2,000$ . The amount raised is divided equally among the $m$ members of the band. Which equation represents the amount, $A$ , each member receives? A. $A=\frac{m}{2,000}$ B. $A=\frac{2,000}{m}$ C. $A=2,000 \mathrm{~m}$ D. $A=2,000-m$

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Problem 2804

Use $f(x)=x^{2}-36$ and $g(x)=x^{2}+36$ to find a formula for each expression. Identify its domain. (a) $(\mathrm{f}+\mathrm{g})(\mathrm{x})$ (b) $(f-g)(x)$ (c) $(\mathrm{fg})(\mathrm{x})$ (d) $(\mathrm{f} / \mathrm{g})(\mathrm{x})$ (a) $(f+g)(x)=2 x^{2}$ (Simplify your answer. Do not factor.)
Identify its domain. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\{x \mid$ $\square$ \} (Use a comma to separate answers as needed.) B. All real numbers (b) $(f-g)(x)=$ $\square$ (Simplify your answer. Do not factor.)
Identify its domain. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\{x \mid\}$ (Use a comma to separate answers as needed.) B. All real numbers (c) $(\mathrm{fg})(\mathrm{x})=$ $\square$ (Simplify your answer. Do not factor.)

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Problem 2805

The polynomial is a $\square$ $-15 y^{3}+32 y^{2}$
The degree of this polynomial is $\square$

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Problem 2806

- Q20: Solve and express in interval notation: $|3 x+1| \geq 4$ . - Q21: Solve and express in interval notation: $|2 x-7|>3$ .

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Problem 2807

The product rule for logarithms states that $\log _{b}(M N)=$ $\square$ The logarithm of a product is the $\square$ of the logarithms.

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Problem 2808

Complete the sentence.
If the graph of a logarithmic function $f(x)=\log _{a} x, a>0, a \neq 1$ , is increasing, then its base must be larger than $\square$

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Problem 2809

Oliver read for 450 minutes this month. His goal is to read for $10 \%$ more minutes next month.
If Oliver meets his goal, how many minutes will he read in all during the two months? $\square$ minutes

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Problem 2810

16. $3 n-n+7=25$

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Problem 2811

Find the x-intercepts of the quadratic function $F(x) = 2x^2 + 9x + 4$ .

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Problem 2812

(3) A marine biologist is studying how fast a dotphin swims. The delphin swims at a constant speed for 5 seconds. The distance it swims is 55 meters. The relationship between time and distance for the trip is proportiona? a. Make a graph showing the change in the dolphin's distance over time. How far does the dolphin swim in 1 second? Show your work.

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Problem 2813

Question
Which expression is equivalent to $\left(5^{-1}\right)^{2} ?$
Answer $\frac{1}{25}$ 125 5 $\frac{1}{125}$

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Problem 2814

Describe the basic differences between linear growth and exponential growth.
Choose the correct answer below. A. Linear growth occurs when a quantity grows by the same relative amount, that is, by the same percentage, in each unit of time, and exponential growth occurs when a quantity grows by the same absolute amount in each unit of time. B. Linear growth occurs when a quantity grows by random amounts in each unit of time, and exponential growth occurs when a quantity grows by different, but proportional amounts, in each unit of time. C. Linear growth occurs when a quantity grows by different, but proportional amounts, in each unit of time, and exponential growth occurs when a quantity grows by random amounts in each unit of time. D. Linear growth occurs when a quantity grows by the same absolute amount in each unit of time, and exponential growth occurs when a quantity grows by the same relative amount, that is, by the same percentage, in each unit of time.

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Problem 2815

Simplify the expression $a^{2} b^{-1} c^{-8}$ .

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Problem 2816

Use the given zeros to write the complete factored form of $f(x)$ . $f(x)=2 x^{2}-13 x+20 ;$ zeros: $\frac{5}{2}$ and 4 $f(x)=$ $\square$ (Type your answer in factored form. Use integers or fractions for any numbers in

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Problem 2817

Write the complete factored form of $f(x)$ . $f(x)=-3 x^{3}-2 x^{2}+61 x-20 ; \text { zeros: }-5, \frac{1}{3}, 4$ $f(x)=\square$ (Type your answer in factored form. Use integers or fractions

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Problem 2818

Write the complete factored form of $f(x)$ . $\begin{array}{l} f(x)=-4 x^{3}+13 x^{2}+13 x-4 ; \text { zeros: }-1, \frac{1}{4}, 4 \\ f(x)=\square \end{array}$ $\square$ (Type your answer in factored form. Use integers or fractions

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Problem 2819

$\frac{c}{0.2}+0.9=3.9$

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Problem 2820

State whether the decay is linear or exponential, and answer the associated question. The value of a car is decreasing by $8 \%$ per year. If the car is worth $\$ 12,000$ today, what will it be worth in two years?
State whether the decay is linear or exponential. The decay is $\square$ since the quantity decreases by the same $\square$ amount.

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Problem 2821

Use properties of logarithms to expand each logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. $\ln \sqrt[15]{x}$

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Problem 2822

Write the complex number in the form $a+b i$ . $\sqrt{11}\left(\cos \frac{3 \pi}{2}+i \sin \frac{3 \pi}{2}\right)$

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Problem 2823

$-8 x^{3}\left(10 x^{3} y\right)$
Answer Attempt 1 out of 2

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Problem 2824

$-3 x+2=-10 x+30$
Simplify your answer as much as possible. $x=$

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Problem 2825

$\text{Encuentra una función cuya gráfica sea una curva con el dominio } \mathbb{R} \text{ y el rango } \mathbb{R} \setminus \{-1\}.$

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Problem 2826

Solve for $y$ . $5 y+9=17 y-4 y+81$
Simplify your answer as much as possible.

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Problem 2827

$\frac{3}{8}d + \frac{3}{4}$

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Problem 2828

$\log _{4} 128$

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Problem 2829

Solve the inequality for $w$ . $17<w+6$
Simplify your answer as much as possible.

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Problem 2830

rind the domain and tne tarlys
Write your answers as inequalities, using $x$ or $y$ as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) domain: $\square$ (b) range: $\square$ Empty All set reals

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Problem 2831

Express the following fraction in simplest form using only posl exponents. $\frac{3(w)^{3}}{2 w^{6}}$

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Problem 2832

A line has a slope of $-\frac{7}{9}$ and includes the points $(3, w)$ and $(-6,-1)$ . What is the value of $w$ ? $w=$

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Problem 2833

A line has a slope of $-\frac{3}{2}$ and includes the points $(5,0)$ and $(3, v)$ . What is the value of $v$ ? $v=$

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Problem 2834

$3 e^{\operatorname{fin}} - 3 \sin (6 \pi x)$

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Problem 2835

Factor the algebraic expression. $\begin{array}{r} 40 \mathrm{a}+35 \\ 40 \mathrm{a}+35= \end{array}$ $\square$ (Factor completely.)

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Problem 2836

Rewrite using a single exponent. $\left(4^{8}\right)^{3}$

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Problem 2837

Problem solving process:
1. Draw a complete force diagram for each object. Include components and tick marks where appropriate.
2. Obtain the $\Sigma F_{x}$ and $\Sigma_{y}$ equations.
3. Substitute in formulas or known values.
4. Solve for unknown.
1. You are trying to push a 100 kg crate across a level floor. The coefficient of static friction between the crate and the floor is 0.25 , and the kinetic coefficient is 0.20 . a. Draw a force diagram under the figure. $\begin{array}{l} \begin{aligned} \Sigma F_{y}=F_{r}-F_{g} & =m a=0 \\ F_{N}=F_{g} & =9.80100 \\ & =980 \end{aligned} \end{array}$ b. What horizontal force must you apply to the crate to get the crate moving? c. What horizontal force must you apply to the crate to keep the crate moving with constant velocity? Kine tic C. $F_{F_{K}}=0.20 \cdot 980$

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Problem 2838

3. A diamond necklace worn by Princess Diana was first purchased for $\$ 25,000$ . Experts say its value will increase by $15 \%$ per year. When will the value of the necklace be $\$ 80,000 ?$

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Problem 2839

Write the equation in exponential form. Assume that all constants are positive and not equal to 1. $\log _{p}(b)=w$

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Problem 2840

Complex Roots (Lever I)
Score: $3 / 5$ Penalty: none Show Examples
Question What are the roots of the equation $x^{2}+6 x+58=0$ in simplest $a+b i$ form? Attempt 1 out of 2

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Problem 2841

The doubling time of a population of flies is 8 hours. By what factor does the population increase in 29 hours? By what factor does the population increase in 2 weeks?
By what factor does the population increase in 29 hours? $\square$ (Type exponential notation with positive exponents. Use integers or decimals for any numbers in the expression.)

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Problem 2842

Id the range and the domain of the function shown.
Write your answers as inequalities, using $x$ or $y$ as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) range: $\square$ (b) domain: $\square$ Empty All set reals Explanation Check

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Problem 2843

7) $\left(\frac{-2 a^{2}}{3 y^{3}}\right)^{3}$

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Problem 2844

Every summer, Kendra plants a vegetable garden in her yard. Last year she planted 6 rows of tomatoes and 8 rows of peppers. Kendra wants to keep the same ratio this year, but she only plans to plant 3 rows of tomatoes.
How many rows of peppers will Kendra plant this year? $\square$ rows of peppers

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Problem 2845

20. What is the formula for calculating simple interest? $I=P(R+T)$ $I=P /(T-R)$ I = PRT $I=P T / R$

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Problem 2846

x ^ { 2 } + 4 \longdiv { 2 x ^ { 4 } - x ^ { 3 } + 7 x ^ { 2 } - 4 x - 4 }

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Problem 2847

Simplify the expression: $10+-5 x+-2$ $\square$ Submit

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Problem 2848

Solve the equation: $-6 c+21=81$

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Problem 2849

If you deposit \$1000 into a bank account that compounds annually at a 5\% interest rate, how much money will you have in the account after 3 years? \$1157.63 \$1500.00 \$1100.00 \$1150.00 Show Your Work

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Problem 2850

EOC Review - Algebra: Concepts an Which function can be used to model the data in this table? \begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline 0 & -1 \\ \hline 2 & 0 \\ \hline 6 & 2 \\ \hline \end{tabular} (a) $f(x)=3 x$ (b) $f(x)=\frac{x}{2}-1$ (C) $f(x)=x-1$ (d) $f(x)=2 x-1$

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Problem 2851

Complete the following for $f(x)=(x-3)^{3}$ . (a) Find the $x$ - and $y$ -intercepts. (b) Determine the multiplicity of each zero of f . (c) Sketch a graph of $y=f(x)$ . (a) The $x$ -intercept(s) is/are $\square$ . (Type an ordered pair. Use a comma to separate answers as nee

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Problem 2852

Question Show Exampl
What are the roots of the equation $9 x^{2}-36 x+37=0$ in simplest $a+b i$ form?
Answer Attempt 1 out of 2. ( Additional Solution $\Theta$ No Solution

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Problem 2853

$-\frac{2}{3}(x+12)+\frac{2}{3} x=-\frac{5}{4} x+2$

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Problem 2854

Section D-Use if your filing status is Head of household. Complete the row below that applies to you. \begin{tabular}{|c|c|c|c|c|c|} \hline Taxable income. If line 11b is- & \begin{tabular}{l} (a) \\ Enter the amount from line 11b \end{tabular} & \begin{tabular}{l} (b) \\ Multiplication amount \end{tabular} & (c) Multiply (a) by (b) & \begin{tabular}{l} (d) \\ Subtraction amount \end{tabular} & ``` Tax. Subtract (d) from (c). Enter the result here and on the entry space on line 12a. ``` \\ \hline At least $\$ 100,000$ but not over \160,700 & \$ & \times 24 \%(0.24) & \$ & \$ 7,246.00 & \$ \\ \hline Over \ $160,700$ but not over \204,100 & \$ & \times 32 \% (0.32) & \$ & \$20,102.00 & \$ \\ \hline Over \$204,100 but not over \$510,300 & \$ & \times 35 \% (0.35) & \$ & \$26,225.00 & \$ \\ \hline Over \$510,300 & 4 & \times 37 \%$ (0.37) & \$ & \$36,431.00 & \$ \\ \hline \end{tabular}
Let $x$ represent a head-of-household taxpayer's taxable income that is over \ $510,300. Write an expression for this taxpayer's tax in terms of$ x $. 37\%-\$38,431.00$ \square$
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Check My Work

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Problem 2855

Enter the correct value for each blank. - Press each hotspot. - Label the corresponding number below with the requested value.
Press to hear a reminder or hint for this problem.
Rewrite the negative exponents as the expression's reciprocal with a positive exponent. Be sure to account for the negative signs on the bases when expanding and evaluating the exponents. $3^{-2}=$ - $27^{0}=$ (2) $(-3)^{0}=$ $\theta$ $(-2)^{-4}=$ $\square$ $\left(\frac{1}{2}\right)^{-3}=$ $\left(-\frac{1}{2}\right)^{4}=$ $\square$

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Problem 2856

Angie sells handmade bracelets at craft fairs. She bought 2 packs of charms. One pack has 150 small charm and 60 large charms. The other pack has the same ratio of small to large charms. The second pack has 50 small charms.
How many large charms are in the second pack? $\square$ large charms

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Problem 2857

1. Rewrite in Fractional/Exponential Form a. $\sqrt{5}$ b. $\sqrt[5]{2}$ c. $\sqrt[2]{6^{3}}$
2. Rewrite in Radical/Root form a. $x^{\frac{2}{3}}$ b. $4^{\frac{5}{7}}$ c. $(10 x)^{\frac{3}{2}}$
3. Simplify each of the following $\frac{\sqrt{32 m^{7} n^{11}}}{\sqrt{28 x^{9} y^{6}}}$ a. b. $4 \sqrt[3]{216 x^{12} y^{15}}$ $\left(-256 x^{3} y^{7}\right)^{\frac{1}{3}}$ c. d. e. $\sqrt[4]{32 x^{5} y^{8}}$ f. $\sqrt[5]{180 m^{16} n^{11}}$

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Problem 2858

SImplify the expression: Videc $8+4 y+3 y+7+6 y+4 y$ $\square$ Submit

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Problem 2859

Question Watch Video Show Examples
Expand the logarithm fully using the properties of logs. Express the final answer in terms of $\log x$ , and $\log y$ . $\log x y^{3}$

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Problem 2860

Simplify the expression: Video $6 h+4 h+6 h-4 h+3 h$ $\square$ Submit

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Problem 2861

26 If $C=G-3 F$ , find the trinomial that represents $C$ when $F=2 x^{2}+6 x-5$ and $G=3 x^{2}+4$ . $\begin{array}{l} F=2 x^{2}+6 x-5+3 x^{2}+4 G=3 x^{2}+4 \\ (2 x+2)(x+3) \end{array}$

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Problem 2862

8. Solve Quadratic Equations Using Zero Factor Property - Q22: Solve for $x: x^{2}-5 x=0$ . - Q23: Solve for $x: 2 x^{2}+7 x=3$ .

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Problem 2863

Solve the exponential equation. Express the solution in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution. $e^{x}=19.56$
The solution set expressed in terms of logarithms is $\{\ln 19.56\}$ . (Use a comma to separate answers as needed. Simplify your answer. Use integers or decimals for any numbers in the expression. Use In for natural logarithm and log for common logarithm.) Now use a calculator to obtain a decimal approximation for the solution. The solution set is $\square$ (Use a comma to separate answers as needed. Round to two decimal places as needed.)

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Problem 2864

Jose wants to spend no more than $\$ 30$ on apples and grapes for the month. Apples cost $\$ 1.50$ per pound, and grapes cost $\$ 2$ per pound. Jose also wants his monthly caloric intake from apples and grapes to be greater than 2,000 calories. He determines that 1 pound of apples has 200 calories and 1 pound of grapes has 300 calories. Let a represent the number of pounds of apples and $g$ represent the number of pounds of grapes.
Which system of inequalities can be used to determine the number of pounds of apples and the number of pounds of grapes that Jose can buy for a month? (a) $\left\{\begin{array}{l}1.5 a+2 g \geq 30 \\ 200 a+300 g>2,000\end{array}\right.$ (b) $\left\{\begin{array}{l}1.5 a+2 g \leq 30 \\ 200 a+300 g>2,000\end{array}\right.$ (C) $\left\{\begin{array}{l}2 a+1.5 g \leq 30 \\ 300 a+200 g>2,000\end{array}\right.$ (d) $\left\{\begin{array}{l}2 a+1.5 g \geq 30 \\ 200 a+300 g<2,000\end{array}\right.$

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Problem 2865

Graph the exponential function. $f(x)=-2\left(\frac{2}{3}\right)^{x}$
Plot five points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.

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Problem 2866

Score: 1/2 Penalty: 1 off Watch Video Show Example
Question Expand the logarithm fully using the properties of logs. Express the final answer terms of $\log x, \log y$ , and $\log z$ . $\log \frac{y}{x^{4} \sqrt{z^{5}}}$
Answer Attempt 1 out of 2 Submit Answer

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Problem 2867

The Data: Here are three times and the measured height of the plane at those times. \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Time $(t)$ in \\ seconds \end{tabular} & \begin{tabular}{c} Height $(h)$ in \\ feet \end{tabular} \\ \hline 2 & 24205 \\ \hline 20 & 32305 \\ \hline 40 & 33705 \\ \hline \end{tabular}
To find the coefficients for your model, plug the data into the equation: $h=a t^{2}+b t+c$
The data points are just like $x$ and $y$ values, where the $x$ value is the time $t$ in seconds and the $y$ value is the altitude $h$ in feet. Plug these into the model to get three linear equations with variables $a, b$ , and $c$ . \begin{tabular}{|c|c|c|} \hline Data Values & Enter the resulting equation & \\ \hline $(2,24205)$ & \\ \hline $(20,32305)$ & \\ \hline $(40,33705)$ & \\ \hline \end{tabular}

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Problem 2868

Find all vertical asymptotes of the following function. $f(x)=\frac{25 x^{2}-64}{15 x+24}$

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Problem 2869

$f(x)=x^{3} \text { and } g(x)=x^{2}+4$
Find the formula for $(g \circ f)(x)$ and simplify your answer.

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Problem 2870

A bacteria culture starts with 3000 bacteria. After 3 h , the estimated count is 48000 . What is the doubling period? $d=?$

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Problem 2871

Ine grapn of $J(x)$ is given Delow. Un what intervais(s) is the varue or $J(x)$ increasing? Give your answer in intervainoration
Provide your answer below: $f(x)$ is increasing over $\square$

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Problem 2872

$\begin{array}{r} 16 a+14=14 \\ 16 a=0 \end{array}$ $a=$ $\square$ Divide both sides by 16

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Problem 2873

17. $\log (4 x+3)+\log (5)=2$

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Problem 2874

$f(x)=\frac{-3 x+3}{x^{2}+9}$

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Problem 2875

The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 1989. Your answer is $\square$ billion

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Problem 2876

2) $(-2,0) ; \begin{array}{l}8 x-3 y=-16 \\ 50=-9 x-2 y\end{array}$

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Problem 2877

State whether the growth (or decay) is linear or exponential, and answer the associated question. The value of a house is increasing by $\$ 1500$ per year. If it is worth $\$ 170,000$ today, what will it be worth in three years?
Is the increase in value linear or exponential? linear exponential
What will the house be worth in three years? $\$$ $\square$

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Problem 2878

$9 x=19$ and $y=38$

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Problem 2879

$(7,-4) ; \begin{array}{l}9 b+4 a=-8 \\ 6 a+5 b-42=0\end{array}$

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Problem 2880

Part 2 of 2
Four glasses of milk and 3 snack bars have a total of 81 carbohydrates (carbs), and 3 glasses of milk and 4 snack bars have a total of 80 carbs. Determine how many carbs are in one glass of milk and in one snack bar.
There are $\square$ carbs in one glass of milk.
There are $\square$ carbs in in one snack bar.

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Problem 2881

1. Determine the $x$ -intercepts of each function. a) $f(x)=\frac{-3 x}{2 x+5}$

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Problem 2882

The half-life of a drug in the bloodstream is 22 hours. What fraction of the original drug dose remains in 48 hours? in 72 hours?
What fraction of the original drug dose remains in 48 hours? $\square$ (Do not round until the final answer. Then round to the nearest hundredth as needed.) What fraction of the original drug dose remains in 72 hours? $\square$ (Do not round until the final answer. Then round to the nearest hundredth as needed.)

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Problem 2883

B) Check whether $(6,9)$ is a solution of the systems of linear equations. 5) $s+7 t=69$ $6 t+4 s=78$ 6) $\begin{array}{l} -2 p+5 q=34 \\ -7 q=-61-8 p \end{array}$ C) Write a system of linear equations that has the solution $(4,3)$ .

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Problem 2884

Find the domain and the range of the function shown
Write your answers as inequalities, using $x$ or $y$ as ap Or, you may instead click on "Empty set" or "All reals (a) domain: $\square$ (b) range: $\square$ Empty set All reals

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Problem 2885

$x\left(2 x^{-3}\right)$

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Problem 2886

ind the range and the domain of the funct
Nrite your answers as inequalities, using $x$ r, you may instead click on "Empty set" o (a) range: $\square$ $\square<\square$ ロ>ロ $\square \leq \square$ $\square \geq \square$ 믐 $\square$ 믐 (b) domain: $\square$ Empty All reals

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Problem 2887

The table defines a quadratic function. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-1 & 5 \\ \hline 0 & 1 \\ \hline 1 & -1 \\ \hline 3 & 1 \\ \hline \end{tabular}
What is the average rate of change between $x=-1$ and $x=1$ ? (a) undefined (b) $-\frac{1}{3}$ (C) -3 (d) -4

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Problem 2888

For the real-valued functions $f(x)=\frac{x-6}{x+5}$ and $g(x)=2 x-11$ , $(f \circ g)(x)=$
Domain of $f \circ g$ :

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Problem 2889

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. $\begin{aligned} 5 x+y & =-3 \\ -5 x-y & =3 \end{aligned}$
Answer One Solution No Solutions Submit Answer Infinitely Many Solutions

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Problem 2890

Given $f(x)=-x^{2}+9 x+11$ , find $f(-3)$
Answer $\square$ Submit Answer

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Problem 2891

2. Solve algebraically. Check each solution. a) $\frac{x-3}{10}=4 x$ b) $\frac{3}{x}-2=\frac{5}{x}$ c) $\frac{3}{x+2}-\frac{1}{x}=\frac{1}{5 x}$

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Problem 2892

Use the Read-Draw-Write process to solve the problem.
2. Shen and Liz set up chairs in a classroom. Liz makes 6 rows of 4 chairs. Shen says there are 2 fewer chairs than they need.
How many chairs do they need?

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Problem 2893

Solve for $x$ . $\log _{3}(2 x-5)-\log _{3}(x+1)=2$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ 3 . (Simplify your answer. Type an integer or a fraction. Use a comma $\qquad$ para. vers as needed.) B. The solution set is the empty set.

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Problem 2894

Find the domain of the function. $g(x)=\log _{8}(x-4)$
The domain of g is $\square$ $\square$ . (Type your answer in interval notation.)

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Problem 2895

The following model represents the percentage of people of some country at age A years who say they do volunteer work. $f(A)=-0.0194 A^{2}+1.82 A+9.85$
Complete parts a through d. \begin{tabular}{|c|c|c|} \hline \begin{tabular}{c} Age Group \\ (years) \end{tabular} & \begin{tabular}{c} Age used to \\ represent age \\ group (years) \end{tabular} & Percent \\ \hline $18-24$ & 21.0 & 39 \\ $25-34$ & 29.5 & 45 \\ $35-54$ & 44.5 & 53 \\ $55-64$ & 59.5 & 51 \\ $65-74$ & 69.5 & 45 \\ over 74 & 80.0 & 29 \\ \hline \end{tabular} a. Estimate the percentage of 25 -year-olds who say they volunteer.
The percentage of 25-year-olds who say they volunteer is 43 . (Round to the nearest whole number as needed.) Did you perform interpolation or extrapolation? Extrapolation Interpolation

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Problem 2896

The following model represents the percentage of people of some country at age A years who say they do volunteer work. $f(A)=-0.0194 A^{2}+1.82 A+9.85$
Complete parts a through d. \begin{tabular}{|c|c|c|} \hline \begin{tabular}{c} Age Group \\ (years) \end{tabular} & \begin{tabular}{c} Age used to \\ represent age \\ group (years) \end{tabular} & Percent \\ \hline $18-24$ & 21.0 & 39 \\ $25-34$ & 29.5 & 45 \\ $35-54$ & 44.5 & 53 \\ $55-64$ & 59.5 & 51 \\ $65-74$ & 69.5 & 45 \\ over 74 & 80.0 & 29 \\ \hline \end{tabular} a. Estimate the percentage of 25 -year-olds who say they volunteer.
The percentage of 25-year-olds who say they volunteer is 43 . (Round to the nearest whole number as needed.) Did you perform interpolation or extrapolation? Extrapolation Interpolation b. Estimate the percentage of 13-year-olds who say they volunteer.
The percentage of 13-year-olds who say they volunteer is $\square$ $\square$ . (Round to the nearest whole number as needed.)

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Problem 2897

To grow his ranch, a rancher is purchasing some bulls, which cost $\$ 5,100$ apiece, and some cows, which cost $\$ 1,000$ apiece. He doesn't want to spend more than $\$ 21,000$ at this time.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables. $x=$ the number of bulls $y=$ the number of cows

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Problem 2898

Given the function $f(x)=-2+5 x^{2}$ , express the value of $\frac{f(x+h)-f(x)}{h}$ in simplest form.
Answer $\square$ Submit Answer

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Problem 2899

The frequency of the middle A note on a piano is 440.00 Hz . What is the wavelength of this note in centimeters? The speed of sound in air is $343.06 \mathrm{~m} / \mathrm{s}$ .

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Problem 2900

3-2:Multiply Rational Numbers
Part 1 of 2
Suppose there is a $1.2^{\circ} \mathrm{F}$ drop in temperature for every thousand feet that an airplane climbs into the sky. The temperature on the a. Write a multiplication equation to represent the change in temperature after the plane ascends $10,000 \mathrm{ft}$ . b. What will be the temperature when the plane reaches an altitude of $10,000 \mathrm{ft}$ ? a. The change in temperature would be| (Type an integer or a decimal.) $\square$ $=$ $\square$ ${ }^{\circ} \mathrm{F}$ .

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Algebra

Problem 2801

Problem 2802

The polynomial is a Select an answer ∨\vee∨. 11+15u3+10u411+15 u^{3}+10 u^{4}11+15u3+10u4The degree of this polynomial is □\square□

Problem 2803

Problem 2804

Problem 2805

The polynomial is a □\square□ −15y3+32y2-15 y^{3}+32 y^{2}−15y3+32y2The degree of this polynomial is □\square□

Problem 2806

- Q20: Solve and express in interval notation: ∣3x+1∣≥4|3 x+1| \geq 4∣3x+1∣≥4. - Q21: Solve and express in interval notation: ∣2x−7∣>3|2 x-7|>3∣2x−7∣>3.

Problem 2807

The product rule for logarithms states that log⁡b(MN)=\log _{b}(M N)=logb​(MN)= □\square□ The logarithm of a product is the □\square□ of the logarithms.

Problem 2808

Complete the sentence.If the graph of a logarithmic function f(x)=log⁡ax,a>0,a≠1f(x)=\log _{a} x, a>0, a \neq 1f(x)=loga​x,a>0,a=1, is increasing, then its base must be larger than □\square□

Problem 2809

Oliver read for 450 minutes this month. His goal is to read for 10%10 \%10% more minutes next month.If Oliver meets his goal, how many minutes will he read in all during the two months? □\square□ minutes

Problem 2810

16. 3n−n+7=253 n-n+7=253n−n+7=25

Problem 2811

Find the x-intercepts of the quadratic function F(x)=2x2+9x+4 F(x) = 2x^2 + 9x + 4 F(x)=2x2+9x+4.

Problem 2812

Problem 2813

QuestionWhich expression is equivalent to (5−1)2?\left(5^{-1}\right)^{2} ?(5−1)2?Answer 125\frac{1}{25}251​ 125 5 1125\frac{1}{125}1251​

Problem 2814

Problem 2815

Simplify the expression a2b−1c−8a^{2} b^{-1} c^{-8}a2b−1c−8.

Problem 2816

Use the given zeros to write the complete factored form of f(x)f(x)f(x). f(x)=2x2−13x+20;f(x)=2 x^{2}-13 x+20 ;f(x)=2x2−13x+20; zeros: 52\frac{5}{2}25​ and 4 f(x)=f(x)=f(x)= □\square□ (Type your answer in factored form. Use integers or fractions for any numbers in

Problem 2817

Write the complete factored form of f(x)f(x)f(x). f(x)=−3x3−2x2+61x−20; zeros: −5,13,4f(x)=-3 x^{3}-2 x^{2}+61 x-20 ; \text { zeros: }-5, \frac{1}{3}, 4f(x)=−3x3−2x2+61x−20; zeros: −5,31​,4 f(x)=□f(x)=\squaref(x)=□ (Type your answer in factored form. Use integers or fractions

Problem 2818

Problem 2819

c0.2+0.9=3.9\frac{c}{0.2}+0.9=3.90.2c​+0.9=3.9

Problem 2820

Problem 2821

Use properties of logarithms to expand each logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. ln⁡x15\ln \sqrt[15]{x}ln15x​

Problem 2822

Write the complex number in the form a+bia+b ia+bi. 11(cos⁡3π2+isin⁡3π2)\sqrt{11}\left(\cos \frac{3 \pi}{2}+i \sin \frac{3 \pi}{2}\right)11​(cos23π​+isin23π​)

Problem 2823

−8x3(10x3y)-8 x^{3}\left(10 x^{3} y\right)−8x3(10x3y)Answer Attempt 1 out of 2

Problem 2824

−3x+2=−10x+30-3 x+2=-10 x+30−3x+2=−10x+30Simplify your answer as much as possible. x=x=x=

Problem 2825

Problem 2826

Solve for yyy. 5y+9=17y−4y+815 y+9=17 y-4 y+815y+9=17y−4y+81Simplify your answer as much as possible.

Problem 2827

38d+34\frac{3}{8}d + \frac{3}{4}83​d+43​

Problem 2828

log⁡4128\log _{4} 128log4​128

Problem 2829

Solve the inequality for www. 17<w+617<w+617<w+6Simplify your answer as much as possible.

Problem 2830

rind the domain and tne tarlysWrite your answers as inequalities, using xxx or yyy as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) domain: □\square□ (b) range: □\square□ Empty All set reals

Problem 2831

Express the following fraction in simplest form using only posl exponents. 3(w)32w6\frac{3(w)^{3}}{2 w^{6}}2w63(w)3​

Problem 2832

A line has a slope of −79-\frac{7}{9}−97​ and includes the points (3,w)(3, w)(3,w) and (−6,−1)(-6,-1)(−6,−1). What is the value of www ? w=w=w=

Problem 2833

A line has a slope of −32-\frac{3}{2}−23​ and includes the points (5,0)(5,0)(5,0) and (3,v)(3, v)(3,v). What is the value of vvv ? v=v=v=

Problem 2834

3efin⁡−3sin⁡(6πx) 3 e^{\operatorname{fin}} - 3 \sin (6 \pi x) 3efin−3sin(6πx)

Problem 2835

Factor the algebraic expression. 40a+3540a+35=\begin{array}{r} 40 \mathrm{a}+35 \\ 40 \mathrm{a}+35= \end{array}40a+3540a+35=​ □\square□ (Factor completely.)

Problem 2836

Rewrite using a single exponent. (48)3\left(4^{8}\right)^{3}(48)3

Problem 2837

Problem 2838

3. A diamond necklace worn by Princess Diana was first purchased for $25,000\$ 25,000$25,000. Experts say its value will increase by 15%15 \%15% per year. When will the value of the necklace be $80,000?\$ 80,000 ?$80,000?

Problem 2839

Write the equation in exponential form. Assume that all constants are positive and not equal to 1. log⁡p(b)=w\log _{p}(b)=wlogp​(b)=w

Problem 2840

Complex Roots (Lever I)Score: 3/53 / 53/5 Penalty: none Show ExamplesQuestion What are the roots of the equation x2+6x+58=0x^{2}+6 x+58=0x2+6x+58=0 in simplest a+bia+b ia+bi form? Attempt 1 out of 2

Problem 2841

Problem 2842

Id the range and the domain of the function shown.Write your answers as inequalities, using xxx or yyy as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) range: □\square□ (b) domain: □\square□ Empty All set reals Explanation Check

Problem 2843

7) (−2a23y3)3\left(\frac{-2 a^{2}}{3 y^{3}}\right)^{3}(3y3−2a2​)3

Problem 2844

Problem 2845

20. What is the formula for calculating simple interest? I=P(R+T)I=P(R+T)I=P(R+T) I=P/(T−R)I=P /(T-R)I=P/(T−R) I = PRT I=PT/RI=P T / RI=PT/R

The polynomial is a Select an answer $\vee$ . $11+15 u^{3}+10 u^{4}$
The degree of this polynomial is $\square$

The polynomial is a $\square$ $-15 y^{3}+32 y^{2}$
The degree of this polynomial is $\square$

- Q20: Solve and express in interval notation: $|3 x+1| \geq 4$ . - Q21: Solve and express in interval notation: $|2 x-7|>3$ .

The product rule for logarithms states that $\log _{b}(M N)=$ $\square$ The logarithm of a product is the $\square$ of the logarithms.

Complete the sentence.
If the graph of a logarithmic function $f(x)=\log _{a} x, a>0, a \neq 1$ , is increasing, then its base must be larger than $\square$

Oliver read for 450 minutes this month. His goal is to read for $10 \%$ more minutes next month.
If Oliver meets his goal, how many minutes will he read in all during the two months? $\square$ minutes

16. $3 n-n+7=25$

Find the x-intercepts of the quadratic function $F(x) = 2x^2 + 9x + 4$ .

Question
Which expression is equivalent to $\left(5^{-1}\right)^{2} ?$
Answer $\frac{1}{25}$ 125 5 $\frac{1}{125}$

Simplify the expression $a^{2} b^{-1} c^{-8}$ .

Use the given zeros to write the complete factored form of $f(x)$ . $f(x)=2 x^{2}-13 x+20 ;$ zeros: $\frac{5}{2}$ and 4 $f(x)=$ $\square$ (Type your answer in factored form. Use integers or fractions for any numbers in

Write the complete factored form of $f(x)$ . $f(x)=-3 x^{3}-2 x^{2}+61 x-20 ; \text { zeros: }-5, \frac{1}{3}, 4$ $f(x)=\square$ (Type your answer in factored form. Use integers or fractions

$\frac{c}{0.2}+0.9=3.9$

Use properties of logarithms to expand each logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. $\ln \sqrt[15]{x}$

Write the complex number in the form $a+b i$ . $\sqrt{11}\left(\cos \frac{3 \pi}{2}+i \sin \frac{3 \pi}{2}\right)$

$-8 x^{3}\left(10 x^{3} y\right)$
Answer Attempt 1 out of 2

$-3 x+2=-10 x+30$
Simplify your answer as much as possible. $x=$

Solve for $y$ . $5 y+9=17 y-4 y+81$
Simplify your answer as much as possible.

$\frac{3}{8}d + \frac{3}{4}$

$\log _{4} 128$

Solve the inequality for $w$ . $17<w+6$
Simplify your answer as much as possible.

rind the domain and tne tarlys
Write your answers as inequalities, using $x$ or $y$ as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) domain: $\square$ (b) range: $\square$ Empty All set reals

Express the following fraction in simplest form using only posl exponents. $\frac{3(w)^{3}}{2 w^{6}}$

A line has a slope of $-\frac{7}{9}$ and includes the points $(3, w)$ and $(-6,-1)$ . What is the value of $w$ ? $w=$

A line has a slope of $-\frac{3}{2}$ and includes the points $(5,0)$ and $(3, v)$ . What is the value of $v$ ? $v=$

$3 e^{\operatorname{fin}} - 3 \sin (6 \pi x)$

Factor the algebraic expression. $\begin{array}{r} 40 \mathrm{a}+35 \\ 40 \mathrm{a}+35= \end{array}$ $\square$ (Factor completely.)

Rewrite using a single exponent. $\left(4^{8}\right)^{3}$

3. A diamond necklace worn by Princess Diana was first purchased for $\$ 25,000$ . Experts say its value will increase by $15 \%$ per year. When will the value of the necklace be $\$ 80,000 ?$

Write the equation in exponential form. Assume that all constants are positive and not equal to 1. $\log _{p}(b)=w$

Complex Roots (Lever I)
Score: $3 / 5$ Penalty: none Show Examples
Question What are the roots of the equation $x^{2}+6 x+58=0$ in simplest $a+b i$ form? Attempt 1 out of 2

Id the range and the domain of the function shown.
Write your answers as inequalities, using $x$ or $y$ as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) range: $\square$ (b) domain: $\square$ Empty All set reals Explanation Check

7) $\left(\frac{-2 a^{2}}{3 y^{3}}\right)^{3}$

20. What is the formula for calculating simple interest? $I=P(R+T)$ $I=P /(T-R)$ I = PRT $I=P T / R$

Simplify the expression: $10+-5 x+-2$ $\square$ Submit

Solve the equation: $-6 c+21=81$

Question Show Exampl
What are the roots of the equation $9 x^{2}-36 x+37=0$ in simplest $a+b i$ form?
Answer Attempt 1 out of 2. ( Additional Solution $\Theta$ No Solution

$-\frac{2}{3}(x+12)+\frac{2}{3} x=-\frac{5}{4} x+2$

Angie sells handmade bracelets at craft fairs. She bought 2 packs of charms. One pack has 150 small charm and 60 large charms. The other pack has the same ratio of small to large charms. The second pack has 50 small charms.
How many large charms are in the second pack? $\square$ large charms

SImplify the expression: Videc $8+4 y+3 y+7+6 y+4 y$ $\square$ Submit

Question Watch Video Show Examples
Expand the logarithm fully using the properties of logs. Express the final answer in terms of $\log x$ , and $\log y$ . $\log x y^{3}$

Simplify the expression: Video $6 h+4 h+6 h-4 h+3 h$ $\square$ Submit

8. Solve Quadratic Equations Using Zero Factor Property - Q22: Solve for $x: x^{2}-5 x=0$ . - Q23: Solve for $x: 2 x^{2}+7 x=3$ .

Graph the exponential function. $f(x)=-2\left(\frac{2}{3}\right)^{x}$
Plot five points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.

Find all vertical asymptotes of the following function. $f(x)=\frac{25 x^{2}-64}{15 x+24}$

$f(x)=x^{3} \text { and } g(x)=x^{2}+4$
Find the formula for $(g \circ f)(x)$ and simplify your answer.

A bacteria culture starts with 3000 bacteria. After 3 h , the estimated count is 48000 . What is the doubling period? $d=?$

Ine grapn of $J(x)$ is given Delow. Un what intervais(s) is the varue or $J(x)$ increasing? Give your answer in intervainoration
Provide your answer below: $f(x)$ is increasing over $\square$

$\begin{array}{r} 16 a+14=14 \\ 16 a=0 \end{array}$ $a=$ $\square$ Divide both sides by 16

17. $\log (4 x+3)+\log (5)=2$

$f(x)=\frac{-3 x+3}{x^{2}+9}$