Algebra

Problem 23401

Find $f(10)$ for the function $f(x)=\frac{x}{2}+8$ . Options: 4, 9, 13, 36.

See Solution

Problem 23402

Find functions for average yearly earnings based on these points: Men (0,21), (30,66) and Women (0,20), (30,45).
(a) Determine $M(x)=m x+b$ for men.
(b) Determine $W(x)=m x+b$ for women.

See Solution

Problem 23403

Match the data tables with their corresponding equations and explain why. Simplify: $2x + x(x + 6)$ .

See Solution

Problem 23404

Find the equivalent expression for $9 w^{2}+\frac{3}{5}(20 w^{2}-15 w+10)+2 w$ . Choices are A, B, C, D.

See Solution

Problem 23405

Find the polynomial sum of $(16 x^{2}-16) + (-12 x^{2}-12 x+12)$ . Choices: A. $4 x^{2}-12 x-4$ , B. $4 x^{2}-12 x+28$ , C. $16 x^{2}-28 x-16$ , D. $28 x^{2}-28 x-12$ .

See Solution

Problem 23406

Find the polynomial representing the difference: $2x^{2}+7x+6 - (3x^{2}-x)$ . Options: A. $-x^{2}+8x+6$ , B. $2x^{2}+4x+6$ , C. $-x^{2}+6x+6$ , D. $2x^{2}+5x+6$ .

See Solution

Problem 23407

Find the equivalent expression for $5 q^{2}-\frac{2}{3}(6 q^{2}-6 q-3)+3 q$ . Options: A, B, C, D.

See Solution

Problem 23408

Simplify: $8 \sqrt{3} + 4 \sqrt{3} - 10 \sqrt{3} - 9 =$ (exact answer with radicals).

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Problem 23409

Subtract the polynomials: $(3 x^{2}+2 x+4)-(x^{2}+2 x+1)=?$ A. $2 x^{2}+3$ B. $2 x^{2}+4 x+3$ C. $2 x^{2}+5$ D. $2 x^{2}+4 x+5$

See Solution

Problem 23410

Find the side length $x$ of a square sheet to create a box with volume 100 cubic feet using $V(x)=(x-2)^{2}$ .

See Solution

Problem 23411

Subtract the polynomials: (4x² - x + 6) - (x² + 3) = ? A. 5x² - x + 9 B. 3x² - x + 3 C. 4x² - 2x + 9 D. 4x² - 2x + 3

See Solution

Problem 23412

Find the zeros of the function $f(x)=x^{2}-7 x$ by factoring. What are the $x$ -intercepts?

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Problem 23413

Find the next equation in the sequence:
1 = $1^2$ , 1 + 2 + 1 = $2^2$ , 1 + 2 + 3 + 2 + 1 = $3^2$ , 1 + 2 + 3 + 4 + 3 + 2 + 1 = $4^2$ .
Verify your answer.

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Problem 23414

Todd used 3 gallons for 150 miles. Find the rate of change in gallons per mile: slope = $\frac{150 \text{ miles}}{3 \text{ gallons}}$ .

See Solution

Problem 23415

Find the cost in 2014 using the model $C=2.85n+30.52$ , where $n$ is the years since 1990.

See Solution

Problem 23416

Find the intercepts of the line given by $-4x + 7y = 3$ . Provide exact values.

See Solution

Problem 23417

Graph the equations: $x+y=-2$ and $x-y=4$ . Find their intersection point.

See Solution

Problem 23418

Find the volume of a volleyball with radius $10.5 \mathrm{~cm}$ . Also, write a function for Proxy car rental costs: \$0.32 per mile + \$18 surcharge.

See Solution

Problem 23419

Check if $(-2,1)$ satisfies the equations: $-x-5y=-3$ and $-3x-4y=2$ . Is it a solution? Yes or No.

See Solution

Problem 23420

Graph the system: $x+y=-2$ and $x-y=4$ . Choose A (ordered pair), B (equation), or C (no solution: $\varnothing$ ).

See Solution

Problem 23421

Solve for real $x$ in the equation: $4 x^{3}-8 x^{2}=0$ . Provide answers as a comma-separated list.

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Problem 23422

Graph the system of equations: $x+y=-1$ and $x-y=7$ .

See Solution

Problem 23423

Find $f \circ g$ , $g \circ f$ , and $g \circ g$ for $f(x)=x^{2}$ and $g(x)=x-1$ .

See Solution

Problem 23424

Find $f \circ g$ , $g \circ f$ , and $g \circ g$ for $f(x)=x^{2}$ and $g(x)=x-1$ .

See Solution

Problem 23425

Diego paid a \$2.25 pickup fee and \$1.75 per mile. If his total fare was \$28.50, how far did he travel?

See Solution

Problem 23426

Find $f \circ g$ and $g \circ f$ for $f(x)=\sqrt{x+8}$ and $g(x)=x^{2}$ . Determine the domains in interval notation.

See Solution

Problem 23427

Find the compositions of the functions $f(x)=4x+7$ and $g(x)=-8x-7$ : (a) $(f \circ g)(x)$ , (b) $(g \circ f)(x)$ , (c) $(f \circ f)(x)$ . Simplify your answers.

See Solution

Problem 23428

Find the intercepts of the line given by $y-3=5(x-2)$ . $y$ -intercept: $x$ -intercept:

See Solution

Problem 23429

Find Rosalyn's regular hourly wage given she worked 44 hours and earned \$1025, with overtime pay at 2.5 times her wage.

See Solution

Problem 23430

Evaluate the function $g(x)=4x+1$ for: (a) $g(-4)$ , (b) $g(a)$ , (c) $g(x^{3})$ , (d) $g(4x-3)$ .

See Solution

Problem 23431

Graph the system of equations: $x+y=-1$ and $x-y=7$ . Identify the solution set: A, B, or C.

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Problem 23432

Find the abundance of ${ }^{10} \mathrm{~B}$ and ${ }^{11} \mathrm{~B}$ given their masses and average atomic mass of boron, $10.81 \mathrm{~u}$ .

See Solution

Problem 23433

Evaluate $g(x)=5 x^{2}-8$ for: (a) $g(-7)$ , (b) $g(b)$ , (c) $g(x^{3})$ , (d) $g(5 x-7)$ .

See Solution

Problem 23434

Transform $y=x^{4}$ to $y=4[3(x+2)]^{4}-6$ . Describe transformations, complete the table, sketch the graph, and state domain, range, vertex, and axis of symmetry.

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Problem 23435

Identify $a_{1}$ and $d$ in the sequence $12, 22, 32, 42, 52$ using $a_{n}=a_{1}+(n-1)d$ . Explain $a_{2}, a_{3}, a_{4}, a_{5}$ .

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Problem 23436

Evaluate $(f \circ g)(6)$ for $f(x)=\sqrt{x+28}$ and $g(x)=x^{2}$ . What is the simplified result?

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Problem 23437

Find the cost function $C(x)$ for a theater with fixed costs of \$39000 and \$2400 per performance.

See Solution

Problem 23438

Evaluate $(f \circ g)(6)$ and $(g \circ f)(-3)$ for $f(x)=\sqrt{x+28}$ and $g(x)=x^{2}$ .

See Solution

Problem 23439

Identify the arithmetic sequence from the formula $a_{n}=10n+12$ and the terms 12, 22, 32, 42, 52.

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Problem 23440

Find all real solutions for the equation $x^{3} = 81x$ . Enter answers as a comma-separated list.

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Problem 23441

Transform $y=x^{4}$ to $y=4[3(x+2)]^{4}-6$ . Identify transformations, complete the table, and sketch the graph.

See Solution

Problem 23442

Multiply and simplify: $(\sqrt{10}+8 \sqrt{6})(2 \sqrt{6}+5 \sqrt{10})$ .

See Solution

Problem 23443

Find functions $f$ and $g$ where $(f \circ g)(x)=h(x)$ with $h(x)=\sqrt[3]{x^{2}-3}$ .

See Solution

Problem 23444

Multiply and simplify: $(5 \sqrt{10}+7 \sqrt{6})(2 \sqrt{6}-8 \sqrt{10})$

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Problem 23445

Evaluate $f(g(-5))$ and $g(f(3))$ for $f(x)=7x-1$ and $g(x)=|x|$ .

See Solution

Problem 23446

Find all real solutions for the equation: $6x^5 - 24x = 0$ .

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Problem 23447

Evaluate the following using $f(x)=7x-1$ and $g(x)=|x|$ : (a) $(f \circ g)(-5)$ (b) $(g \circ f)(3)$ Find $(f \circ g)(-5)=$ (Simplify your answer.)

See Solution

Problem 23448

Solve for all real values of $x$ in the equation $x = 5x^5 - 45x$ .

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Problem 23449

Calculate the value of $\left(4^{4}\right)^{3}$ .

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Problem 23450

Find $t$ when the rocket's height $h=92$ feet, given $h=188t-16t^2$ . Round to the nearest hundredth.

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Problem 23451

Determine if the function $f(x)=\frac{-x^{3}}{9 x^{2}-3}$ is even, odd, or neither.

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Problem 23452

Solve for all real solutions of the equation: $x = x^3 - 4x^2 + x - 4 = x^2 + 1$ .

See Solution

Problem 23453

Evaluate $f(x)=7x-1$ and $g(x)=|x|$ for: (a) $(f \circ g)(-5)$ , (b) $(g \circ f)(3)$ .

See Solution

Problem 23454

Calculate the value of $\frac{3^{12}}{3^{3}}$ .

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Problem 23455

Find $(f \circ g)(x)$ and $(g \circ f)(x)$ for $f(x)=2x-4$ and $g(x)=\frac{x+4}{2}$ . Simplify both.

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Problem 23456

Is $8 \times 8^{5}$ the same as $(8 \times 8)^{5}$ ? Justify your answer.

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Problem 23457

Find and interpret $(A \circ r)(t)$ where $r(t)=0.7 t$ and $A(r)=\pi r^{2}$ .

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Problem 23458

Find all real solutions for the equation $z + \frac{16}{z+2} = 6$ . Enter answers as a comma-separated list.

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Problem 23459

Find the real zeros and their multiplicities for $f(x)=\frac{1}{5} x^{2}(x^{2}-3)$ and state if the graph crosses or touches the $\mathrm{x}$ -axis.

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Problem 23460

Rationalize and simplify the expression: $\sqrt{\frac{13}{3}}$ .

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Problem 23461

The weekly cost $C$ for producing $x$ units is $C(x)=50x+2250$ , with $x(t)=60t$ .
(a) Find $(C \circ x)(t)$ . (b) Calculate the cost for 4 hours. (c) Determine time for cost to reach \$15,000.

See Solution

Problem 23462

Calculate the slope of the line connecting the points $(-4,9)$ and $(10,-6)$ .

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Problem 23463

Rationalize and simplify the expression: $\frac{\sqrt{21}}{\sqrt{77}}$ .

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Problem 23464

Solve the equation for real values of $x$ : $\frac{15}{x}-\frac{9}{x-2}+4=0$ . List answers as comma-separated values.

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Problem 23465

Determine the final function after shifting $y=\sqrt{x}$ up 9 units, reflecting it about the $y$ axis, and shifting left 3 units.

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Problem 23466

Find the line equation in slope-intercept form with slope $m=\frac{5}{9}$ and y-intercept $(0,1)$ .

See Solution

Problem 23467

Solve for real values of $x$ in the equation $x=\frac{x^{2}}{x+20}=10$ .

See Solution

Problem 23468

Find the x-intercepts of the function $f(x)=\frac{x^{2}+2}{x^{2}+9x+9}$ .

See Solution

Problem 23469

Solve for $x$ in the equation $x^2 - 3x - 4 = -4$ .

See Solution

Problem 23470

Solve for $x$ in the equation $\frac{x^{2}}{x+20}=10$ . What are the real solutions?

See Solution

Problem 23471

Calculate $3^{3}-3^{4} \div 3^{3}$ .

See Solution

Problem 23472

Find all real solutions of the equation $\frac{x^{2}}{x+20}=10$ .

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Problem 23473

Describe the solution set for $16 x^{2}-8 x+1=0$ : how many real solutions are there and why?

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Problem 23474

Find the revenue function $R(x)$ if the cost is $C(x) = 39000 + 2400x$ and each unit sells for \$3150.

See Solution

Problem 23475

a. Cost function: $C(x)=39000+2400 x$ b. Revenue function: $R(x)=3150 x$ c. Find the break-even point by solving $C(x)=R(x)$ .

See Solution

Problem 23476

Determine the vertical asymptotes of the function $g(x)=\frac{8 x}{(x+9)(x-6)}$ .

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Problem 23477

Find the average yearly salaries of individuals with a bachelor's and master's degree, given their combined earnings of \$124,000.

See Solution

Problem 23478

Simplify: $9^{10} \cdot 9$

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Problem 23479

Find the break-even point for the cost function $C(x)=39000+2400x$ and revenue function $R(x)=3150x$ .

See Solution

Problem 23480

Find $UW$ given $UV=5$ , $VW=x+5$ , and $UW=6x$ .

See Solution

Problem 23481

Find the composite function $(f \circ g)(x)$ for $f(x)=x^{2}+9$ and $g(x)=x^{2}-6$ .

See Solution

Problem 23482

If $BC=6x$ , $CD=9$ , and $BD=9x$ , find the value of $BC$ . Simplify your answer as a fraction, mixed number, or integer.

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Problem 23483

Find $x$ such that $f(x)=x^2-3x-4=-4$ and also calculate $f(4)$ .

See Solution

Problem 23484

Find the composite function of the given functions: $f(x)=\frac{4}{x-2}$ , $g(x)=\frac{5}{6x}$ . Calculate $(f \circ g)(x)$ .

See Solution

Problem 23485

Find $K L$ given $K L=6 x$ , $L M=15 x-11$ , and $K M=20 x+3$ . Simplify your answer.

See Solution

Problem 23486

Find the drug amount $D(h)=9e^{-0.4h}$ after 5 hours. Round to two decimals.

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Problem 23487

Set up and solve the equation for Joe's miles driven if he was reimbursed \$ 260 for lodging and travel costs.

See Solution

Problem 23488

Find the inverse of the one-to-one function $f(x) = 8x$ .

See Solution

Problem 23489

Find the cost function $C(x)$ for canoes with fixed cost \$20000, production cost \$40, and selling price \$80.

See Solution

Problem 23490

Solve the equation: $(\frac{1}{5})^{x} = 625$ .

See Solution

Problem 23491

Find the value of $\ln e^{8}$ .

See Solution

Problem 23492

Solve for $x$ in the equation $e^{5 x} = 3$ .

See Solution

Problem 23493

Determine the domain of the function $f(x)=\log_{10}(x^{2}-10x+24)$ .

See Solution

Problem 23494

Find the revenue function $R(x)$ given the cost function $C(x)=20000+40x$ and price per unit is $80$ .

See Solution

Problem 23495

Determine the final function after shifting $y=|x|$ up 7 units, reflecting it over the $x-$ axis, and shifting right 9 units.

See Solution

Problem 23496

Find the inverse of the one-to-one function $f(x)=\frac{3}{7 x+8}$ .

See Solution

Problem 23497

a. Write the cost function: $C(x)=20000+40x$ . b. Write the revenue function: $R(x)=80x$ . c. Find the break-even point as an ordered pair without commas in large numbers.

See Solution

Problem 23498

Write the line equation in point-slope and slope-intercept forms with slope $=-7$ and passing through $(-8,-3)$ .

See Solution

Problem 23499

Simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=x^{2}+4x+8$ , where $h \neq 0$ .

See Solution

Problem 23500

Solve the equation: $\left(\frac{256}{81}\right)^{x+1}=\left(\frac{3}{4}\right)^{x-1}$ .

See Solution

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Algebra

Problem 23401

Find f(10)f(10)f(10) for the function f(x)=x2+8f(x)=\frac{x}{2}+8f(x)=2x​+8. Options: 4, 9, 13, 36.

Problem 23402

Find functions for average yearly earnings based on these points: Men (0,21), (30,66) and Women (0,20), (30,45). (a) Determine M(x)=mx+bM(x)=m x+bM(x)=mx+b for men. (b) Determine W(x)=mx+bW(x)=m x+bW(x)=mx+b for women.

Problem 23403

Match the data tables with their corresponding equations and explain why. Simplify: 2x+x(x+6)2x + x(x + 6)2x+x(x+6).

Problem 23404

Find the equivalent expression for 9w2+35(20w2−15w+10)+2w9 w^{2}+\frac{3}{5}(20 w^{2}-15 w+10)+2 w9w2+53​(20w2−15w+10)+2w. Choices are A, B, C, D.

Problem 23405

Problem 23406

Find the polynomial representing the difference: 2x2+7x+6−(3x2−x)2x^{2}+7x+6 - (3x^{2}-x)2x2+7x+6−(3x2−x). Options: A. −x2+8x+6-x^{2}+8x+6−x2+8x+6, B. 2x2+4x+62x^{2}+4x+62x2+4x+6, C. −x2+6x+6-x^{2}+6x+6−x2+6x+6, D. 2x2+5x+62x^{2}+5x+62x2+5x+6.

Problem 23407

Find the equivalent expression for 5q2−23(6q2−6q−3)+3q5 q^{2}-\frac{2}{3}(6 q^{2}-6 q-3)+3 q5q2−32​(6q2−6q−3)+3q. Options: A, B, C, D.

Problem 23408

Simplify: 83+43−103−9=8 \sqrt{3} + 4 \sqrt{3} - 10 \sqrt{3} - 9 = 83​+43​−103​−9= (exact answer with radicals).

Problem 23409

Subtract the polynomials: (3x2+2x+4)−(x2+2x+1)=?(3 x^{2}+2 x+4)-(x^{2}+2 x+1)=?(3x2+2x+4)−(x2+2x+1)=? A. 2x2+32 x^{2}+32x2+3 B. 2x2+4x+32 x^{2}+4 x+32x2+4x+3 C. 2x2+52 x^{2}+52x2+5 D. 2x2+4x+52 x^{2}+4 x+52x2+4x+5

Problem 23410

Find the side length xxx of a square sheet to create a box with volume 100 cubic feet using V(x)=(x−2)2V(x)=(x-2)^{2}V(x)=(x−2)2.

Problem 23411

Subtract the polynomials: (4x² - x + 6) - (x² + 3) = ? A. 5x² - x + 9 B. 3x² - x + 3 C. 4x² - 2x + 9 D. 4x² - 2x + 3

Problem 23412

Find the zeros of the function f(x)=x2−7xf(x)=x^{2}-7 xf(x)=x2−7x by factoring. What are the xxx-intercepts?

Problem 23413

Find the next equation in the sequence: 1 = 121^212, 1 + 2 + 1 = 222^222, 1 + 2 + 3 + 2 + 1 = 323^232, 1 + 2 + 3 + 4 + 3 + 2 + 1 = 424^242. Verify your answer.

Problem 23414

Todd used 3 gallons for 150 miles. Find the rate of change in gallons per mile: slope = 150 miles3 gallons\frac{150 \text{ miles}}{3 \text{ gallons}}3 gallons150 miles​.

Problem 23415

Find the cost in 2014 using the model C=2.85n+30.52C=2.85n+30.52C=2.85n+30.52, where nnn is the years since 1990.

Problem 23416

Find the intercepts of the line given by −4x+7y=3-4x + 7y = 3−4x+7y=3. Provide exact values.

Problem 23417

Graph the equations: x+y=−2x+y=-2x+y=−2 and x−y=4x-y=4x−y=4. Find their intersection point.

Problem 23418

Find the volume of a volleyball with radius 10.5 cm10.5 \mathrm{~cm}10.5 cm. Also, write a function for Proxy car rental costs: \$0.32 per mile + \$18 surcharge.

Problem 23419

Check if (−2,1)(-2,1)(−2,1) satisfies the equations: −x−5y=−3-x-5y=-3−x−5y=−3 and −3x−4y=2-3x-4y=2−3x−4y=2. Is it a solution? Yes or No.

Problem 23420

Graph the system: x+y=−2x+y=-2x+y=−2 and x−y=4x-y=4x−y=4. Choose A (ordered pair), B (equation), or C (no solution: ∅\varnothing∅).

Problem 23421

Solve for real xxx in the equation: 4x3−8x2=04 x^{3}-8 x^{2}=04x3−8x2=0. Provide answers as a comma-separated list.

Problem 23422

Graph the system of equations: x+y=−1x+y=-1x+y=−1 and x−y=7x-y=7x−y=7.

Problem 23423

Find f∘gf \circ gf∘g, g∘fg \circ fg∘f, and g∘gg \circ gg∘g for f(x)=x2f(x)=x^{2}f(x)=x2 and g(x)=x−1g(x)=x-1g(x)=x−1.

Problem 23424

Find f∘gf \circ gf∘g, g∘fg \circ fg∘f, and g∘gg \circ gg∘g for f(x)=x2f(x)=x^{2}f(x)=x2 and g(x)=x−1g(x)=x-1g(x)=x−1.

Problem 23425

Diego paid a \$2.25 pickup fee and \$1.75 per mile. If his total fare was \$28.50, how far did he travel?

Problem 23426

Find f∘gf \circ gf∘g and g∘fg \circ fg∘f for f(x)=x+8f(x)=\sqrt{x+8}f(x)=x+8​ and g(x)=x2g(x)=x^{2}g(x)=x2. Determine the domains in interval notation.

Problem 23427

Find the compositions of the functions f(x)=4x+7f(x)=4x+7f(x)=4x+7 and g(x)=−8x−7g(x)=-8x-7g(x)=−8x−7: (a) (f∘g)(x)(f \circ g)(x)(f∘g)(x), (b) (g∘f)(x)(g \circ f)(x)(g∘f)(x), (c) (f∘f)(x)(f \circ f)(x)(f∘f)(x). Simplify your answers.

Problem 23428

Find the intercepts of the line given by y−3=5(x−2)y-3=5(x-2)y−3=5(x−2). yyy-intercept: xxx-intercept:

Problem 23429

Find Rosalyn's regular hourly wage given she worked 44 hours and earned \$1025, with overtime pay at 2.5 times her wage.

Problem 23430

Evaluate the function g(x)=4x+1g(x)=4x+1g(x)=4x+1 for: (a) g(−4)g(-4)g(−4), (b) g(a)g(a)g(a), (c) g(x3)g(x^{3})g(x3), (d) g(4x−3)g(4x-3)g(4x−3).

Problem 23431

Graph the system of equations: x+y=−1x+y=-1x+y=−1 and x−y=7x-y=7x−y=7. Identify the solution set: A, B, or C.

Problem 23432

Find the abundance of 10 B{ }^{10} \mathrm{~B}10 B and 11 B{ }^{11} \mathrm{~B}11 B given their masses and average atomic mass of boron, 10.81 u10.81 \mathrm{~u}10.81 u.

Problem 23433

Evaluate g(x)=5x2−8g(x)=5 x^{2}-8g(x)=5x2−8 for: (a) g(−7)g(-7)g(−7), (b) g(b)g(b)g(b), (c) g(x3)g(x^{3})g(x3), (d) g(5x−7)g(5 x-7)g(5x−7).

Problem 23434

Transform y=x4y=x^{4}y=x4 to y=4[3(x+2)]4−6y=4[3(x+2)]^{4}-6y=4[3(x+2)]4−6. Describe transformations, complete the table, sketch the graph, and state domain, range, vertex, and axis of symmetry.

Problem 23435

Identify a1a_{1}a1​ and ddd in the sequence 12,22,32,42,5212, 22, 32, 42, 5212,22,32,42,52 using an=a1+(n−1)da_{n}=a_{1}+(n-1)dan​=a1​+(n−1)d. Explain a2,a3,a4,a5a_{2}, a_{3}, a_{4}, a_{5}a2​,a3​,a4​,a5​.

Problem 23436

Evaluate (f∘g)(6)(f \circ g)(6)(f∘g)(6) for f(x)=x+28f(x)=\sqrt{x+28}f(x)=x+28​ and g(x)=x2g(x)=x^{2}g(x)=x2. What is the simplified result?

Problem 23437

Find the cost function C(x)C(x)C(x) for a theater with fixed costs of \$39000 and \$2400 per performance.

Problem 23438

Evaluate (f∘g)(6)(f \circ g)(6)(f∘g)(6) and (g∘f)(−3)(g \circ f)(-3)(g∘f)(−3) for f(x)=x+28f(x)=\sqrt{x+28}f(x)=x+28​ and g(x)=x2g(x)=x^{2}g(x)=x2.

Problem 23439

Identify the arithmetic sequence from the formula an=10n+12a_{n}=10n+12an​=10n+12 and the terms 12, 22, 32, 42, 52.

Problem 23440

Find all real solutions for the equation x3=81xx^{3} = 81xx3=81x. Enter answers as a comma-separated list.

Find $f(10)$ for the function $f(x)=\frac{x}{2}+8$ . Options: 4, 9, 13, 36.

Find functions for average yearly earnings based on these points: Men (0,21), (30,66) and Women (0,20), (30,45).
(a) Determine $M(x)=m x+b$ for men.
(b) Determine $W(x)=m x+b$ for women.

Match the data tables with their corresponding equations and explain why. Simplify: $2x + x(x + 6)$ .

Find the equivalent expression for $9 w^{2}+\frac{3}{5}(20 w^{2}-15 w+10)+2 w$ . Choices are A, B, C, D.

Find the polynomial representing the difference: $2x^{2}+7x+6 - (3x^{2}-x)$ . Options: A. $-x^{2}+8x+6$ , B. $2x^{2}+4x+6$ , C. $-x^{2}+6x+6$ , D. $2x^{2}+5x+6$ .

Find the equivalent expression for $5 q^{2}-\frac{2}{3}(6 q^{2}-6 q-3)+3 q$ . Options: A, B, C, D.

Simplify: $8 \sqrt{3} + 4 \sqrt{3} - 10 \sqrt{3} - 9 =$ (exact answer with radicals).

Subtract the polynomials: $(3 x^{2}+2 x+4)-(x^{2}+2 x+1)=?$ A. $2 x^{2}+3$ B. $2 x^{2}+4 x+3$ C. $2 x^{2}+5$ D. $2 x^{2}+4 x+5$

Find the side length $x$ of a square sheet to create a box with volume 100 cubic feet using $V(x)=(x-2)^{2}$ .

Find the zeros of the function $f(x)=x^{2}-7 x$ by factoring. What are the $x$ -intercepts?

Find the next equation in the sequence:
1 = $1^2$ , 1 + 2 + 1 = $2^2$ , 1 + 2 + 3 + 2 + 1 = $3^2$ , 1 + 2 + 3 + 4 + 3 + 2 + 1 = $4^2$ .
Verify your answer.

Todd used 3 gallons for 150 miles. Find the rate of change in gallons per mile: slope = $\frac{150 \text{ miles}}{3 \text{ gallons}}$ .

Find the cost in 2014 using the model $C=2.85n+30.52$ , where $n$ is the years since 1990.

Find the intercepts of the line given by $-4x + 7y = 3$ . Provide exact values.

Graph the equations: $x+y=-2$ and $x-y=4$ . Find their intersection point.

Find the volume of a volleyball with radius $10.5 \mathrm{~cm}$ . Also, write a function for Proxy car rental costs: \$0.32 per mile + \$18 surcharge.

Check if $(-2,1)$ satisfies the equations: $-x-5y=-3$ and $-3x-4y=2$ . Is it a solution? Yes or No.

Graph the system: $x+y=-2$ and $x-y=4$ . Choose A (ordered pair), B (equation), or C (no solution: $\varnothing$ ).

Solve for real $x$ in the equation: $4 x^{3}-8 x^{2}=0$ . Provide answers as a comma-separated list.

Graph the system of equations: $x+y=-1$ and $x-y=7$ .

Find $f \circ g$ , $g \circ f$ , and $g \circ g$ for $f(x)=x^{2}$ and $g(x)=x-1$ .

Find $f \circ g$ , $g \circ f$ , and $g \circ g$ for $f(x)=x^{2}$ and $g(x)=x-1$ .

Find $f \circ g$ and $g \circ f$ for $f(x)=\sqrt{x+8}$ and $g(x)=x^{2}$ . Determine the domains in interval notation.

Find the compositions of the functions $f(x)=4x+7$ and $g(x)=-8x-7$ : (a) $(f \circ g)(x)$ , (b) $(g \circ f)(x)$ , (c) $(f \circ f)(x)$ . Simplify your answers.

Find the intercepts of the line given by $y-3=5(x-2)$ . $y$ -intercept: $x$ -intercept:

Evaluate the function $g(x)=4x+1$ for: (a) $g(-4)$ , (b) $g(a)$ , (c) $g(x^{3})$ , (d) $g(4x-3)$ .

Graph the system of equations: $x+y=-1$ and $x-y=7$ . Identify the solution set: A, B, or C.

Find the abundance of ${ }^{10} \mathrm{~B}$ and ${ }^{11} \mathrm{~B}$ given their masses and average atomic mass of boron, $10.81 \mathrm{~u}$ .

Evaluate $g(x)=5 x^{2}-8$ for: (a) $g(-7)$ , (b) $g(b)$ , (c) $g(x^{3})$ , (d) $g(5 x-7)$ .

Transform $y=x^{4}$ to $y=4[3(x+2)]^{4}-6$ . Describe transformations, complete the table, sketch the graph, and state domain, range, vertex, and axis of symmetry.

Identify $a_{1}$ and $d$ in the sequence $12, 22, 32, 42, 52$ using $a_{n}=a_{1}+(n-1)d$ . Explain $a_{2}, a_{3}, a_{4}, a_{5}$ .

Evaluate $(f \circ g)(6)$ for $f(x)=\sqrt{x+28}$ and $g(x)=x^{2}$ . What is the simplified result?

Find the cost function $C(x)$ for a theater with fixed costs of \$39000 and \$2400 per performance.

Evaluate $(f \circ g)(6)$ and $(g \circ f)(-3)$ for $f(x)=\sqrt{x+28}$ and $g(x)=x^{2}$ .

Identify the arithmetic sequence from the formula $a_{n}=10n+12$ and the terms 12, 22, 32, 42, 52.

Find all real solutions for the equation $x^{3} = 81x$ . Enter answers as a comma-separated list.

Transform $y=x^{4}$ to $y=4[3(x+2)]^{4}-6$ . Identify transformations, complete the table, and sketch the graph.

Multiply and simplify: $(\sqrt{10}+8 \sqrt{6})(2 \sqrt{6}+5 \sqrt{10})$ .

Find functions $f$ and $g$ where $(f \circ g)(x)=h(x)$ with $h(x)=\sqrt[3]{x^{2}-3}$ .

Multiply and simplify: $(5 \sqrt{10}+7 \sqrt{6})(2 \sqrt{6}-8 \sqrt{10})$

Evaluate $f(g(-5))$ and $g(f(3))$ for $f(x)=7x-1$ and $g(x)=|x|$ .

Find all real solutions for the equation: $6x^5 - 24x = 0$ .

Evaluate the following using $f(x)=7x-1$ and $g(x)=|x|$ : (a) $(f \circ g)(-5)$ (b) $(g \circ f)(3)$ Find $(f \circ g)(-5)=$ (Simplify your answer.)

Solve for all real values of $x$ in the equation $x = 5x^5 - 45x$ .

Calculate the value of $\left(4^{4}\right)^{3}$ .

Find $t$ when the rocket's height $h=92$ feet, given $h=188t-16t^2$ . Round to the nearest hundredth.

Determine if the function $f(x)=\frac{-x^{3}}{9 x^{2}-3}$ is even, odd, or neither.

Solve for all real solutions of the equation: $x = x^3 - 4x^2 + x - 4 = x^2 + 1$ .

Evaluate $f(x)=7x-1$ and $g(x)=|x|$ for: (a) $(f \circ g)(-5)$ , (b) $(g \circ f)(3)$ .

Calculate the value of $\frac{3^{12}}{3^{3}}$ .

Find $(f \circ g)(x)$ and $(g \circ f)(x)$ for $f(x)=2x-4$ and $g(x)=\frac{x+4}{2}$ . Simplify both.

Is $8 \times 8^{5}$ the same as $(8 \times 8)^{5}$ ? Justify your answer.

Find and interpret $(A \circ r)(t)$ where $r(t)=0.7 t$ and $A(r)=\pi r^{2}$ .

Find all real solutions for the equation $z + \frac{16}{z+2} = 6$ . Enter answers as a comma-separated list.

Find the real zeros and their multiplicities for $f(x)=\frac{1}{5} x^{2}(x^{2}-3)$ and state if the graph crosses or touches the $\mathrm{x}$ -axis.

Rationalize and simplify the expression: $\sqrt{\frac{13}{3}}$ .

The weekly cost $C$ for producing $x$ units is $C(x)=50x+2250$ , with $x(t)=60t$ .
(a) Find $(C \circ x)(t)$ . (b) Calculate the cost for 4 hours. (c) Determine time for cost to reach \$15,000.

Calculate the slope of the line connecting the points $(-4,9)$ and $(10,-6)$ .

Rationalize and simplify the expression: $\frac{\sqrt{21}}{\sqrt{77}}$ .

Solve the equation for real values of $x$ : $\frac{15}{x}-\frac{9}{x-2}+4=0$ . List answers as comma-separated values.

Determine the final function after shifting $y=\sqrt{x}$ up 9 units, reflecting it about the $y$ axis, and shifting left 3 units.

Find the line equation in slope-intercept form with slope $m=\frac{5}{9}$ and y-intercept $(0,1)$ .

Solve for real values of $x$ in the equation $x=\frac{x^{2}}{x+20}=10$ .

Find the x-intercepts of the function $f(x)=\frac{x^{2}+2}{x^{2}+9x+9}$ .

Solve for $x$ in the equation $x^2 - 3x - 4 = -4$ .

Solve for $x$ in the equation $\frac{x^{2}}{x+20}=10$ . What are the real solutions?

Calculate $3^{3}-3^{4} \div 3^{3}$ .

Find all real solutions of the equation $\frac{x^{2}}{x+20}=10$ .

Describe the solution set for $16 x^{2}-8 x+1=0$ : how many real solutions are there and why?

Find the revenue function $R(x)$ if the cost is $C(x) = 39000 + 2400x$ and each unit sells for \$3150.