Math

Problem 2401

Find the sum of $2x^2 + 3x + 2$ and $3x^2 - 5x - 1$ .

See Solution

Problem 2402

Find the values of $-22+5$ , $-22-(-5)$ , $(-22)(-5)$ , and $-22 \div 5$ .

See Solution

Problem 2403

Deon aims to bike 310 miles in a month. He's biked 145 miles so far. With 4 days left, how many miles should he bike daily to reach his $310$ mile goal?

See Solution

Problem 2404

Determine if ordered pairs satisfy a system of two linear equations: $y = \frac{1}{3}x - 2, y = \frac{2}{6}x - \frac{12}{6}$ . Complete a table and find the number of solutions.

See Solution

Problem 2405

Convert $2 \frac{2}{3}$ feet to inches using $1 \mathrm{ft} = 12$ inches.

See Solution

Problem 2406

Solve the linear equation $612 + 25x = 912$ for the unknown variable $x$ .

See Solution

Problem 2407

Solve the linear equation $2x - 14 = 50$ for the value of $x$ .

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Problem 2408

(A) Find the exact cost of producing the 71st food processor, given $C(x)=1900+40x-0.2x^2$ . (B) Use the marginal cost to approximate the cost of producing the 71st food processor. (A) The exact cost of producing the 71st food processor is $\$2,662$ . (B) Using the marginal cost, the approximate cost of producing the 71st food processor is $\$2,660$ .

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Problem 2409

Graph a line with equation $f(x) = -0.25x + 4$ . Select two points on the line to create the graph.

See Solution

Problem 2410

Solve the equation $4y - 7 = 5x^2 - x + 2 + 3y$ for $x$ and $y$ .

See Solution

Problem 2411

Rearrange the steps to solve $5^{(6 x-9)}=125$ .

See Solution

Problem 2412

Find the value of $z$ that satisfies the equation $\frac{z+12}{-4}=0$ .

See Solution

Problem 2413

Solve for the value of $p$ given the equation $2(p+1)=16$ .

See Solution

Problem 2414

Solve the linear equation $\frac{2}{3}(x-7) = -2$ for the value of $x$ .

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Problem 2415

Find the change in $x$ and $y$ when $y$ varies at a constant rate of 4 with respect to $x$ , for the given ranges of $x$ .
a. If $x$ varies from $x=3.7$ to $x=8.8$ , then: i. The change in $x$ is $\Delta x=5.1$ ii. The corresponding change in $y$ is $\Delta y=20.4$
b. If $x$ varies from $x=2$ to $x=-7$ , then: i. The change in $x$ is $\Delta x=-9$ ii. The corresponding change in $y$ is $\Delta y=-36$

See Solution

Problem 2416

Sketch the function $f(x) = -x^3 - 3x^2$ and select the correct graph.

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Problem 2417

Bakery has a 13% off sale on bread. You buy 6 loaves. Let $\mathrm{b}$ be the original price. Expand $6(b-0.13b)$ . What do the terms represent?

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Problem 2418

Solve the linear equation $-5b - 12 = 18$ for the variable $b$ .

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Problem 2419

Draw and determine the properties of quadratic functions: - Opening - Symmetry - Vertex - Stretch
1. Determine the properties and draw the graphs of the following functions: a) $f(x)=\frac{1}{2} x^{2}+2 x$ b) $f(x)=x^{2}+x-2$ c) $f(x)=2 x^{2}-4 x+8$ d) $f(x)=\frac{1}{4} x^{2}-3 x$

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Problem 2420

Find the value of $2^{-5}$ .

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Problem 2421

Solve the linear equation $-\frac{x}{3}-2=0$ for the value of $x$ .

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Problem 2422

Find the values of $y$ for $x = 1, 2, 3$ when the function is $y = 3x + 4$ .

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Problem 2423

Solve for $\gamma$ and $y$ in the equation $4^{6 \gamma} = 8^{2 y + 4}$ .

See Solution

Problem 2424

Solve the absolute value equation $|\\frac{6 x+3}{3}|+4=8$ and express the solution set.

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Problem 2425

Solve for $x$ where $g(x) = -7x + 1 = -16$ , rounded to the nearest hundredth.

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Problem 2426

Solve $10x + y = -x^2 + 2$ for real solutions. Determine if there are 0, 1, or 2 real solutions.

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Problem 2427

Solve the equation $|2x - 1| = 18$ and find the solutions.

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Problem 2428

Solve the equation, eliminating any extraneous solutions. $\frac{x^{2}+5}{(x+5)}=\frac{30}{(x+5)}$ . The solutions are $x=-5,5$ .

See Solution

Problem 2429

Find the derivative of $y=\ln \left[x\left(x^{5}-2\right)^{10}\right]$ using logarithm properties.

See Solution

Problem 2430

Find the derivative of $y = (\ln x)^{\ln x}$ .

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Problem 2431

Find the common difference and recursive/explicit formulas for the sequence $12, 16, 20, 24, 28, \ldots$ .

See Solution

Problem 2432

Solve for the value of $p$ given the equation $\frac{r-p}{9}=S$ .

See Solution

Problem 2433

Find the standard form of $g(x) = (5x + 14)(4x + 8)$ .

See Solution

Problem 2434

Predict homework time from TV time using the linear equation $y=-0.76x+26.04$ for 23 students. (a) Predicted homework time for 12 hours of TV: $-0.76(12)+26.04=10.92$ hours. (b) Predicted homework time for 0 hours of TV: $-0.76(0)+26.04=26.04$ hours. (c) Predicted decrease in homework time for 1 hour increase in TV time: $-0.76$ hours.

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Problem 2435

Express $w$ as the sum of 158 and 128.

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Problem 2436

Find the square root of $(d-3)^{2}+25=0$ to get the values of $d$ .

See Solution

Problem 2437

Find the axis of symmetry of $f(x)=x^2+5$ and the graph of $y=-36-3x+3x^2$ .

See Solution

Problem 2438

Find the midpoint of the class interval 95-99.

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Problem 2439

Determine the type of equation: $15+7x=-13$ . Is it division-addition, division-subtraction, multiplication-addition, or multiplication-subtraction?

See Solution

Problem 2440

Solve inequality $4|y-2|-3>17$ . If all real numbers are solutions, click "All reals". If no solution, click "No solution".

See Solution

Problem 2441

Solve for $x$ in the equation $10=\frac{4}{3}(8x+6)$ .

See Solution

Problem 2442

Simplify the fraction $\frac{3}{12}$ .

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Problem 2443

A running back carried the ball for yardages $4, -3, 2, -1, 5, -2, -2$ . Find his total yards and average yards per carry.
The total yards for the running back was $3$ . His average yards per carry was $\frac{3}{7}$ .

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Problem 2444

Solve for $x$ in the equation $\frac{|x|}{6}=4$ . Write both solutions as equations.

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Problem 2445

Find and simplify the expressions for $f(x+h)$ , $f(x+h) - f(x)$ , and $\frac{f(x+h) - f(x)}{h}$ where $f(x) = 3x^{2} - 7x + 6$ .

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Problem 2446

Folsom Dam holds 1 million acre-feet of water. 1 acre-foot = $326,000$ gallons. Find the total gallons in the reservoir, expressed in scientific notation. Also write the direct variation equation using the given point.
$1 \text{ million acre-feet} \times 326,000 \text{ gallons/acre-foot} = 3.26 \times 10^{11} \text{ gallons}$
The direct variation equation is $y = kx$ , where $k = 326,000$ gallons/acre-foot and the given point is $(1 \text{ million}, 3.26 \times 10^{11} \text{ gallons})$ .

See Solution

Problem 2447

Find the inverse of the quadratic function $f(x) = x^2 + 6x + 15$ by completing the square.

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Problem 2448

Determine the units for the operation $5 \mathrm{~m} \cdot 2 \mathrm{kg}$ . If the units cancel out, choose "No Unit". If the operation is not valid, choose "Not Valid".

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Problem 2449

19. (1 point) For the equation $2x + 3 = 13$ , which operation should you undo first?
20. (2 points) Solve the equation $y - 17 = 82$ . (SHOW YOUR WORK)

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Problem 2450

Find $f'(1)$ if the normal line to $f$ at $(1,2)$ has equation $x+5y=11$ .

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Problem 2451

Compute the values of a periodic function $g(x)=\frac{x+1}{x^{2}-x+4}$ with period 7 on the interval $[-2,5)$ . Find all roots of $g(x)$ .

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Problem 2452

Suppose $x$ has a binomial distribution with $n=200$ and $p=.5$ . Use normal approximation to calculate:
1. $P(x=80)$
2. $P(x \leq 95)$
3. $P(x<65)$
4. $P(x \geq 100)$
5. $P(x>100)$ Where $\mu=\$n p\$ and$ \sigma=\$\sqrt{n p (1-p)}\$.

See Solution

Problem 2453

Find all values of $x$ that solve the equation $2x^2 - 13x + 36 = 15$ .

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Problem 2454

Solve for $x$ : $x - 12 = 52$ . $x = 64$ .

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Problem 2455

Factor the expression $z^{4} - 16$ . If the expression is prime, enter PRIME.

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Problem 2456

Simplify the inequality $x-2+6 x \neq 6+8 x$ and solve for $x$ .

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Problem 2457

Solve for $u$ in the equation $5(u+3)=8u+24$ . Simplify the solution.

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Problem 2458

Taylor uses Intermediate Value Theorem to solve $x^3 - 3x^2 - 9 = K$ over $[3, 9]$ . What is the possible value of $K$ ?

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Problem 2459

Calculate $e^{2 \ln 3} - 3$ and provide the numerical result.

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Problem 2460

A patient weighing 195 lbs requires 279 mg of medicine. Find the amount of medicine required for a patient weighing 130 lbs.

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Problem 2461

Find the excluded numbers from the domains of $f(x)=\sqrt{x}$ and $g(x)=\sqrt{x-2}$ by writing inequalities.

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Problem 2462

Find the two values of $x$ that satisfy the quadratic equation $5.15 x^{2} + 2.03 x - 1.69 = 0$ .

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Problem 2463

Solve for the variable in each equation. Write final solution as an equation.
1. $-8t + 4 = -60$
2. $3 = 6 - 3z$
3. $\frac{6}{5}d + 1 = -11$
4. $-\frac{1}{6}x - 4 = -1$

See Solution

Problem 2464

Write an equation to solve for $y$ in terms of $x$ given that $2y = 5x$ .

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Problem 2465

Find the derivative of $f(x)=\frac{6 x}{(2-4 x)^{4}}$ .

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Problem 2466

Find the value of $y$ in the linear equation $2x + 3y = 12$ .

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Problem 2467

Solve the equation $e^{-\ln (-x)} = 1$ . Write the numeric solution.

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Problem 2468

Find the inverse function $f^{-1}(x)$ for the rational function $f(x) = \frac{7-5x}{5x+2}$ .

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Problem 2469

Solve the linear equation $-\frac{2}{3}(15 x+3)=-3 x-9$ for the unknown variable $x$ .

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Problem 2470

Find the value of $y$ given $y \leq -75$ . Options: A) $y=75$ , B) $y=-74$ , C) $y>-75$ , D) $y=-75$ .

See Solution

Problem 2471

Find the value of $\left(10^{5}\right)^{6}$ . Options: $10^{30}$ , $10^{11}$ , $10^{3}$ .

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Problem 2472

Find the number of lions at the zoo given that there are 78 penguins and the ratio of penguins to lions is 13: $x$ .

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Problem 2473

Solve for the value of $y$ given the equation $y+1.6=3.52$ .

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Problem 2474

Solve for the value of $w$ in the equation $w + 7 = 5$ .

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Problem 2475

Find the equation that is not true: A. $-4+(-3)=-7$ B. $-8(2)=-16$ C. $3-(-2)=5$ D. $-12 /(-3)=-4$

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Problem 2476

Find derivatives of $s=T x^{2}+7 x G+T^{2}$ with respect to $x$ , $G$ , and $T$ .

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Problem 2477

Find the values of $x$ and $y$ that satisfy the system of equations $x=7y$ and $y^{3}=x$ with $y \geq 0$ .

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Problem 2478

Find all numbers $x$ that are 9 units away from 11, expressed using absolute value.

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Problem 2479

Jessica wants to run a mile faster than 8.5 minutes. Which inequality model represents this? $m < 8.5$

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Problem 2480

Find all boundary points and solve the rational inequality $\frac{x+7}{2x-3} > 1$ . Express the solution using interval notation.

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Problem 2481

Find the value of $5v$ when $v=3$ .

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Problem 2482

The velocity needed to remove a foreign object from a 26-mm radius windpipe is $V(r) = k(26r^2 - r^3)$ , where $0 \leq r \leq 26$ . The object that needs maximum velocity to remove has a radius of $13$ mm.

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Problem 2483

Can $-4 x(-x-3)$ ever be negative? Choose the best: No, $4 x^{2}$ and $12 x$ are positive; Yes, $4 x^{2}+12 x$ is negative when $x$ is between -3 and 0; No, both factors are negative, so the product must be positive.

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Problem 2484

Solve the linear equation $-\frac{4}{5} x + 14 = 86$ for the value of $x$ .

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Problem 2485

The newspaper has $\frac{40}{0.08}$ readers.

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Problem 2486

Multiply $2 x^{2} + 6 x - 8$ and $x + 3$ , then express the product in standard form.

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Problem 2487

Write and solve an inequality for the sum of 2 consecutive integers greater than 73. Solve the inequality and find the pair with the least sum.
$\text{Let } x \text{ be the first integer and } x+1 \text{ be the second integer.}$ $x + (x+1) > 73$ $2x + 1 > 73$ $2x > 72$ $x > 36$ The pair of integers with the least sum is 37 and 38.

See Solution

Problem 2488

Find the value of $5 \times p$ when $p=2$ .

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Problem 2489

Find the values of $x$ that make $9x(x+8) = 0$ .

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Problem 2490

Étudier la fonction $g(x)=1+\frac{\ln x}{x}$ définie sur $\left]0;+\infty\right[$ . Résoudre $g(x)=0$ et déterminer le signe de $g$ . Étudier la famille de fonctions $h_n(x)=x^2-n+n\ln x$ avec $n\in\mathbb{N}^*$ , trouver leurs zéros et leur signe. Étudier la famille de fonctions $f_n(x)=x-n-\frac{n\ln x}{x}$ , leurs asymptotes, variations et minimum. Calculer une primitive de $f_n$ .

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Problem 2491

Find the number of terms in the polynomial $-7r$ .

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Problem 2492

Solve the differential equation $\frac{dy}{dx} = \frac{1}{5} \sqrt{y} \cos^2 \sqrt{y}$ .

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Problem 2493

Solve for the absolute value of $h$ when $9-|h|=9$ .

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Problem 2494

Find the smallest inside length in meters of a cubical steel tank that holds 280 L of water, rounded to the nearest 0.01 m.

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Problem 2495

Express $f(x)+g(x)$ as a simplified rational function. Given $f(x)=\frac{6}{x-7}, g(x)=\frac{5}{x+6}$ , find $f(x)+g(x)$ .

See Solution

Problem 2496

Find $g(a+1)$ when $g(x) = \frac{1}{2} x + 5$ .

See Solution

Problem 2497

Solve the linear equation $3x - 5 = 16$ .

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Problem 2498

Solve the inequality $\frac{2 x+10}{x+3} \geq 1$ and find the solution set.

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Problem 2499

Find the value of $d$ given the equation $d-47=231$ .

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Problem 2500

Linda sold $t$ -shirts at a festival, earning $\$ 65$ after paying $\$ 10$ for her booth. She earned $\$ 5$ per $t$ -shirt. Write an equation to find the number of $t$ -shirts she sold.

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Math

Problem 2401

Find the sum of 2x2+3x+22x^2 + 3x + 22x2+3x+2 and 3x2−5x−13x^2 - 5x - 13x2−5x−1.

Problem 2402

Find the values of −22+5-22+5−22+5, −22−(−5)-22-(-5)−22−(−5), (−22)(−5)(-22)(-5)(−22)(−5), and −22÷5-22 \div 5−22÷5.

Problem 2403

Deon aims to bike 310 miles in a month. He's biked 145 miles so far. With 4 days left, how many miles should he bike daily to reach his 310310310 mile goal?

Problem 2404

Determine if ordered pairs satisfy a system of two linear equations: y=13x−2,y=26x−126y = \frac{1}{3}x - 2, y = \frac{2}{6}x - \frac{12}{6}y=31​x−2,y=62​x−612​. Complete a table and find the number of solutions.

Problem 2405

Convert 2232 \frac{2}{3}232​ feet to inches using 1ft=121 \mathrm{ft} = 121ft=12 inches.

Problem 2406

Solve the linear equation 612+25x=912612 + 25x = 912612+25x=912 for the unknown variable xxx.

Problem 2407

Solve the linear equation 2x−14=502x - 14 = 502x−14=50 for the value of xxx.

Problem 2408

Problem 2409

Graph a line with equation f(x)=−0.25x+4f(x) = -0.25x + 4f(x)=−0.25x+4. Select two points on the line to create the graph.

Problem 2410

Solve the equation 4y−7=5x2−x+2+3y4y - 7 = 5x^2 - x + 2 + 3y4y−7=5x2−x+2+3y for xxx and yyy.

Problem 2411

Rearrange the steps to solve 5(6x−9)=1255^{(6 x-9)}=1255(6x−9)=125.

Problem 2412

Find the value of zzz that satisfies the equation z+12−4=0\frac{z+12}{-4}=0−4z+12​=0.

Problem 2413

Solve for the value of ppp given the equation 2(p+1)=162(p+1)=162(p+1)=16.

Problem 2414

Solve the linear equation 23(x−7)=−2\frac{2}{3}(x-7) = -232​(x−7)=−2 for the value of xxx.

Problem 2415

Problem 2416

Sketch the function f(x)=−x3−3x2f(x) = -x^3 - 3x^2f(x)=−x3−3x2 and select the correct graph.

Problem 2417

Bakery has a 13% off sale on bread. You buy 6 loaves. Let b\mathrm{b}b be the original price. Expand 6(b−0.13b)6(b-0.13b)6(b−0.13b). What do the terms represent?

Problem 2418

Solve the linear equation −5b−12=18-5b - 12 = 18−5b−12=18 for the variable bbb.

Problem 2419

Problem 2420

Find the value of 2−52^{-5}2−5.

Problem 2421

Solve the linear equation −x3−2=0-\frac{x}{3}-2=0−3x​−2=0 for the value of xxx.

Problem 2422

Find the values of yyy for x=1,2,3x = 1, 2, 3x=1,2,3 when the function is y=3x+4y = 3x + 4y=3x+4.

Problem 2423

Solve for γ\gammaγ and yyy in the equation 46γ=82y+44^{6 \gamma} = 8^{2 y + 4}46γ=82y+4.

Problem 2424

Solve the absolute value equation ∣frac6x+33∣+4=8|\\frac{6 x+3}{3}|+4=8∣frac6x+33∣+4=8 and express the solution set.

Problem 2425

Solve for xxx where g(x)=−7x+1=−16g(x) = -7x + 1 = -16g(x)=−7x+1=−16, rounded to the nearest hundredth.

Problem 2426

Solve 10x+y=−x2+210x + y = -x^2 + 210x+y=−x2+2 for real solutions. Determine if there are 0, 1, or 2 real solutions.

Problem 2427

Solve the equation ∣2x−1∣=18|2x - 1| = 18∣2x−1∣=18 and find the solutions.

Problem 2428

Solve the equation, eliminating any extraneous solutions. x2+5(x+5)=30(x+5)\frac{x^{2}+5}{(x+5)}=\frac{30}{(x+5)}(x+5)x2+5​=(x+5)30​. The solutions are x=−5,5x=-5,5x=−5,5.

Problem 2429

Find the derivative of y=ln⁡[x(x5−2)10]y=\ln \left[x\left(x^{5}-2\right)^{10}\right]y=ln[x(x5−2)10] using logarithm properties.

Problem 2430

Find the derivative of y=(ln⁡x)ln⁡xy = (\ln x)^{\ln x}y=(lnx)lnx.

Problem 2431

Find the common difference and recursive/explicit formulas for the sequence 12,16,20,24,28,…12, 16, 20, 24, 28, \ldots12,16,20,24,28,….

Problem 2432

Solve for the value of ppp given the equation r−p9=S\frac{r-p}{9}=S9r−p​=S.

Problem 2433

Find the standard form of g(x)=(5x+14)(4x+8)g(x) = (5x + 14)(4x + 8)g(x)=(5x+14)(4x+8).

Problem 2434

Problem 2435

Express www as the sum of 158 and 128.

Problem 2436

Find the square root of (d−3)2+25=0(d-3)^{2}+25=0(d−3)2+25=0 to get the values of ddd.

Problem 2437

Find the axis of symmetry of f(x)=x2+5f(x)=x^2+5f(x)=x2+5 and the graph of y=−36−3x+3x2y=-36-3x+3x^2y=−36−3x+3x2.

Problem 2438

Find the midpoint of the class interval 95-99.

Problem 2439

Determine the type of equation: 15+7x=−1315+7x=-1315+7x=−13. Is it division-addition, division-subtraction, multiplication-addition, or multiplication-subtraction?

Problem 2440

Solve inequality 4∣y−2∣−3>174|y-2|-3>174∣y−2∣−3>17. If all real numbers are solutions, click "All reals". If no solution, click "No solution".

Problem 2441

Solve for xxx in the equation 10=43(8x+6)10=\frac{4}{3}(8x+6)10=34​(8x+6).

Problem 2442

Find the sum of $2x^2 + 3x + 2$ and $3x^2 - 5x - 1$ .

Find the values of $-22+5$ , $-22-(-5)$ , $(-22)(-5)$ , and $-22 \div 5$ .

Deon aims to bike 310 miles in a month. He's biked 145 miles so far. With 4 days left, how many miles should he bike daily to reach his $310$ mile goal?

Determine if ordered pairs satisfy a system of two linear equations: $y = \frac{1}{3}x - 2, y = \frac{2}{6}x - \frac{12}{6}$ . Complete a table and find the number of solutions.

Convert $2 \frac{2}{3}$ feet to inches using $1 \mathrm{ft} = 12$ inches.

Solve the linear equation $612 + 25x = 912$ for the unknown variable $x$ .

Solve the linear equation $2x - 14 = 50$ for the value of $x$ .

Graph a line with equation $f(x) = -0.25x + 4$ . Select two points on the line to create the graph.

Solve the equation $4y - 7 = 5x^2 - x + 2 + 3y$ for $x$ and $y$ .

Rearrange the steps to solve $5^{(6 x-9)}=125$ .

Find the value of $z$ that satisfies the equation $\frac{z+12}{-4}=0$ .

Solve for the value of $p$ given the equation $2(p+1)=16$ .

Solve the linear equation $\frac{2}{3}(x-7) = -2$ for the value of $x$ .

Sketch the function $f(x) = -x^3 - 3x^2$ and select the correct graph.

Bakery has a 13% off sale on bread. You buy 6 loaves. Let $\mathrm{b}$ be the original price. Expand $6(b-0.13b)$ . What do the terms represent?

Solve the linear equation $-5b - 12 = 18$ for the variable $b$ .

Find the value of $2^{-5}$ .

Solve the linear equation $-\frac{x}{3}-2=0$ for the value of $x$ .

Find the values of $y$ for $x = 1, 2, 3$ when the function is $y = 3x + 4$ .

Solve for $\gamma$ and $y$ in the equation $4^{6 \gamma} = 8^{2 y + 4}$ .

Solve the absolute value equation $|\\frac{6 x+3}{3}|+4=8$ and express the solution set.

Solve for $x$ where $g(x) = -7x + 1 = -16$ , rounded to the nearest hundredth.

Solve $10x + y = -x^2 + 2$ for real solutions. Determine if there are 0, 1, or 2 real solutions.

Solve the equation $|2x - 1| = 18$ and find the solutions.

Solve the equation, eliminating any extraneous solutions. $\frac{x^{2}+5}{(x+5)}=\frac{30}{(x+5)}$ . The solutions are $x=-5,5$ .

Find the derivative of $y=\ln \left[x\left(x^{5}-2\right)^{10}\right]$ using logarithm properties.

Find the derivative of $y = (\ln x)^{\ln x}$ .

Find the common difference and recursive/explicit formulas for the sequence $12, 16, 20, 24, 28, \ldots$ .

Solve for the value of $p$ given the equation $\frac{r-p}{9}=S$ .

Find the standard form of $g(x) = (5x + 14)(4x + 8)$ .

Express $w$ as the sum of 158 and 128.

Find the square root of $(d-3)^{2}+25=0$ to get the values of $d$ .

Find the axis of symmetry of $f(x)=x^2+5$ and the graph of $y=-36-3x+3x^2$ .

Determine the type of equation: $15+7x=-13$ . Is it division-addition, division-subtraction, multiplication-addition, or multiplication-subtraction?

Solve inequality $4|y-2|-3>17$ . If all real numbers are solutions, click "All reals". If no solution, click "No solution".

Solve for $x$ in the equation $10=\frac{4}{3}(8x+6)$ .

Simplify the fraction $\frac{3}{12}$ .

A running back carried the ball for yardages $4, -3, 2, -1, 5, -2, -2$ . Find his total yards and average yards per carry.
The total yards for the running back was $3$ . His average yards per carry was $\frac{3}{7}$ .

Solve for $x$ in the equation $\frac{|x|}{6}=4$ . Write both solutions as equations.

Find and simplify the expressions for $f(x+h)$ , $f(x+h) - f(x)$ , and $\frac{f(x+h) - f(x)}{h}$ where $f(x) = 3x^{2} - 7x + 6$ .

Find the inverse of the quadratic function $f(x) = x^2 + 6x + 15$ by completing the square.

Determine the units for the operation $5 \mathrm{~m} \cdot 2 \mathrm{kg}$ . If the units cancel out, choose "No Unit". If the operation is not valid, choose "Not Valid".

19. (1 point) For the equation $2x + 3 = 13$ , which operation should you undo first?
20. (2 points) Solve the equation $y - 17 = 82$ . (SHOW YOUR WORK)

Find $f'(1)$ if the normal line to $f$ at $(1,2)$ has equation $x+5y=11$ .

Compute the values of a periodic function $g(x)=\frac{x+1}{x^{2}-x+4}$ with period 7 on the interval $[-2,5)$ . Find all roots of $g(x)$ .

Find all values of $x$ that solve the equation $2x^2 - 13x + 36 = 15$ .

Solve for $x$ : $x - 12 = 52$ . $x = 64$ .

Factor the expression $z^{4} - 16$ . If the expression is prime, enter PRIME.

Simplify the inequality $x-2+6 x \neq 6+8 x$ and solve for $x$ .

Solve for $u$ in the equation $5(u+3)=8u+24$ . Simplify the solution.

Taylor uses Intermediate Value Theorem to solve $x^3 - 3x^2 - 9 = K$ over $[3, 9]$ . What is the possible value of $K$ ?

Calculate $e^{2 \ln 3} - 3$ and provide the numerical result.

Find the excluded numbers from the domains of $f(x)=\sqrt{x}$ and $g(x)=\sqrt{x-2}$ by writing inequalities.

Find the two values of $x$ that satisfy the quadratic equation $5.15 x^{2} + 2.03 x - 1.69 = 0$ .

Solve for the variable in each equation. Write final solution as an equation.
1. $-8t + 4 = -60$
2. $3 = 6 - 3z$
3. $\frac{6}{5}d + 1 = -11$
4. $-\frac{1}{6}x - 4 = -1$

Write an equation to solve for $y$ in terms of $x$ given that $2y = 5x$ .

Find the derivative of $f(x)=\frac{6 x}{(2-4 x)^{4}}$ .

Find the value of $y$ in the linear equation $2x + 3y = 12$ .

Solve the equation $e^{-\ln (-x)} = 1$ . Write the numeric solution.

Find the inverse function $f^{-1}(x)$ for the rational function $f(x) = \frac{7-5x}{5x+2}$ .

Solve the linear equation $-\frac{2}{3}(15 x+3)=-3 x-9$ for the unknown variable $x$ .

Find the value of $y$ given $y \leq -75$ . Options: A) $y=75$ , B) $y=-74$ , C) $y>-75$ , D) $y=-75$ .

Find the value of $\left(10^{5}\right)^{6}$ . Options: $10^{30}$ , $10^{11}$ , $10^{3}$ .

Find the number of lions at the zoo given that there are 78 penguins and the ratio of penguins to lions is 13: $x$ .

Solve for the value of $y$ given the equation $y+1.6=3.52$ .

Solve for the value of $w$ in the equation $w + 7 = 5$ .