Algebra

Problem 23501

Simplify the expression $\left(\frac{x^{-1 / 5}}{y^{1 / 6}}\right)^{120}$ using exponent properties.

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Problem 23502

Find the inverse of the one-to-one function $f(x)=\sqrt[3]{x+5}$ .

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Problem 23503

Kane runs 3 miles and increases by $\frac{1}{4}$ mile each week. Write an expression for distance after $w$ weeks.

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Problem 23504

Find the composite function for $f(x)=4 x^{2}+5 x+6$ and $g(x)=5 x-3$ : $(g \circ f)(x)$ .

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Problem 23505

Simplify the radical expression using Property 1: $\operatorname{sqrt}(x)$ for $\sqrt{x}$ and $\operatorname{root}(x)(y)$ for $\sqrt[x]{y}$ . Find $\sqrt[3]{625 a^{6} b^{9}}.$

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Problem 23506

Find the absolute value of -7 and 3. What is $|-7|$ and $|3|$ ?

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Problem 23507

Solve the equation: $\left|\frac{1}{3} x-8\right|=4$

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Problem 23508

Find the composite function for $f(x)=\frac{2}{x-6}$ and $g(x)=\frac{3}{2 x}$ . Compute $(f \circ g)(x)$ .

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Problem 23509

Is it true that $-7 < |3|$ ?

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Problem 23510

Determine the domain of the function $f(x) = \frac{x}{\sqrt{x-8}}$ .

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Problem 23511

Combine the terms: sqrt(32) - sqrt(32) + sqrt(8) = ?

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Problem 23512

Solve for $x$ in the equation: $2x + 4 - \frac{3}{2}x = \frac{1}{3}(x + 5)$ .

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Problem 23513

Multiply: (sqrt(2)+sqrt(5))(sqrt(2)-sqrt(5))=

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Problem 23514

Solve for $y$ in the equation: $y + b = 20$ .

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Problem 23515

Rationalize the denominator: $\frac{8}{sqrt(x)-sqrt(y)}=$

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Problem 23516

Find $A$ from the equation $W=\frac{A}{4}$ .

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Problem 23517

Solve for m in the equation: mg = W.

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Problem 23518

Evaluate $y^2 + 6y + 9$ for $y = -4$ .

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Problem 23519

Find the mass in grams of a liquid with density $1.15 \mathrm{~g} / \mathrm{mL}$ to fill a 50.00 - $\mathrm{mL}$ container. Use algebraic manipulation.

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Problem 23520

Graph the function $f(x)=\sqrt[3]{x}$ .

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Problem 23521

How long in minutes does a snail moving at $1.3^{3}$ ft/min take to cross a $1.3^{12}$ ft wide road? Use exponents.

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Problem 23522

Solve for $x$ in the equation $\sqrt{8 x-1}=\sqrt{9 x-7}$ .

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Problem 23523

Solve for $x$ in the equation: $\sqrt{40 - 6x} = 2x$ . What are the real solutions?

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Problem 23524

Solve the equation for real $x$ : $\sqrt{8x + 4} + 2 = x$ . What are the solutions?

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Problem 23525

Find functions $f(x)$ and $g(x)$ such that $h(x)=(f \circ g)(x)$ with $h(x)=(2-3 x)^{2}$ and $g(x)=2-3 x$ .

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Problem 23526

Solve for $x$ in the equation: $\sqrt{1+x}+\sqrt{1-x}=2$ . What are the real solutions?

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Problem 23527

Solve for real $x$ in the equation $x^{4}-10 x^{2}+21=0$ . Enter answers as comma-separated values.

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Problem 23528

Solve the equation $x=\sqrt{x}-2\sqrt[4]{x}-3=0$ for all real solutions.

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Problem 23529

Solve the equation $x^{2}-6x=0$ .

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Problem 23530

Find the value of the box: $21 \cdot \square=7$ .

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Problem 23531

Calculate the energy in joules to ionize a hydrogen atom from the $n=6$ level, knowing ground-state ionization is $2.18 \times 10^{-18} \mathrm{~J}$ .

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Problem 23532

Solve the equation $\sqrt{x}-4 \sqrt[4]{x}-5=0$ . What are the real solutions?

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Problem 23533

Find real solutions for $x$ using the Quadratic Formula for $x^{2}-0.014 x-0.066=0$ .

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Problem 23534

Find two consecutive even integers whose squares sum to 1060.

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Problem 23535

Find the product and express it as $a + b i$ : $(7 - 2 i)(1 + i)$ .

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Problem 23536

Evaluate the quotient and express it as $a + b i$ : $\frac{4 - 3 i}{1 - 4 i}$

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Problem 23537

Determine if the graphs of $f(x)=-\sqrt{x}$ and $g(x)=\sqrt{-x}$ are identical.

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Problem 23538

Find the wavelength of photons from hydrogen transitioning from $n=4$ to $n=3$ in $\mathrm{nm}$ and identify the spectrum region: A. ultraviolet or B. X-ray.

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Problem 23539

Evaluate the quotient and express it as $a$ : $\frac{3-7 i}{1-3 i}$

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Problem 23540

What is the map length for an actual distance of 70 miles, given the scale $1 / 2$ inch $=20$ miles?

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Problem 23541

Calculate the total number of leaves that have fallen by the end of the $18^{\text{th}}$ day if they quadruple daily, starting from 1.

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Problem 23542

Model the city's population growth from 2020 ( $1,596,000$ with a $3.5\%$ annual increase) using the function $f(x)$ .

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Problem 23543

Find the slope-intercept form of the line through (1,3) and (0,-3).

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Problem 23544

What was the initial population of a California town modeled by $f(x)=16,612(1.024)^{x}$ on January 1, 2013?

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Problem 23545

Find the balance on a credit card after 9 months using $f(x)=500(1+0.13)^{x}$ . Round to the nearest cent.

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Problem 23546

A child is 20 inches long at birth. Use the function $f(x)=20+47 \log (x+2)$ to find when she reaches $60\%$ of her height.

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Problem 23547

Calculate the pH of a solution with $\left[\mathrm{H}^{+}\right]=2.9 \times 10^{-8}$ . Round to the nearest hundredth.

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Problem 23548

A psychologist models recall as $f(t)=92-22 \ln (t+1)$ for $1 \leq t \leq 12$ . What is $f(3)$ rounded to the nearest percent?

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Problem 23549

Find the pH of apple juice with a hydrogen ion concentration of $[\mathrm{H}^+]=0.00015$ . Round to the nearest hundredth.

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Problem 23550

Milk's price rises by $2\%$ yearly. If it’s \$2.75 in 2017, what will it cost in 2020?

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Problem 23551

Find the frequency of note F# which is 3 half steps below A3 (220 Hz) using $F(x)=F_{0}(1.059463)^{x}$ . Round to the nearest whole number.

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Problem 23552

Solve the inequality: $r+10 \leq -3(2r-3) + 6(r+3)$ .

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Problem 23553

Find the intensity $I$ of an earthquake with a magnitude of 4.7 using $R=\log \left(\frac{I}{1}\right)$ . Round to the nearest whole number.

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Problem 23554

To make 464 liters of Petrolyn oil with a ratio of 5 liters natural to 3 liters synthetic, how much synthetic oil is needed?

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Problem 23555

The equation for "3 less than the product of 4 and 5" is: $4 \times 5 - 3$ .

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Problem 23556

A company's net income was \ $200,000 in 2020 and grows by 10% yearly. When will it reach \$1,000,000? Use$ f(x)=200,000(1+0.1)^{x}$.

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Problem 23557

A child is 20 inches long at birth. Find the percentage of adult height at age 3 using $f(x)=20+47 \log (x+2)$ .

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Problem 23558

Find the earthquake magnitude using $R=\log \left(\frac{I}{1}\right)$ for $I=4 \times 10^{4}$ . Round to the nearest hundredth.

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Problem 23559

A pool has 15,600 gallons and loses $5\%$ of water daily. How much will remain in 11 days? Round to the nearest whole number.

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Problem 23560

Find the balance after 12 months using the exponential function $f(x)=500(1+0.096)^{x}$ . Round to the nearest cent.

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Problem 23561

If the credit card balance grows exponentially as $f(x)=800(1+0.122)^{x}$ , what is the balance after 39 months? Round to the nearest cent.

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Problem 23562

Luis cooks for 20+ people, with vegetarian meals at \$3 and meat meals at \$4.50. Budget is \$100, with at least 6 of each. Write the inequalities.

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Problem 23563

Find total cookbook sales on January 1, 2026, using $f(x)=18,838(1.044)^{x}$ , where $x$ is years since 2013.

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Problem 23564

A child is 20 inches at birth. Find the percent of adult height at age 15 using $f(x)=20+47 \log (x+2)$ .

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Problem 23565

Which expressions are equivalent: (A) $7+21v$ vs $2(5+3v)$ , (B) $7+21v$ vs $3(4+7v)$ , (C) $7+21v$ vs $7(1+3v)$ ?

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Problem 23566

Find the operation $\circ$ such that $-.64 \circ ? = 1.29$ . What is $?$

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Problem 23567

Find the coordinate of $P$ as the weighted average of points: $W = -7$ (weight 2), $X = -4$ (weight 1), $Y = 0$ (weight 3).

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Problem 23568

Let $x$ be hours worked in housecleaning and $y$ in sales. Write the inequalities: $x + y \leq 41$ and $5x + 8y \geq 254$ .

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Problem 23569

Which expressions are equal? (A) $17(3 m+4)$ vs $51 m+68$ , (B) $51 m+67$ , (C) $51 m-68$ , (D) $47 m+51$ .

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Problem 23570

Which two expressions are equal: (A) $\frac{32 p}{2}$ and $17 p$ , (B) $\frac{32 p}{2}$ and $18 p$ , (C) $\frac{32 p}{2}$ and $16 p$ , (D) $\frac{32 p}{2}$ and $14 p$ ?

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Problem 23571

Find coordinates of $P$ as the weighted average of $U(-8,-5)$ and $X(2,0)$ , with $U$ weighing twice as much as $X$ .

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Problem 23572

At 10:00 a.m. (t=0), bacteria grow as follows: 30, 90, 270, 810. Find a function $f(t)$ to model this growth.

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Problem 23573

Pilar buys pizzas at \$9 each and cookies at \$5 per pound, with a max budget of \$50. She needs at least 3 pizzas and 2 pounds of cookies. Find the inequalities and graph them.

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Problem 23574

Analyze the quadratic function $f(x)=-3 x^{2}-30 x-77$ . Does it have a minimum or maximum? Where does it occur, and what is the value?

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Problem 23575

Which two expressions are equivalent? (A) $\left(\frac{5}{25}\right)x$ and $\left(\frac{1}{3}\right)x$ (B) $\left(\frac{1}{5}\right)x$ (C) $\left(\frac{1}{4}\right)x$ (D) $\left(\frac{1}{6}\right)x$

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Problem 23576

Which expressions are equivalent: $\frac{64 k}{4}$ , $4 k$ , $14 k$ , $16 k$ , or $15 k$ ?

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Problem 23577

Solve the inequality: $18\left(q-\frac{3}{4}\right) \leq -2\left(q+\frac{7}{4}\right)$ .

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Problem 23578

Determine which option equals $575d - 100$ : (1) $25(22d - 4)$ , (2) $25(23d - 4)$ , (3) $25(23d + 4)$ , (4) $25(25d - 4)$ .

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Problem 23579

Simplify $(800+444 y) / 4$ and choose the correct equivalent expression from the options provided.

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Problem 23580

Simplify $5(19-8y)$ and find its equivalent expression from the options: (A) $95-35y$ , (B) $95+40y$ , $85-40y$ , $95-40y$ .

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Problem 23581

Simplify $3(26 p - 7 + 14 h)$ and find the equivalent expression from the options given.

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Problem 23582

Find $z$ in the equation $-z + 7 = 6$ . What is the value of $z$ ?

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Problem 23583

Find $b$ in the equation: $43 - \frac{b}{3} = 59$ .

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Problem 23584

Solve for $x$ in the equation: $2x + 5 = 11$ . What is the value of $x$ ?

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Problem 23585

Find the number of days when the cost of renting a truck from Company A ( $40d$ ) equals Company B ( $60 + 40d$ ). Show your work.

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Problem 23586

Find $b$ in the equation: $44 = -11b + 33$ .

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Problem 23587

Simplify $5(6 x+17 y-9 z)$ and find the equivalent expression from the options provided.

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Problem 23588

Which equations equal $4(2+10)$ ? Choose all that apply: (1) $6+46$ , (ii) $6+6c$ , (c) $8 \times 40$ , (11) $8+40$ , (1) $(4 \times 2)+(4 \times 16)$ , (1) $(4 \times 2) \times(4 \times 10)$ .

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Problem 23589

Express "One does not think hard" symbolically, given $s$ : "One thinks hard".

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Problem 23590

Solve for $v$ : $v^{2}+10 v+25=0$ . If multiple solutions, list them; if none, say "No solution." $v=$

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Problem 23591

Find $b$ in the equation: $-76 = -3b - 49$ .

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Problem 23592

Mara's golf ball traveled 492 feet, three times Lori's distance. How far did Lori's ball travel?

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Problem 23593

Solve for x: 4(2x - 4) - 5x + 4 = -30

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Problem 23594

5. Finn bought 12 movie tickets. Student tickets cost $\$ 4$ , and adult tickets cost $\$ 8$ . Finn spent a total of $\$ 60$ . Write and graph a system of equations to find the number of student and adult tickets Finn bought. Lesson 5-2 $\begin{array}{l} x+y=12 \\ 4 x+8 y=60 \end{array}$
6. What value of $m$ gives the system infinitely many solutions? Lesson 5-1 $\begin{array}{l} -x+4 y=32 \\ y=m x+8 \end{array}$
Types of Movie Tickets

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Problem 23595

The graph of $g(z)$ , shown below, is obtainad by transtorming the graph of $f(x)$ . $f(x)=-(x+1)^{2}+9$ a) In the space below, describe a sequence of transformations that would transform the graph of $y=f(x)$ into the graph of $y=g(x)$ . Your answers below wiv nor be auto-graded $\square$ b) In the space below, state the equation of $g(x)$ , both in terms ai $f(x)$ and in terms of $x$ . In terms of $f(x): g(x)=$ $\square$ in terms of $x g(x)=$ $\square$ c) A new function $h(x)$ is obtained by reflecting the groph of $g(x)$ (the green graph) about the line $y=x$ . Describe the transformation $\square$ d) Stote the domain ond range of $h(x)$ in interval notation $\square$ D. $\square$

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Problem 23596

Divide the polynomial $P=6 x^{3}+3 x+2$ by $D=3 x^{2}-1$ . Find the quotient $Q$ and remainder $R$ such that $\frac{P}{D}=Q+\frac{R}{D}$ $\begin{array}{l} Q(x)= \\ R(x)= \end{array}$

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Problem 23597

For $\log _{5} 14$ , (a) Estimate the value of the logarithm between two consecutive integers. For example, $\log _{2} 7$ is between 2 and 3 because $2^{2}<7<2^{3}$ . (b) Use the change-of-base formula and a calculator to approximate the logarithm to 4 decimal places. (c) Check the result by using the related exponential form.
Part: $0 / 3$
Part 1 of 3 (a) Estimate the value of the logarithm between two consecutive integers. $\square<\log _{5} 14<\square$

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Problem 23598

7 of 7
Determine which of the following infinite geometric series have a finite sum. ।. $4+5+\frac{25}{4}+\ldots$ II. $-7+\frac{14}{3}-\frac{28}{9}+\ldots$ III. $\frac{1}{2}-1+2+\ldots$ IV. $4+\frac{8}{5}+\frac{16}{25}+\ldots$ I, III only II, IV only III only I, II, IV only

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Problem 23599

12-6
1. What is the value of $a \div a^{-4}$ when $a=2$ $2 \div 2^{-4}=2$
2. For $x=1$ and $y=-1$ , give the value of the expression $15 x^{2} y^{-3}+18 y x^{-1}+27 x y^{4}$
3. Find the integer k such that $3^{3}+3^{3}+3^{3}=243 \cdot 3^{\mathrm{k}}$ (Hint: Express 243 as a power of 3 .)
4. Let $a$ and $b$ be nonzero numbers. Simplify $\left(6 a^{2} b\right)^{2} \div\left(3 a^{2} b^{3}\right)$ . Express your answer as a number times a power of a times a power of $b$ .
5. $4-8\left((-2)^{2}-4(-3)\right)$
6. $5 \cdot 2^{5}-(2 \cdot 3)^{2}$

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Problem 23600

Rewrite the following fractions as partial fractions using the given formats. (a) $\frac{x-1}{x^{2}+3 x-28}=\frac{A_{1}}{F_{1}(x)}+\frac{A_{2}}{F_{2}(x)}$ where $A_{1}$ and $A_{2}$ represent constants. $\begin{array}{l} F_{1}(x)= \\ F_{2}(x)= \end{array}$

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Algebra

Problem 23501

Simplify the expression (x−1/5y1/6)120\left(\frac{x^{-1 / 5}}{y^{1 / 6}}\right)^{120}(y1/6x−1/5​)120 using exponent properties.

Problem 23502

Find the inverse of the one-to-one function f(x)=x+53f(x)=\sqrt[3]{x+5}f(x)=3x+5​.

Problem 23503

Kane runs 3 miles and increases by 14\frac{1}{4}41​ mile each week. Write an expression for distance after www weeks.

Problem 23504

Find the composite function for f(x)=4x2+5x+6f(x)=4 x^{2}+5 x+6f(x)=4x2+5x+6 and g(x)=5x−3g(x)=5 x-3g(x)=5x−3: (g∘f)(x)(g \circ f)(x)(g∘f)(x).

Problem 23505

Simplify the radical expression using Property 1: sqrt⁡(x)\operatorname{sqrt}(x)sqrt(x) for x\sqrt{x}x​ and root⁡(x)(y)\operatorname{root}(x)(y)root(x)(y) for yx\sqrt[x]{y}xy​. Find 625a6b93.\sqrt[3]{625 a^{6} b^{9}}.3625a6b9​.

Problem 23506

Find the absolute value of -7 and 3. What is ∣−7∣|-7|∣−7∣ and ∣3∣|3|∣3∣?

Problem 23507

Solve the equation: ∣13x−8∣=4 \left|\frac{1}{3} x-8\right|=4 ∣∣​31​x−8∣∣​=4

Problem 23508

Find the composite function for f(x)=2x−6f(x)=\frac{2}{x-6}f(x)=x−62​ and g(x)=32xg(x)=\frac{3}{2 x}g(x)=2x3​. Compute (f∘g)(x)(f \circ g)(x)(f∘g)(x).

Problem 23509

Is it true that −7<∣3∣-7 < |3|−7<∣3∣?

Problem 23510

Determine the domain of the function f(x)=xx−8f(x) = \frac{x}{\sqrt{x-8}}f(x)=x−8​x​.

Problem 23511

Combine the terms: sqrt(32) - sqrt(32) + sqrt(8) = ?

Problem 23512

Solve for xxx in the equation: 2x+4−32x=13(x+5)2x + 4 - \frac{3}{2}x = \frac{1}{3}(x + 5)2x+4−23​x=31​(x+5).

Problem 23513

Multiply: (sqrt(2)+sqrt(5))(sqrt(2)-sqrt(5))=

Problem 23514

Solve for yyy in the equation: y+b=20y + b = 20y+b=20.

Problem 23515

Rationalize the denominator: 8sqrt(x)−sqrt(y)=\frac{8}{sqrt(x)-sqrt(y)}=sqrt(x)−sqrt(y)8​=

Problem 23516

Find AAA from the equation W=A4W=\frac{A}{4}W=4A​.

Problem 23517

Solve for m in the equation: mg = W.

Problem 23518

Evaluate y2+6y+9y^2 + 6y + 9y2+6y+9 for y=−4y = -4y=−4.

Problem 23519

Find the mass in grams of a liquid with density 1.15 g/mL1.15 \mathrm{~g} / \mathrm{mL}1.15 g/mL to fill a 50.00 - mL\mathrm{mL}mL container. Use algebraic manipulation.

Problem 23520

Graph the function f(x)=x3f(x)=\sqrt[3]{x}f(x)=3x​.

Problem 23521

How long in minutes does a snail moving at 1.331.3^{3}1.33 ft/min take to cross a 1.3121.3^{12}1.312 ft wide road? Use exponents.

Problem 23522

Solve for xxx in the equation 8x−1=9x−7\sqrt{8 x-1}=\sqrt{9 x-7}8x−1​=9x−7​.

Problem 23523

Solve for xxx in the equation: 40−6x=2x\sqrt{40 - 6x} = 2x40−6x​=2x. What are the real solutions?

Problem 23524

Solve the equation for real xxx: 8x+4+2=x\sqrt{8x + 4} + 2 = x8x+4​+2=x. What are the solutions?

Problem 23525

Find functions f(x)f(x)f(x) and g(x)g(x)g(x) such that h(x)=(f∘g)(x)h(x)=(f \circ g)(x)h(x)=(f∘g)(x) with h(x)=(2−3x)2h(x)=(2-3 x)^{2}h(x)=(2−3x)2 and g(x)=2−3xg(x)=2-3 xg(x)=2−3x.

Problem 23526

Solve for xxx in the equation: 1+x+1−x=2\sqrt{1+x}+\sqrt{1-x}=21+x​+1−x​=2. What are the real solutions?

Problem 23527

Solve for real xxx in the equation x4−10x2+21=0x^{4}-10 x^{2}+21=0x4−10x2+21=0. Enter answers as comma-separated values.

Problem 23528

Solve the equation x=x−2x4−3=0x=\sqrt{x}-2\sqrt[4]{x}-3=0x=x​−24x​−3=0 for all real solutions.

Problem 23529

Solve the equation x2−6x=0x^{2}-6x=0x2−6x=0.

Problem 23530

Find the value of the box: 21⋅□=721 \cdot \square=721⋅□=7.

Problem 23531

Calculate the energy in joules to ionize a hydrogen atom from the n=6n=6n=6 level, knowing ground-state ionization is 2.18×10−18 J2.18 \times 10^{-18} \mathrm{~J}2.18×10−18 J.

Problem 23532

Solve the equation x−4x4−5=0\sqrt{x}-4 \sqrt[4]{x}-5=0x​−44x​−5=0. What are the real solutions?

Problem 23533

Find real solutions for xxx using the Quadratic Formula for x2−0.014x−0.066=0x^{2}-0.014 x-0.066=0x2−0.014x−0.066=0.

Problem 23534

Find two consecutive even integers whose squares sum to 1060.

Problem 23535

Find the product and express it as a+bia + b ia+bi: (7−2i)(1+i)(7 - 2 i)(1 + i)(7−2i)(1+i).

Problem 23536

Evaluate the quotient and express it as a+bia + b ia+bi: 4−3i1−4i\frac{4 - 3 i}{1 - 4 i}1−4i4−3i​

Problem 23537

Determine if the graphs of f(x)=−xf(x)=-\sqrt{x}f(x)=−x​ and g(x)=−xg(x)=\sqrt{-x}g(x)=−x​ are identical.

Problem 23538

Find the wavelength of photons from hydrogen transitioning from n=4n=4n=4 to n=3n=3n=3 in nm\mathrm{nm}nm and identify the spectrum region: A. ultraviolet or B. X-ray.

Problem 23539

Evaluate the quotient and express it as aaa: 3−7i1−3i\frac{3-7 i}{1-3 i}1−3i3−7i​

Problem 23540

Simplify the expression $\left(\frac{x^{-1 / 5}}{y^{1 / 6}}\right)^{120}$ using exponent properties.

Find the inverse of the one-to-one function $f(x)=\sqrt[3]{x+5}$ .

Kane runs 3 miles and increases by $\frac{1}{4}$ mile each week. Write an expression for distance after $w$ weeks.

Find the composite function for $f(x)=4 x^{2}+5 x+6$ and $g(x)=5 x-3$ : $(g \circ f)(x)$ .

Simplify the radical expression using Property 1: $\operatorname{sqrt}(x)$ for $\sqrt{x}$ and $\operatorname{root}(x)(y)$ for $\sqrt[x]{y}$ . Find $\sqrt[3]{625 a^{6} b^{9}}.$

Find the absolute value of -7 and 3. What is $|-7|$ and $|3|$ ?

Solve the equation: $\left|\frac{1}{3} x-8\right|=4$

Find the composite function for $f(x)=\frac{2}{x-6}$ and $g(x)=\frac{3}{2 x}$ . Compute $(f \circ g)(x)$ .

Is it true that $-7 < |3|$ ?

Determine the domain of the function $f(x) = \frac{x}{\sqrt{x-8}}$ .

Solve for $x$ in the equation: $2x + 4 - \frac{3}{2}x = \frac{1}{3}(x + 5)$ .

Solve for $y$ in the equation: $y + b = 20$ .

Rationalize the denominator: $\frac{8}{sqrt(x)-sqrt(y)}=$

Find $A$ from the equation $W=\frac{A}{4}$ .

Evaluate $y^2 + 6y + 9$ for $y = -4$ .

Find the mass in grams of a liquid with density $1.15 \mathrm{~g} / \mathrm{mL}$ to fill a 50.00 - $\mathrm{mL}$ container. Use algebraic manipulation.

Graph the function $f(x)=\sqrt[3]{x}$ .

How long in minutes does a snail moving at $1.3^{3}$ ft/min take to cross a $1.3^{12}$ ft wide road? Use exponents.

Solve for $x$ in the equation $\sqrt{8 x-1}=\sqrt{9 x-7}$ .

Solve for $x$ in the equation: $\sqrt{40 - 6x} = 2x$ . What are the real solutions?

Solve the equation for real $x$ : $\sqrt{8x + 4} + 2 = x$ . What are the solutions?

Find functions $f(x)$ and $g(x)$ such that $h(x)=(f \circ g)(x)$ with $h(x)=(2-3 x)^{2}$ and $g(x)=2-3 x$ .

Solve for $x$ in the equation: $\sqrt{1+x}+\sqrt{1-x}=2$ . What are the real solutions?

Solve for real $x$ in the equation $x^{4}-10 x^{2}+21=0$ . Enter answers as comma-separated values.

Solve the equation $x=\sqrt{x}-2\sqrt[4]{x}-3=0$ for all real solutions.

Solve the equation $x^{2}-6x=0$ .

Find the value of the box: $21 \cdot \square=7$ .

Calculate the energy in joules to ionize a hydrogen atom from the $n=6$ level, knowing ground-state ionization is $2.18 \times 10^{-18} \mathrm{~J}$ .

Solve the equation $\sqrt{x}-4 \sqrt[4]{x}-5=0$ . What are the real solutions?

Find real solutions for $x$ using the Quadratic Formula for $x^{2}-0.014 x-0.066=0$ .

Find the product and express it as $a + b i$ : $(7 - 2 i)(1 + i)$ .

Evaluate the quotient and express it as $a + b i$ : $\frac{4 - 3 i}{1 - 4 i}$

Determine if the graphs of $f(x)=-\sqrt{x}$ and $g(x)=\sqrt{-x}$ are identical.

Find the wavelength of photons from hydrogen transitioning from $n=4$ to $n=3$ in $\mathrm{nm}$ and identify the spectrum region: A. ultraviolet or B. X-ray.

Evaluate the quotient and express it as $a$ : $\frac{3-7 i}{1-3 i}$

What is the map length for an actual distance of 70 miles, given the scale $1 / 2$ inch $=20$ miles?

Calculate the total number of leaves that have fallen by the end of the $18^{\text{th}}$ day if they quadruple daily, starting from 1.

Model the city's population growth from 2020 ( $1,596,000$ with a $3.5\%$ annual increase) using the function $f(x)$ .

What was the initial population of a California town modeled by $f(x)=16,612(1.024)^{x}$ on January 1, 2013?

Find the balance on a credit card after 9 months using $f(x)=500(1+0.13)^{x}$ . Round to the nearest cent.

A child is 20 inches long at birth. Use the function $f(x)=20+47 \log (x+2)$ to find when she reaches $60\%$ of her height.

Calculate the pH of a solution with $\left[\mathrm{H}^{+}\right]=2.9 \times 10^{-8}$ . Round to the nearest hundredth.

A psychologist models recall as $f(t)=92-22 \ln (t+1)$ for $1 \leq t \leq 12$ . What is $f(3)$ rounded to the nearest percent?

Find the pH of apple juice with a hydrogen ion concentration of $[\mathrm{H}^+]=0.00015$ . Round to the nearest hundredth.

Milk's price rises by $2\%$ yearly. If it’s \$2.75 in 2017, what will it cost in 2020?

Find the frequency of note F# which is 3 half steps below A3 (220 Hz) using $F(x)=F_{0}(1.059463)^{x}$ . Round to the nearest whole number.

Solve the inequality: $r+10 \leq -3(2r-3) + 6(r+3)$ .

Find the intensity $I$ of an earthquake with a magnitude of 4.7 using $R=\log \left(\frac{I}{1}\right)$ . Round to the nearest whole number.

The equation for "3 less than the product of 4 and 5" is: $4 \times 5 - 3$ .

A company's net income was \ $200,000 in 2020 and grows by 10% yearly. When will it reach \$1,000,000? Use$ f(x)=200,000(1+0.1)^{x}$.

A child is 20 inches long at birth. Find the percentage of adult height at age 3 using $f(x)=20+47 \log (x+2)$ .

Find the earthquake magnitude using $R=\log \left(\frac{I}{1}\right)$ for $I=4 \times 10^{4}$ . Round to the nearest hundredth.

A pool has 15,600 gallons and loses $5\%$ of water daily. How much will remain in 11 days? Round to the nearest whole number.

Find the balance after 12 months using the exponential function $f(x)=500(1+0.096)^{x}$ . Round to the nearest cent.

If the credit card balance grows exponentially as $f(x)=800(1+0.122)^{x}$ , what is the balance after 39 months? Round to the nearest cent.

Find total cookbook sales on January 1, 2026, using $f(x)=18,838(1.044)^{x}$ , where $x$ is years since 2013.

A child is 20 inches at birth. Find the percent of adult height at age 15 using $f(x)=20+47 \log (x+2)$ .

Which expressions are equivalent: (A) $7+21v$ vs $2(5+3v)$ , (B) $7+21v$ vs $3(4+7v)$ , (C) $7+21v$ vs $7(1+3v)$ ?

Find the operation $\circ$ such that $-.64 \circ ? = 1.29$ . What is $?$

Find the coordinate of $P$ as the weighted average of points: $W = -7$ (weight 2), $X = -4$ (weight 1), $Y = 0$ (weight 3).

Let $x$ be hours worked in housecleaning and $y$ in sales. Write the inequalities: $x + y \leq 41$ and $5x + 8y \geq 254$ .

Which expressions are equal? (A) $17(3 m+4)$ vs $51 m+68$ , (B) $51 m+67$ , (C) $51 m-68$ , (D) $47 m+51$ .

Which two expressions are equal: (A) $\frac{32 p}{2}$ and $17 p$ , (B) $\frac{32 p}{2}$ and $18 p$ , (C) $\frac{32 p}{2}$ and $16 p$ , (D) $\frac{32 p}{2}$ and $14 p$ ?

Find coordinates of $P$ as the weighted average of $U(-8,-5)$ and $X(2,0)$ , with $U$ weighing twice as much as $X$ .

At 10:00 a.m. (t=0), bacteria grow as follows: 30, 90, 270, 810. Find a function $f(t)$ to model this growth.

Analyze the quadratic function $f(x)=-3 x^{2}-30 x-77$ . Does it have a minimum or maximum? Where does it occur, and what is the value?