Numbers & Operations

Problem 2401

Spin two game board spinners, one with $1,2,3$ and one with $5,6,7,8$ . The first spinner's digit is the tens, the second's is the ones. Construct a tree diagram to show all possible prize amounts.

See Solution

Problem 2402

Find the exact solution of the equation $12 \tan ^{-1} \mathrm{x}=4 \pi$ . The solution set is $\{\pm \frac{\pi}{3}\}$ .

See Solution

Problem 2403

Solve the linear equation $2(3x+8) = 70$ for the unknown variable $x$ .

See Solution

Problem 2404

Determine if the events "the person is female" and "the person prefers classic rock" are independent. Justify your answer based on the provided $2 \times 4$ contingency table.

See Solution

Problem 2405

Find the exact value of $\sec^{-1}(-\sqrt{2})$ . Choose A and enter the simplified expression, or B if no solution exists.

See Solution

Problem 2406

A $34\mathrm{ft}$ ladder leans against a building at an $85^{\circ}$ angle. Find the ladder's height on the building in $\mathrm{ft}$ .

See Solution

Problem 2407

Determine the number of zeros for the quadratic equation $0=3 x^{2}-7 x+4$ using the discriminant.

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Problem 2408

8. Convert equation $y=3(x+2)(x-3)$ to standard form. (0.5 Points)
9. Convert equation $y=3x^2-9x-30$ to intercept form. (0.5 Points)
10. Another name for intercept form of a quadratic equation is Factored form. (0.5 Points)

See Solution

Problem 2409

Solve the equation $-5 m(x)=-3 \sqrt{x+4}+5$ for $m(x)$ .

See Solution

Problem 2410

Solve the equation $x^{2}-4=0$ by graphing the associated parabola. Use the graph to give the solution(s).

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Problem 2411

a) The nursing home's annual profit is approximately $P(18, 70, 350000, 10) = \$ 2,289,526$
b) The partial derivatives of $P$ are: $\frac{\partial P}{\partial w} = -0.487294w^{-1.647}r^{1.097}s^{0.867}t^{2.461}$

See Solution

Problem 2412

Evaluate the factorial expression $\frac{2! \, 5!}{6! \, 3!}$ and simplify the result.

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Problem 2413

Determine the vertical intercept, zeros, vertical asymptotes, and horizontal asymptote of the function $f(x)=\frac{x^{2}+6}{(6 x-11)(x+5)}$ .
a. $f(0)=\frac{6}{-55}$ b. $x=\frac{11}{6}, -5$ c. $x=\frac{11}{6}, -5$ d. $y=0$

See Solution

Problem 2414

Solve for $x$ when angles in a linear pair sum to $180^{\circ}$ . $12x = 180$ .

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Problem 2415

Find the limit, continuity, and type of discontinuity of the piecewise function f(x) = \\begin{cases} 2x+1, & x>-1 \\\\ x^2+1, & x \\leq-1 \\end{cases} at $x=a$ .

See Solution

Problem 2416

Evaluate $7+9(x-6)^{3}$ for $x=8$ . When $x=8$ , the expression simplifies to $\square$ .

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Problem 2417

Evaluate and simplify the expression $\frac{7 ! 5 !}{4 ! 6 !}$ .

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Problem 2418

Determine if the equation $x^{2} + y^{2} = 100$ is symmetric with respect to the $y$ -axis, $x$ -axis, or origin.

See Solution

Problem 2419

Maximize $P=40x+50y$ subject to $2x+y\leq18$ , $x+y\leq10$ , $x+2y\leq16$ , and $x,y\geq0$ . What is the maximum value of $P$ ?

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Problem 2420

Evaluate the expressions: $-(7)^{2}$ and $-(-2)^{3}$ .

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Problem 2421

Trova l'equazione di una parabola con asse di simmetria sull'asse $y$ , vertice in $0(0 ; 0)$ e passante per $A(2 ; 1)$ .

See Solution

Problem 2422

Solve $10^{2x} - 11 \cdot 10^x + 24 = 0$ . Solve $e^{4x} + 4e^{2x} = 45$ .

See Solution

Problem 2423

A. $(\mathrm{f}-\mathrm{g})(12)=\sqrt{12-3}-12^{2}+12$

See Solution

Problem 2424

Solve for $x$ in the equations $8^{x}=4$ and $16^{x}=8$ .

See Solution

Problem 2425

Find the perimeter of parallelogram FACE given $FA=5x+5$ , $EC=9x-11$ , and $FE=15$ cm.

See Solution

Problem 2426

Solve the linear equation $2x + 5 = -3x + 10$ for the unknown variable $x$ .

See Solution

Problem 2427

Find all values of $y$ in the equation $|-6y|=36$ . Options: $y=6$ , $y=-6$ , $y=6$ and $-6$ , No solution.

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Problem 2428

Evaluate the integral $2 \cdot \int x^{2} \ln x d x$

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Problem 2429

The given statement $\sqrt{-400}=20 i$ is false. The correct solution is $\sqrt{-400}=20i$ .

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Problem 2430

Solve for $y$ in the two-variable equation $\frac{y}{9}-\frac{2x}{9}=\frac{1}{3}$ . Select the correct solution.

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Problem 2431

Find all possible rational roots of $f(x)=-3 x^{5}-9 x^{4}+9 x^{3}+9 x^{2}-3 x-4$ using the rational root theorem. Express your answer as integers or simplified fractions, separated by commas.

See Solution

Problem 2432

Find the polynomial equivalent to $(f \cdot g)(x)$ , where $f(x) = x + 1$ and $g(x) = \frac{2}{x}$ .

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Problem 2433

Coastal city's tide peaks every 11.8 hours, ranging from 5.2 to 2.4 feet. Find the equation modeling the tide height after $t$ hours, given the high tide is at $t=0$ . Round values to the nearest tenth. Use a $\underline{sin}$ function. Amplitude $=1.4$ feet, Period $=2\pi$ radians, Phase Shift $=0$ radians, Vertical Shift $=3.8$ feet.

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Problem 2434

Find the quotient of $2 x^{3}-12 x^{2}+15 x \div 3 x$ . Choose the correct expression.

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Problem 2435

Find the slope of $y=x^3-x$ at $x=a$ . What is the slope at $x=1$ ? Where does the slope equal $11$ ?

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Problem 2436

Solve for $x$ in the equation $9=27x$ . Simplify the solution.

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Problem 2437

Solve for $a$ in the equation $25 = 35a$ . Simplify the solution $a = \frac{25}{35}$ .

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Problem 2438

Rewrite the rational function $y=\frac{e x+f}{g x+h}$ in the form $y=\frac{a}{x-h}+k$ . Find the equations of the asymptotes in terms of $e, f, g$ , and $h$ .

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Problem 2439

Find the solution to the equation $5 e^{x+2} = 7$ .

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Problem 2440

Solve the rational equation and explain the unique solution. $\frac{x^{2}-7 x-18}{x+2}=x-9$ . A. The equation reduces to $x=\boxed{3}$ . This is the only solution.

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Problem 2441

Flip a coin. What is the probability of not getting heads? Express your answer as a percentage.

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Problem 2442

Find the relationship between $z$ , $x$ , and $y$ in the equation $z=\pi xy^{2}$ .

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Problem 2443

Solve the quadratic equation $4x^2 - 8x = 64$ using the complete the square method. The solutions are $x = 5, x = 3$ .

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Problem 2444

Find the price that maximizes revenue for personal CD players, given that a $\$ 1$ decrease in price leads to 5 more units sold over 2 weeks, and the regular price is $\$ 90$ .

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Problem 2445

Multiply $73 \times 4$ using partial products. Show step-by-step work.

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Problem 2446

Find the expected value of a randomly chosen student's score on last year's final exam given the score distribution.
$X$ = score of a randomly chosen student Expected value of $X$ = $\frac{(19 \times 3) + (35 \times 3) + (60 \times 4)}{10}$

See Solution

Problem 2447

Evaluate the integral $\int_{e^{3 x}}^{e^{4 x}} \frac{1}{x \ln x+x} dx$ .

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Problem 2448

Solve the quadratic equation $x^{2} + \frac{1}{2}x + \frac{1}{16} = \frac{4}{9}$ , then factor the left side to find the solution.

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Problem 2449

Graph the quadratic equation $y = 8 - x^2$ and find 7 integer solutions in the range $-3 \leq x \leq 3$ .

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Problem 2450

Simplify the expression $\sqrt[4]{\frac{x^{3}}{256}}$ using the quotient rule, assuming all variables are positive real numbers.

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Problem 2451

Find the mean, median, and mode of the test scores: $84, 79, 77, 73, 79, 65, 75$ .

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Problem 2452

Solve for $x$ in the equation $10=1.35 \sqrt{x}$ .

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Problem 2453

Find the equation of the line passing through the points $(-7,0)$ and $(13,0)$ .

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Problem 2454

Find the integral that represents the length of the curve $f(x) = \cos x, 0 \leq x \leq \pi$ .

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Problem 2455

Perform basic arithmetic operations: (a) $-355-(-139)$ , (b) $\frac{-24+42}{-6}$ , (c) $13-(-5)$ , (d) $-216+138$ , (e) $-125-(-341)$ .

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Problem 2456

Find the average of the numbers $16, 8, 21, 16$ . Round to one decimal place if necessary.

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Problem 2457

Find the values of $m$ for which the integral $\int_{0}^{8} x^{m} d x$ converges.

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Problem 2458

Solve the quadratic equation $4x^2 = 7x + 6$ and find the discriminant $b^2 - 4ac$ . (Simplify your answer)

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Problem 2459

Find the value of $a$ that is 0.4% of 40.

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Problem 2460

Find the inverse function $f^{-1}(x)$ of $f(x) = 5^x$ . The inverse is $f^{-1}(x) = \log_5 x$ .

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Problem 2461

Find the missing operator that makes the equation $(6 \times 2) \, ? \, 4 = 8$ true.

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Problem 2462

Find the solutions to the quadratic equation $1=12x^2+11x$ . Round answers to two decimal places and separate with a comma.

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Problem 2463

Plant's height $H$ (cm) after $M$ months: $H = 53 + M$ . Plant's height after 13 months: $53 + 13 = 66$ cm.

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Problem 2464

Solve the rational equation and find the solution set, excluding values that make the equation undefined. $\frac{5}{x}+\frac{4}{5}=\frac{12}{6x}-\frac{17}{5}$

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Problem 2465

Solve the inequality $-\frac{10}{3} \geq 8x$ for the value of $x$ .

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Problem 2466

Ladder on wall: top slips down as base moves away at 5 m/s. Find (29) rate of top when 5 m from ground, and (30) rate of area change when top is 5 m from ground.

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Problem 2467

What is the remainder when $24$ is divided by $5$ ?

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Problem 2468

Find the difference between 4.8 and -8.7.

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Problem 2469

Solve for real number $w$ where $\sqrt{w}=5$ .

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Problem 2470

Solve the absolute value equation $\left|\frac{2 x-3}{5}\right|=11$ .

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Problem 2471

Evaluate the expression $-8+4$ and choose the correct answer from the options given.

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Problem 2472

Multiply the given rational expressions, simplify, and express the result as a rational expression. $\frac{y^2-4}{y^2-2y} \cdot \frac{y}{y^2+10y+16}, y \neq -8, -2, 0, 2$

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Problem 2473

Solve for $j$ in the proportion $\frac{20}{j}=\frac{32}{48}$ .

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Problem 2474

Find the value of $x$ in the equation $4(6x-9.5)=46$ . The possible solutions are $x=-1.5$ , $x=0.3$ , $x=1.79$ , and $x=3.5$ .

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Problem 2475

Construct a grouped frequency distribution for the ages of presidents at inauguration, using classes of width 5 starting from 41-45. Provide the frequency value for each class.
$41 - 45: \square$ $46 - 50: \square$ $51 - 55: \square$ $56 - 60: \square$ $61 - 65: \square$ $66 - 70: \square$

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Problem 2476

Simplify the expression $(-7)^{2}$ .

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Problem 2477

Find the value of 3/4 of 12.

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Problem 2478

Solve the linear equation $\frac{x}{-5} - 8.75 = -10$ for $x$ .

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Problem 2479

Use the second derivative test to find local extrema of $f(x) = -\frac{5x^3}{3} + 10x^2 + 25x$ in $(-5,8)$ . The local maxima occur at $x = \frac{10}{5}$ . The local minima occur at $\varnothing$ .

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Problem 2480

Divide $152$ by $4$ . Write out the times table of the divisor to assist with the calculation.

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Problem 2481

Predict the number of squirrels on a nature preserve with 8 coyotes using the linear model $y=-5x+60$ .

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Problem 2482

Find the function $(r-p)(x)$ where $r(x) = -7x$ and $p(x) = x^2 + 3x$ , and write the domain in interval notation.

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Problem 2483

Solve for $x$ in $2x^2 = 50$ . Options: a) $\pm 0.2$ , b) $\pm 7.07$ , c) $\pm 5$ , d) $\pm 12.5$ .

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Problem 2484

Subtract and simplify the expression $\frac{8}{x^{2}-8 x}-\frac{x}{8 x-64}$ .

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Problem 2485

Simplify the product of two polynomials $(7-14p)(7+14p)$ and determine the degree of the result.

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Problem 2486

Calculate $k$ when $j=3$ . $k=4j+2$ . Options: a) 12, b) 9, c) 6, d) 14.

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Problem 2487

(a) Solve $2(x+2)-5=9$ . (b) Write as single fraction $\frac{2x+1}{3}+\frac{3x-2}{6}$ . (c) Rearrange $T=2\pi\sqrt{\frac{L}{8}}$ to find $L$ . (d) (I) Show $f(x)=x^3-13x+12$ can be written as $(x-1)(x^2+x-12)$ . (II) Completely factorise $f(x)$ .

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Problem 2488

Find the meaning of $f(x)$ and $x$ in the equation $f(x)=7x+15$ which tracks Luke's exercise over the summer.

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Problem 2489

Solve the equation $(c+2)^{2}-5=-21$ and select the correct solution.

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Problem 2490

Approximate the sum of the series $\sum_{n=1}^{\infty}(-1)^{n} \frac{2}{3 n^{4}}$ with error < 0.001.

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Problem 2491

Find the point of intersection of the lines $y=2x-4$ and $y=-x+5$ .

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Problem 2492

Find the price of a used book sold at a bookstore, where the owner buys them for $\$ 2.25$ each and resells them for $300\%$ of the purchase price.

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Problem 2493

Find the value of $x$ that makes $\frac{1}{x}+\frac{4}{3x}-\frac{5}{6x}+1=0$ .

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Problem 2494

Determine the number of college students who got news from only social media using a Venn diagram. Given: 94 students surveyed, 32 from news websites, 25 from social media, and 11 from both.
$n($ News websites only $)=21$ $n($ Social media only $)=\boxed{14}$

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Problem 2495

Find the value of $x+\sqrt{x}$ for $x=0, 0.01, 0.36, 0.64, 1, 25, 100, 3600$ .

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Problem 2496

Find the equation representing the discount price for senior citizens given a 12% discount. $discount\ price = (original\ price)(1-0.12)$

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Problem 2497

Find the equation with solutions $x=7+i$ and $x=7-i$ , written in standard form.

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Problem 2498

Find the values of $y$ that make the expression $\frac{4}{15-3y}$ undefined.

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Problem 2499

Determine the limit of the sequence $\left\{\left(\frac{n+n^{2}}{2 n^{2}}\right)^{n}\right\}$ .

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Problem 2500

Find the derivative of $y=2 x^{2}(3-2 x)$ using the product rule.

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Numbers & Operations

Problem 2401

Spin two game board spinners, one with 1,2,31,2,31,2,3 and one with 5,6,7,85,6,7,85,6,7,8. The first spinner's digit is the tens, the second's is the ones. Construct a tree diagram to show all possible prize amounts.

Problem 2402

Find the exact solution of the equation 12tan⁡−1x=4π12 \tan ^{-1} \mathrm{x}=4 \pi12tan−1x=4π. The solution set is {±π3}\{\pm \frac{\pi}{3}\}{±3π​}.

Problem 2403

Solve the linear equation 2(3x+8)=702(3x+8) = 702(3x+8)=70 for the unknown variable xxx.

Problem 2404

Determine if the events "the person is female" and "the person prefers classic rock" are independent. Justify your answer based on the provided 2×42 \times 42×4 contingency table.

Problem 2405

Find the exact value of sec⁡−1(−2)\sec^{-1}(-\sqrt{2})sec−1(−2​). Choose A and enter the simplified expression, or B if no solution exists.

Problem 2406

A 34ft34\mathrm{ft}34ft ladder leans against a building at an 85∘85^{\circ}85∘ angle. Find the ladder's height on the building in ft\mathrm{ft}ft.

Problem 2407

Determine the number of zeros for the quadratic equation 0=3x2−7x+40=3 x^{2}-7 x+40=3x2−7x+4 using the discriminant.

Problem 2408

8. Convert equation y=3(x+2)(x−3)y=3(x+2)(x-3)y=3(x+2)(x−3) to standard form. (0.5 Points)9. Convert equation y=3x2−9x−30y=3x^2-9x-30y=3x2−9x−30 to intercept form. (0.5 Points)10. Another name for intercept form of a quadratic equation is Factored form. (0.5 Points)

Problem 2409

Solve the equation −5m(x)=−3x+4+5-5 m(x)=-3 \sqrt{x+4}+5−5m(x)=−3x+4​+5 for m(x)m(x)m(x).

Problem 2410

Solve the equation x2−4=0x^{2}-4=0x2−4=0 by graphing the associated parabola. Use the graph to give the solution(s).

Problem 2411

Problem 2412

Evaluate the factorial expression 2! 5!6! 3!\frac{2! \, 5!}{6! \, 3!}6!3!2!5!​ and simplify the result.

Problem 2413

Problem 2414

Solve for xxx when angles in a linear pair sum to 180∘180^{\circ}180∘. 12x=18012x = 18012x=180.

Problem 2415

Find the limit, continuity, and type of discontinuity of the piecewise function f(x) = \\begin{cases} 2x+1, & x>-1 \\\\ x^2+1, & x \\leq-1 \\end{cases} at x=ax=ax=a.

Problem 2416

Evaluate 7+9(x−6)37+9(x-6)^{3}7+9(x−6)3 for x=8x=8x=8. When x=8x=8x=8, the expression simplifies to □\square□.

Problem 2417

Evaluate and simplify the expression 7!5!4!6!\frac{7 ! 5 !}{4 ! 6 !}4!6!7!5!​.

Problem 2418

Determine if the equation x2+y2=100x^{2} + y^{2} = 100x2+y2=100 is symmetric with respect to the yyy-axis, xxx-axis, or origin.

Problem 2419

Maximize P=40x+50yP=40x+50yP=40x+50y subject to 2x+y≤182x+y\leq182x+y≤18, x+y≤10x+y\leq10x+y≤10, x+2y≤16x+2y\leq16x+2y≤16, and x,y≥0x,y\geq0x,y≥0. What is the maximum value of PPP?

Problem 2420

Evaluate the expressions: −(7)2-(7)^{2}−(7)2 and −(−2)3-(-2)^{3}−(−2)3.

Problem 2421

Trova l'equazione di una parabola con asse di simmetria sull'asse yyy, vertice in 0(0;0)0(0 ; 0)0(0;0) e passante per A(2;1)A(2 ; 1)A(2;1).

Problem 2422

Solve 102x−11⋅10x+24=010^{2x} - 11 \cdot 10^x + 24 = 0102x−11⋅10x+24=0. Solve e4x+4e2x=45e^{4x} + 4e^{2x} = 45e4x+4e2x=45.

Problem 2423

A. (f−g)(12)=12−3−122+12(\mathrm{f}-\mathrm{g})(12)=\sqrt{12-3}-12^{2}+12(f−g)(12)=12−3​−122+12

Problem 2424

Solve for xxx in the equations 8x=48^{x}=48x=4 and 16x=816^{x}=816x=8.

Problem 2425

Find the perimeter of parallelogram FACE given FA=5x+5FA=5x+5FA=5x+5, EC=9x−11EC=9x-11EC=9x−11, and FE=15FE=15FE=15 cm.

Problem 2426

Solve the linear equation 2x+5=−3x+102x + 5 = -3x + 102x+5=−3x+10 for the unknown variable xxx.

Problem 2427

Find all values of yyy in the equation ∣−6y∣=36|-6y|=36∣−6y∣=36. Options: y=6y=6y=6, y=−6y=-6y=−6, y=6y=6y=6 and −6-6−6, No solution.

Problem 2428

Evaluate the integral 2⋅∫x2ln⁡xdx2 \cdot \int x^{2} \ln x d x2⋅∫x2lnxdx

Problem 2429

The given statement −400=20i\sqrt{-400}=20 i−400​=20i is false. The correct solution is −400=20i\sqrt{-400}=20i−400​=20i.

Problem 2430

Solve for yyy in the two-variable equation y9−2x9=13\frac{y}{9}-\frac{2x}{9}=\frac{1}{3}9y​−92x​=31​. Select the correct solution.

Problem 2431

Find all possible rational roots of f(x)=−3x5−9x4+9x3+9x2−3x−4f(x)=-3 x^{5}-9 x^{4}+9 x^{3}+9 x^{2}-3 x-4f(x)=−3x5−9x4+9x3+9x2−3x−4 using the rational root theorem. Express your answer as integers or simplified fractions, separated by commas.

Problem 2432

Find the polynomial equivalent to (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x), where f(x)=x+1f(x) = x + 1f(x)=x+1 and g(x)=2xg(x) = \frac{2}{x}g(x)=x2​.

Problem 2433

Problem 2434

Find the quotient of 2x3−12x2+15x÷3x2 x^{3}-12 x^{2}+15 x \div 3 x2x3−12x2+15x÷3x. Choose the correct expression.

Problem 2435

Find the slope of y=x3−xy=x^3-xy=x3−x at x=ax=ax=a. What is the slope at x=1x=1x=1? Where does the slope equal 111111?

Problem 2436

Solve for xxx in the equation 9=27x9=27x9=27x. Simplify the solution.

Problem 2437

Solve for aaa in the equation 25=35a25 = 35a25=35a. Simplify the solution a=2535a = \frac{25}{35}a=3525​.

Problem 2438

Rewrite the rational function y=ex+fgx+hy=\frac{e x+f}{g x+h}y=gx+hex+f​ in the form y=ax−h+ky=\frac{a}{x-h}+ky=x−ha​+k. Find the equations of the asymptotes in terms of e,f,ge, f, ge,f,g, and hhh.

Problem 2439

Find the solution to the equation 5ex+2=75 e^{x+2} = 75ex+2=7.

Problem 2440

Solve the rational equation and explain the unique solution. x2−7x−18x+2=x−9\frac{x^{2}-7 x-18}{x+2}=x-9x+2x2−7x−18​=x−9. A. The equation reduces to x=3x=\boxed{3}x=3​. This is the only solution.

Problem 2441

Flip a coin. What is the probability of not getting heads? Express your answer as a percentage.

Spin two game board spinners, one with $1,2,3$ and one with $5,6,7,8$ . The first spinner's digit is the tens, the second's is the ones. Construct a tree diagram to show all possible prize amounts.

Find the exact solution of the equation $12 \tan ^{-1} \mathrm{x}=4 \pi$ . The solution set is $\{\pm \frac{\pi}{3}\}$ .

Solve the linear equation $2(3x+8) = 70$ for the unknown variable $x$ .

Determine if the events "the person is female" and "the person prefers classic rock" are independent. Justify your answer based on the provided $2 \times 4$ contingency table.

Find the exact value of $\sec^{-1}(-\sqrt{2})$ . Choose A and enter the simplified expression, or B if no solution exists.

A $34\mathrm{ft}$ ladder leans against a building at an $85^{\circ}$ angle. Find the ladder's height on the building in $\mathrm{ft}$ .

Determine the number of zeros for the quadratic equation $0=3 x^{2}-7 x+4$ using the discriminant.

8. Convert equation $y=3(x+2)(x-3)$ to standard form. (0.5 Points)
9. Convert equation $y=3x^2-9x-30$ to intercept form. (0.5 Points)
10. Another name for intercept form of a quadratic equation is Factored form. (0.5 Points)

Solve the equation $-5 m(x)=-3 \sqrt{x+4}+5$ for $m(x)$ .

Solve the equation $x^{2}-4=0$ by graphing the associated parabola. Use the graph to give the solution(s).

Evaluate the factorial expression $\frac{2! \, 5!}{6! \, 3!}$ and simplify the result.

Solve for $x$ when angles in a linear pair sum to $180^{\circ}$ . $12x = 180$ .

Find the limit, continuity, and type of discontinuity of the piecewise function f(x) = \\begin{cases} 2x+1, & x>-1 \\\\ x^2+1, & x \\leq-1 \\end{cases} at $x=a$ .

Evaluate $7+9(x-6)^{3}$ for $x=8$ . When $x=8$ , the expression simplifies to $\square$ .

Evaluate and simplify the expression $\frac{7 ! 5 !}{4 ! 6 !}$ .

Determine if the equation $x^{2} + y^{2} = 100$ is symmetric with respect to the $y$ -axis, $x$ -axis, or origin.

Maximize $P=40x+50y$ subject to $2x+y\leq18$ , $x+y\leq10$ , $x+2y\leq16$ , and $x,y\geq0$ . What is the maximum value of $P$ ?

Evaluate the expressions: $-(7)^{2}$ and $-(-2)^{3}$ .

Trova l'equazione di una parabola con asse di simmetria sull'asse $y$ , vertice in $0(0 ; 0)$ e passante per $A(2 ; 1)$ .

Solve $10^{2x} - 11 \cdot 10^x + 24 = 0$ . Solve $e^{4x} + 4e^{2x} = 45$ .

A. $(\mathrm{f}-\mathrm{g})(12)=\sqrt{12-3}-12^{2}+12$

Solve for $x$ in the equations $8^{x}=4$ and $16^{x}=8$ .

Find the perimeter of parallelogram FACE given $FA=5x+5$ , $EC=9x-11$ , and $FE=15$ cm.

Solve the linear equation $2x + 5 = -3x + 10$ for the unknown variable $x$ .

Find all values of $y$ in the equation $|-6y|=36$ . Options: $y=6$ , $y=-6$ , $y=6$ and $-6$ , No solution.

Evaluate the integral $2 \cdot \int x^{2} \ln x d x$

The given statement $\sqrt{-400}=20 i$ is false. The correct solution is $\sqrt{-400}=20i$ .

Solve for $y$ in the two-variable equation $\frac{y}{9}-\frac{2x}{9}=\frac{1}{3}$ . Select the correct solution.

Find all possible rational roots of $f(x)=-3 x^{5}-9 x^{4}+9 x^{3}+9 x^{2}-3 x-4$ using the rational root theorem. Express your answer as integers or simplified fractions, separated by commas.

Find the polynomial equivalent to $(f \cdot g)(x)$ , where $f(x) = x + 1$ and $g(x) = \frac{2}{x}$ .

Find the quotient of $2 x^{3}-12 x^{2}+15 x \div 3 x$ . Choose the correct expression.

Find the slope of $y=x^3-x$ at $x=a$ . What is the slope at $x=1$ ? Where does the slope equal $11$ ?

Solve for $x$ in the equation $9=27x$ . Simplify the solution.

Solve for $a$ in the equation $25 = 35a$ . Simplify the solution $a = \frac{25}{35}$ .

Rewrite the rational function $y=\frac{e x+f}{g x+h}$ in the form $y=\frac{a}{x-h}+k$ . Find the equations of the asymptotes in terms of $e, f, g$ , and $h$ .

Find the solution to the equation $5 e^{x+2} = 7$ .

Solve the rational equation and explain the unique solution. $\frac{x^{2}-7 x-18}{x+2}=x-9$ . A. The equation reduces to $x=\boxed{3}$ . This is the only solution.

Find the relationship between $z$ , $x$ , and $y$ in the equation $z=\pi xy^{2}$ .

Solve the quadratic equation $4x^2 - 8x = 64$ using the complete the square method. The solutions are $x = 5, x = 3$ .

Find the price that maximizes revenue for personal CD players, given that a $\$ 1$ decrease in price leads to 5 more units sold over 2 weeks, and the regular price is $\$ 90$ .

Multiply $73 \times 4$ using partial products. Show step-by-step work.

Find the expected value of a randomly chosen student's score on last year's final exam given the score distribution.
$X$ = score of a randomly chosen student Expected value of $X$ = $\frac{(19 \times 3) + (35 \times 3) + (60 \times 4)}{10}$

Evaluate the integral $\int_{e^{3 x}}^{e^{4 x}} \frac{1}{x \ln x+x} dx$ .

Solve the quadratic equation $x^{2} + \frac{1}{2}x + \frac{1}{16} = \frac{4}{9}$ , then factor the left side to find the solution.

Graph the quadratic equation $y = 8 - x^2$ and find 7 integer solutions in the range $-3 \leq x \leq 3$ .

Simplify the expression $\sqrt[4]{\frac{x^{3}}{256}}$ using the quotient rule, assuming all variables are positive real numbers.

Find the mean, median, and mode of the test scores: $84, 79, 77, 73, 79, 65, 75$ .

Solve for $x$ in the equation $10=1.35 \sqrt{x}$ .

Find the equation of the line passing through the points $(-7,0)$ and $(13,0)$ .

Find the integral that represents the length of the curve $f(x) = \cos x, 0 \leq x \leq \pi$ .

Perform basic arithmetic operations: (a) $-355-(-139)$ , (b) $\frac{-24+42}{-6}$ , (c) $13-(-5)$ , (d) $-216+138$ , (e) $-125-(-341)$ .

Find the average of the numbers $16, 8, 21, 16$ . Round to one decimal place if necessary.

Find the values of $m$ for which the integral $\int_{0}^{8} x^{m} d x$ converges.

Solve the quadratic equation $4x^2 = 7x + 6$ and find the discriminant $b^2 - 4ac$ . (Simplify your answer)

Find the value of $a$ that is 0.4% of 40.

Find the inverse function $f^{-1}(x)$ of $f(x) = 5^x$ . The inverse is $f^{-1}(x) = \log_5 x$ .

Find the missing operator that makes the equation $(6 \times 2) \, ? \, 4 = 8$ true.

Find the solutions to the quadratic equation $1=12x^2+11x$ . Round answers to two decimal places and separate with a comma.

Plant's height $H$ (cm) after $M$ months: $H = 53 + M$ . Plant's height after 13 months: $53 + 13 = 66$ cm.

Solve the rational equation and find the solution set, excluding values that make the equation undefined. $\frac{5}{x}+\frac{4}{5}=\frac{12}{6x}-\frac{17}{5}$

Solve the inequality $-\frac{10}{3} \geq 8x$ for the value of $x$ .

What is the remainder when $24$ is divided by $5$ ?

Solve for real number $w$ where $\sqrt{w}=5$ .

Solve the absolute value equation $\left|\frac{2 x-3}{5}\right|=11$ .

Evaluate the expression $-8+4$ and choose the correct answer from the options given.

Multiply the given rational expressions, simplify, and express the result as a rational expression. $\frac{y^2-4}{y^2-2y} \cdot \frac{y}{y^2+10y+16}, y \neq -8, -2, 0, 2$

Solve for $j$ in the proportion $\frac{20}{j}=\frac{32}{48}$ .

Find the value of $x$ in the equation $4(6x-9.5)=46$ . The possible solutions are $x=-1.5$ , $x=0.3$ , $x=1.79$ , and $x=3.5$ .