Algebra

Problem 30401

Find the new equation for $y=f(x)$ after shifting left 4 units, up 7 units, and stretching vertically by -8.

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Problem 30402

Find the end behavior of the polynomial $P(x)=3 x^{3}-x^{2}+5 x+1$ .

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Problem 30403

Grade 7 students plan to sell 100-150 hot dogs.
a) How many packs of 12 wieners and 8 buns to avoid leftovers? Justify. b) How many packs for over 300 hot dogs?

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Problem 30404

Simplify: $\frac{2 x}{y^{2}}+\frac{3 x}{2 y}-\frac{4 x}{5}$ . What is the simplest form?

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Problem 30405

Solve the equation $(x+4)^{2}-4=36$ . Find all possible values for $x$ .

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Problem 30406

Find the new equation of $y=f(x)$ after translating left 5 units, up 2 units, and stretching horizontally by 3.

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Problem 30407

Which radical expression simplifies to include absolute value? Options: $\sqrt[3]{64 x^{3}}$ , $\sqrt[3]{-125 x^{3}}$ , $\sqrt[4]{81 x}$ , $\sqrt[4]{16 x^{4}}$ .

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Problem 30408

Find the value of $b$ in the equation $5=\log _{b}(32)$ .

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Problem 30409

Simplify: $\frac{\sqrt{6 x^{3}}}{\sqrt{3 x}} \cdot \sqrt{8 x^{2}}$ and find the result among these: $16 x^{4}$ , $\sqrt{16 x^{4}}$ , $4 x \sqrt{x^{3}}$ , $4 x^{2}$ .

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Problem 30410

Graph the function $g(x)=|x|+2$ based on the graph of $f(x)=|x|$ .

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Problem 30411

Reflect the graph of $f(x)=x^{3}$ about the $x$ -axis, shift it down 9 and right 2. Find $g(x)$ .

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Problem 30412

Solve for $x$ : $x^{2}-8x=24$ . Find the values of $x$ .

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Problem 30413

How much will \ $12,000 grow in 5 years at 2% interest compounded semiannually? Use$ A=P\left(1+\frac{r}{m}\right)^{mt}$.

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Problem 30414

Determine the slope and $y$ -intercept of the line given by the equation $2x + 5y = 21$ .

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Problem 30415

Find the solution for the inequality: $-8 < -6 - f$ . Choose from: $f=9$ , $f=11$ , $f=-9$ , $f=6$ .

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Problem 30416

Find the line equation with slope $m$ through point (4,4). Answer in slope-intercept form: $m=-\frac{2}{3}$ .

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Problem 30417

Solve for $b$ in the equation $T=\frac{b-d}{k}$ .

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Problem 30418

Graph the function $g$ by reflecting $f(x)=x^{2}$ about the $x$ -axis, then shifting up 2 and left 4. Find $g(x)$ .

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Problem 30419

Find $\log_{8} 1,000$ using $\ln 8 \approx 2.08$ and $\ln 1,000 \approx 6.91$ .

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Problem 30420

What does $\ln(10)$ equal among these: $\log(10)$ , $\log_{10}(e)$ , $\log_{e}(10)$ , $10 \cdot \ln(e)$ ?

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Problem 30421

Divide the polynomials $P(x)=-x^{3}-2x+6$ by $D(x)=x+1$ using synthetic or long division. Express $P$ as $P(x)=D(x) \bullet Q(x)+R(x)$ .

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Problem 30422

Solve: $\log 8 x - \log 2 = \log 16$ for $x$ . Options: $1$ , $4$ , $\frac{9}{4}$ , $\frac{\log 16 + \log 2}{\log 8}$ .

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Problem 30423

Find the solutions to the inequality $-122 \leq -12 p$ . Choose from: $p=-3$ , $p=-7$ , $p=-4$ , $p=5$ .

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Problem 30424

Describe how to generate the next terms in the pattern: A: $5, 8, 11, 14, 17, \ldots$

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Problem 30425

Solve for $m$ in the equation $y=mx+b$ .

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Problem 30426

Find the average cost per item for manufacturing 90 items if $C=600+30x$ .

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Problem 30427

Graph the cost equation $c = 10 + \frac{1}{4} m$ and estimate $c$ for $m = 36$ .

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Problem 30428

Solve for $y$ : $3(2y + 4) = 4(2y - \frac{1}{2})$ . What is the value of $y$ ?

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Problem 30429

Solve the equation $x-9=23$ . What is the value of $x$ ? Options: $32$ , $-14$ , $14$ , $-32$ .

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Problem 30430

Find the snow depth, $d$ , on January 30 using the equation $d=-2t+64$ , where $t$ is days since Dec 31.

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Problem 30431

Solve the equation $x - 9 = 23$ . What is the value of $x$ ?

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Problem 30432

Which steps solve $\frac{3 x}{4}=\frac{7}{3}$ ? Find the solution for $x$ .

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Problem 30433

Find the sales in 1989 using the formula $S=70 x+500$ , where $x=0$ is 1982.

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Problem 30434

Find the mass of a gold sample (density 19.3 g/cm³) with a volume of 2.5 cm³ using $d=\frac{m}{v}$ . Mass: g

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Problem 30435

Find $x$ in the equation: $2x - 11 = 7x + 16$ . Options: $3$ , $-5 \frac{2}{5}$ , $-1$ , $\frac{5}{9}$ .

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Problem 30436

Solve for $y$ in the equation $Ax + By = C$ using $x$ , $A$ , $B$ , and $C$ .

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Problem 30437

Find the hours when total costs of ski rentals from Shop A ( $3 + 9h$ ) and Shop B ( $9 + 6h$ ) are equal.

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Problem 30438

Find the width $w$ of a rectangular enclosure with area $\geq 2700 \mathrm{yd}^{2}$ and perimeter $240 \mathrm{yd}$ .

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Problem 30439

Identify the rule for generating terms in these sequences: a. Pattern A: 5, 8, 11, 14, 17, ... b. Pattern B: $\frac{1}{2}, 1, 2, 4, 8, ...$

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Problem 30440

Check if Rebecca's five pairs of like terms are correct and fix any mistakes: $2.5 w$ and $-8 w$ , $\frac{1}{2}$ and $\frac{1}{2}$ , 38 and -15, $-7 c^{2}$ and $c^{2}$ , $5 a$ and $5 b$ .

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Problem 30441

What score does Paul need on his third test to average at least $80$ if he scored 83 and 75 on the first two tests?

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Problem 30442

Solve the equation $\frac{x+1-1}{3}=2-1$ .

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Problem 30443

Solve the equation $\frac{x+1-1}{3} = 2-1$ . What mistake was made? Correctly solve for $x$ .

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Problem 30444

Find the minimum number of backpacks $x$ to sell for profit where $C=98x+7,809$ and $R=190x$ . Choices: A. 718,428 B. \$2,248,992 C. 85 D. 29

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Problem 30445

Solve the inequality: $x^{2}+2 x \geq 8$ .

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Problem 30446

Keiko deposits \$9500 at 17% annual interest. Find the account balance after 1 year and after 2 years.

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Problem 30447

A plane flies at 200 mph for 225 miles ± 50 miles. Find the min and max travel time in hours. At least $h$ and at most $h$ .

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Problem 30448

Prove or disprove that there are no positive integers $a, b, c$ and integer $n>2$ such that $a^{n}+b^{n}=c^{n}$ .

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Problem 30449

Find the number of units $t$ to sell for profit if cost is $C=3t^{2}+7t$ and revenue is $R=4t^{2}+t$ .

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Problem 30450

Estimate the number of employees in educational services in 2010, given 14.5 million in 2005 and 16.5 million in 2014. Use a linear model.

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Problem 30451

There are 48 trails in total, with $37.5\%$ being beginner trails. Find the number of expert trails.

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Problem 30452

Combine the terms in the expression: $4 r + 9 r - 11 r + 7 r$ .

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Problem 30453

Is $q=-20$ a solution to the inequality $-5>\frac{q}{20}$ ? Answer yes or no.

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Problem 30454

Simplify: $-26 r + 7 r - 15 p - 7 p$ .

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Problem 30455

Is $b=-3$ a solution for the inequality $-6+b>-2$ ? Answer yes or no.

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Problem 30456

Find the solutions to the inequality $14 < 7 + t$ . Choose all that apply: $t=8$ , $t=7$ , $t=5$ , $t=10$ .

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Problem 30457

Evaluate $\frac{3 a+1}{b+\frac{c}{a}}$ for $a=3$ , $b=\frac{2}{3}$ , and $c=4$ .

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Problem 30458

Find the quotient and remainder of $2 x^{2}-5 x+3$ divided by $x-3$ using synthetic division.

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Problem 30459

Find the solutions for the inequality $-12 + 10g > -72$ . Which values of $g$ are valid? Options: $g=9$ , $g=-12$ , $g=11$ , $g=-5$ .

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Problem 30460

Is $t=-8$ a solution to the inequality $-52 \geq 6 t - 5$ ? Answer yes or no.

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Problem 30461

You spend \$132 on 5 cans of paint: white at \$24/can and blue at \$28/can. How much would you save by switching colors?

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Problem 30462

Identify the equation that is not equivalent to $c x-a=b$ : 1) $c x-a+b=2 b$ 2) $c x-a+b=0$ 3) $2 c x-2 a=2 b$ 4) $b+a=c x$

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Problem 30463

Find the number of solutions $N$ for $3(x-a)=3x-6$ . Which statements about $a$ and $N$ are correct?

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Problem 30464

Find the quotient and remainder of $x^{3}+2x+1$ divided by $x^{2}-x+3$ using long division.

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Problem 30465

Solve for $d$ in the equation $72 \cdot 5 d =$ .

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Problem 30466

Find the equivalent expression for $\left(\frac{1}{z^{3 / 5}}\right)^{-1 / 5}$ . A. $z^{3 / 25}$ B. $z^{-3 / 25}$ C. $z^{-2 / 5}$ D. $z^{2 / 5}$

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Problem 30467

a) $\log _{x} 49=2$

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Problem 30468

$-6=\frac{5 x-27}{-3}$
Simplify your answer as much as possible. $x=$

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Problem 30469

Solve for $x$ . $\frac{x+41}{6}=5$
Simplify your answer as much as possible. $x=$

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Problem 30470

omial Functions Practice Question 4 iploma
Use the following information to answer the next question. The binomial $x+2$ is a factor of $f(x)=x^{3}+3 x^{2}+k x+4$
Add-on: State the zeros of $f(x)$ $(x+2)^{3}$
The value of $k$ is $\qquad$ $f(-2)=(-2)^{3}+3(-2)^{2}+k(-2)+4=0$

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Problem 30471

9.) Consider the line $y=-8 x+2$ . (a) Find the equation of the line that is perpendicular to this line and passes through the point $(-4,5)$ . (b) Find the equation of the line that is parallel to this line and passes through the point( $4,5)$ .

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Problem 30472

Quadratic Equations Unit Test Part 2
Jedida solved the quadratic equation $x^{2}-96=4 x$ by factoring. Her work is shown below. At which step did Jedida first make a mistake, if at all? $x^{2}-96=4 x$
Step 1: $x^{2}+4 x-96=0$ Add $4 x$ to both sides.
Step 2: $(x+12)(x-8)=0$ Factor. Step 3: $x+12=0$ or $x-8=0$ Use the Zero Product Property. $x=-12 \text { or } x=8$
Step 1 ; she added $4 x$ to both sides instead of subtracting. Step 3; she did not apply the Zero Product Property correctly. Step 2; she did not factor the left side of the equation correctly. She did not make any mistakes.

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Problem 30473

4. A teacher is creating a test for his Algebra 1 students. The test is made up of multiple-choice and free response questions. Each mutliple-choice question is worth 7 points and each free response question is worth 8 points. If the test has 48 questions and is worth a total of 374 points, which equations can be used to find $x$ , the number of multiple-choice questions and $y$ , the number of free response questions on the test? Choose TWO correct answers.

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Problem 30474

d) $\log (x y)+\log \frac{y}{x}$

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Problem 30475

8. Represent and Connect Andre wrote the expression $15(1.5 x-3)$ to represent the relationship shown in the table. Write two other expressions that represent the relationship shown in the table.

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Problem 30476

$3 \quad 3 n=36$

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Problem 30477

Solve the following system of equations for all three variables. $\begin{array}{r} 4 x+3 y-z=10 \\ 8 x+y-z=6 \\ 6 x+y+z=4 \end{array}$

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Problem 30478

Which expression is equivalent to $\sqrt[3]{64 y}$ ? $128 y^{\frac{1}{3}}$ $8 y$ $8 y^{\frac{1}{3}}$ $4 y^{\frac{1}{3}}$ Submit

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Problem 30479

ind the real solutions, if any, of the equation. Use the quadratic formula. 25) $x^{2}-4 x-7=0$

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Problem 30480

Une $f$ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 2 & 7 \\ \hline 4 & 10.5 \\ \hline 7 & 15.75 \\ \hline 11 & 22.75 \\ \hline \end{tabular}
Line $g$ \begin{tabular}{|r|r|} \hline $x$ & \multicolumn{1}{|c|}{ $y$ } \\ \hline-3 & 4 \\ \hline-2 & 0 \\ \hline 1 & -12 \\ \hline 4 & -24 \\ \hline \end{tabular}
Write a system of equations that represents lines fand $g$ . (work space below)

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Problem 30481

Solve for $x$ . $143+(12 x+76)^{\frac{7}{6}}=15$
Write one solution in each box. You can add or remove boxes. If there are no solutions, remove all boxes. $\square$ Submit

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Problem 30482

Solve for $x$ . $-216=\left(x^{2}-3 x-18\right)^{\frac{3}{2}}$
Write one solution in each box. You can add or remove boxes. If there are no solutions, remove all boxes. $\square$ Submit

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Problem 30483

2 Matching 1 point Find the slope of the line that passes through the points given in the first column and match them with the appropriate result. \begin{tabular}{|l|l|l|} \hline $(10,7)$ and $(1,2)$ \\ \hline $(9,9)$ and $(1,16)$ & \\ \hline \\ \hline $(8,3)$ and $(2,1)$ & \\ \hline \end{tabular}

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Problem 30484

39.) Write a quadratic function in standard form that has roots of $\frac{2}{3}$ and -4 .

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Problem 30485

$6 x+1>5 x+4$ or $1-x>-4$

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Problem 30486

positive solution of the equation. $8 x^{\frac{4}{5}}+4=32772$

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Problem 30487

Solve for $t$ in the proportion. $\begin{array}{l} \frac{8}{13.5}=\frac{t}{16.2} \\ t=\square \end{array}$

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Problem 30488

Given $f(x)=2 \sqrt{x}$ and $g(x)=3 x$ , find the following expressions. (a) $(f \circ g)(4)$ (b) $(g \circ f)(2)$ (c) $(f \circ f)(1)$ (d) $(g \circ g)(0)$

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Problem 30489

You start at ( 4,7 ). You move up 3 units and down 1 unit. Where do you end?

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Problem 30490

5. The fence posts around a large pasture are 2.5 m apart. A horse starts running west beside the fence. When the horse passes the fifth fence post, your second hand is on the 9.0 s mark. When the horse passes the fourteenth fence post, the second hand is on 111.5 s . What is the horse's velocity?

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Problem 30491

Video
部, A parabola opening up or down has vertex $(6,-4)$ and passes through $\left(3,-\frac{13}{4}\right)$ .Write its equation in vertex form.
Simplify any fractions. $\square$ $\square$ (I) 2 submit

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Problem 30492

Find the equation for the function that is finally graphed after the following transformations are applied to the graph of $y=x^{2}$ in the order listed. a) Reflect about the $x$ -axis b) Shift up 5 units c) Shift left 2 units

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Problem 30493

6. $n^{2}-25$ a. for $n=-10$ b. for $n=-5$ c. for $n=3$

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Problem 30494

An equation in slope-intercept form of a line passes through the point $(-3,5)$ and is perpendicular to the line represented by $y=-\frac{3}{4} x-4$ .
What are the slope and $y$ -intercept that best represents this linear function? Move the correct answer to each box.
Slope: $\square$ y-intercept: $\frac{4}{3}$ $\square$ Prag and drop the correct cholce into the blank spaces above

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Problem 30495

6. Assume a business is deciding whether to invest in a new project that is projected to generate profits of $\$ 90,000$ each year for the next three years. The project start-up costs are $\$ 225,000$ . (A) If the business normally earns 11 percent on its investments, should the business invest? Show/explain. (B) If the business normally earns 5 percent on its investments, should the business invest? Show/explain.

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Problem 30496

Determine if the equations are parallel, perpendicular, or neither.

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Problem 30497

Algebra $1>2.8$ Using
Find the discriminant. $t^{2}+8 t+7=0$
How many real solutions does the equation have? substrit

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Problem 30498

$4 y-12 \quad 18-6 y$
7. Simplify. State any restrictions on the variables. a) $\frac{x^{2}-5 x y+4 y^{2}}{x^{2}+3 x y-28 y^{2}} \times \frac{x^{2}+2 x y+y^{2}}{x^{2}-y^{2}}$ b) $\frac{2 a^{2}-12 a b+18 b^{2}}{a^{2}-7 a b+10 b^{2}} \div \frac{4 a^{2}-12 a b}{a^{2}-7 a b+10 b^{2}}$ c) $\frac{10 x^{2}+3 x y-y^{2}}{9 x^{2}-y^{2}} \div \frac{6 x^{2}+3 x y}{12 x+4 y}$ d) $\frac{15 m^{2}+m n-2 n^{2}}{2 n-14 m} \times \frac{7 m^{2}-8 m n+n^{2}}{5 m^{2}+7 m n+2 n^{2}}$

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Problem 30499

4. La valeur d'une action varie selon la règle: $y=-3|x-4|+16$ où $x$ représente le nombre de mois écoulés depuis l'émission de l'action et $y$ la valeur de l'action. Au cours d'une période d'un an, détermine l'intervalle dans lequel la valeur de l'action a été supérieure à 10 \ $. A)$ [0,2[\cup] 6,12] $B)$ [0,12] $(C)$ ] 2,6[ $D)$ ]-\infty, 2[\cup] 6,+\infty[$

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Problem 30500

Find the discriminant. $2 v^{2}-v=0$
How many real solutions does the equation have? no real one real two real solutions solution solutions Submit

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1 ...302 303 304 305 306 307 308 ...312

Algebra

Problem 30401

Find the new equation for y=f(x)y=f(x)y=f(x) after shifting left 4 units, up 7 units, and stretching vertically by -8.

Problem 30402

Find the end behavior of the polynomial P(x)=3x3−x2+5x+1P(x)=3 x^{3}-x^{2}+5 x+1P(x)=3x3−x2+5x+1.

Problem 30403

Grade 7 students plan to sell 100-150 hot dogs. a) How many packs of 12 wieners and 8 buns to avoid leftovers? Justify. b) How many packs for over 300 hot dogs?

Problem 30404

Simplify: 2xy2+3x2y−4x5\frac{2 x}{y^{2}}+\frac{3 x}{2 y}-\frac{4 x}{5}y22x​+2y3x​−54x​. What is the simplest form?

Problem 30405

Solve the equation (x+4)2−4=36(x+4)^{2}-4=36(x+4)2−4=36. Find all possible values for xxx.

Problem 30406

Find the new equation of y=f(x)y=f(x)y=f(x) after translating left 5 units, up 2 units, and stretching horizontally by 3.

Problem 30407

Which radical expression simplifies to include absolute value? Options: 64x33\sqrt[3]{64 x^{3}}364x3​, −125x33\sqrt[3]{-125 x^{3}}3−125x3​, 81x4\sqrt[4]{81 x}481x​, 16x44\sqrt[4]{16 x^{4}}416x4​.

Problem 30408

Find the value of bbb in the equation 5=log⁡b(32)5=\log _{b}(32)5=logb​(32).

Problem 30409

Simplify: 6x33x⋅8x2\frac{\sqrt{6 x^{3}}}{\sqrt{3 x}} \cdot \sqrt{8 x^{2}}3x​6x3​​⋅8x2​ and find the result among these: 16x416 x^{4}16x4, 16x4\sqrt{16 x^{4}}16x4​, 4xx34 x \sqrt{x^{3}}4xx3​, 4x24 x^{2}4x2.

Problem 30410

Graph the function g(x)=∣x∣+2g(x)=|x|+2g(x)=∣x∣+2 based on the graph of f(x)=∣x∣f(x)=|x|f(x)=∣x∣.

Problem 30411

Reflect the graph of f(x)=x3f(x)=x^{3}f(x)=x3 about the xxx-axis, shift it down 9 and right 2. Find g(x)g(x)g(x).

Problem 30412

Solve for xxx: x2−8x=24x^{2}-8x=24x2−8x=24. Find the values of xxx.

Problem 30413

How much will \12,000growin5yearsat212,000 grow in 5 years at 2% interest compounded semiannually? Use 12,000growin5yearsat2A=P\left(1+\frac{r}{m}\right)^{mt}$.

Problem 30414

Determine the slope and yyy-intercept of the line given by the equation 2x+5y=212x + 5y = 212x+5y=21.

Problem 30415

Find the solution for the inequality: −8<−6−f-8 < -6 - f−8<−6−f. Choose from: f=9f=9f=9, f=11f=11f=11, f=−9f=-9f=−9, f=6f=6f=6.

Problem 30416

Find the line equation with slope mmm through point (4,4). Answer in slope-intercept form: m=−23m=-\frac{2}{3}m=−32​.

Problem 30417

Solve for bbb in the equation T=b−dkT=\frac{b-d}{k}T=kb−d​.

Problem 30418

Graph the function ggg by reflecting f(x)=x2f(x)=x^{2}f(x)=x2 about the xxx-axis, then shifting up 2 and left 4. Find g(x)g(x)g(x).

Problem 30419

Find log⁡81,000\log_{8} 1,000log8​1,000 using ln⁡8≈2.08\ln 8 \approx 2.08ln8≈2.08 and ln⁡1,000≈6.91\ln 1,000 \approx 6.91ln1,000≈6.91.

Problem 30420

What does ln⁡(10)\ln(10)ln(10) equal among these: log⁡(10)\log(10)log(10), log⁡10(e)\log_{10}(e)log10​(e), log⁡e(10)\log_{e}(10)loge​(10), 10⋅ln⁡(e)10 \cdot \ln(e)10⋅ln(e)?

Problem 30421

Divide the polynomials P(x)=−x3−2x+6P(x)=-x^{3}-2x+6P(x)=−x3−2x+6 by D(x)=x+1D(x)=x+1D(x)=x+1 using synthetic or long division. Express PPP as P(x)=D(x)∙Q(x)+R(x)P(x)=D(x) \bullet Q(x)+R(x)P(x)=D(x)∙Q(x)+R(x).

Problem 30422

Solve: log⁡8x−log⁡2=log⁡16\log 8 x - \log 2 = \log 16log8x−log2=log16 for xxx. Options: 111, 444, 94\frac{9}{4}49​, log⁡16+log⁡2log⁡8\frac{\log 16 + \log 2}{\log 8}log8log16+log2​.

Problem 30423

Find the solutions to the inequality −122≤−12p-122 \leq -12 p−122≤−12p. Choose from: p=−3p=-3p=−3, p=−7p=-7p=−7, p=−4p=-4p=−4, p=5p=5p=5.

Problem 30424

Describe how to generate the next terms in the pattern: A: 5,8,11,14,17,…5, 8, 11, 14, 17, \ldots5,8,11,14,17,…

Problem 30425

Solve for mmm in the equation y=mx+by=mx+by=mx+b.

Problem 30426

Find the average cost per item for manufacturing 90 items if C=600+30xC=600+30xC=600+30x.

Problem 30427

Graph the cost equation c=10+14mc = 10 + \frac{1}{4} mc=10+41​m and estimate ccc for m=36m = 36m=36.

Problem 30428

Solve for yyy: 3(2y+4)=4(2y−12)3(2y + 4) = 4(2y - \frac{1}{2})3(2y+4)=4(2y−21​). What is the value of yyy?

Problem 30429

Solve the equation x−9=23x-9=23x−9=23. What is the value of xxx? Options: 323232, −14-14−14, 141414, −32-32−32.

Problem 30430

Find the snow depth, ddd, on January 30 using the equation d=−2t+64d=-2t+64d=−2t+64, where ttt is days since Dec 31.

Problem 30431

Solve the equation x−9=23x - 9 = 23x−9=23. What is the value of xxx?

Problem 30432

Which steps solve 3x4=73\frac{3 x}{4}=\frac{7}{3}43x​=37​? Find the solution for xxx.

Problem 30433

Find the sales in 1989 using the formula S=70x+500S=70 x+500S=70x+500, where x=0x=0x=0 is 1982.

Problem 30434

Find the mass of a gold sample (density 19.3 g/cm³) with a volume of 2.5 cm³ using d=mvd=\frac{m}{v}d=vm​. Mass: g

Problem 30435

Find xxx in the equation: 2x−11=7x+162x - 11 = 7x + 162x−11=7x+16. Options: 333, −525-5 \frac{2}{5}−552​, −1-1−1, 59\frac{5}{9}95​.

Problem 30436

Solve for yyy in the equation Ax+By=CAx + By = CAx+By=C using xxx, AAA, BBB, and CCC.

Problem 30437

Find the hours when total costs of ski rentals from Shop A (3+9h3 + 9h3+9h) and Shop B (9+6h9 + 6h9+6h) are equal.

Problem 30438

Find the width www of a rectangular enclosure with area ≥2700yd2\geq 2700 \mathrm{yd}^{2}≥2700yd2 and perimeter 240yd240 \mathrm{yd}240yd.

Problem 30439

Identify the rule for generating terms in these sequences: a. Pattern A: 5, 8, 11, 14, 17, ... b. Pattern B: 12,1,2,4,8,...\frac{1}{2}, 1, 2, 4, 8, ...21​,1,2,4,8,...

Problem 30440

Find the new equation for $y=f(x)$ after shifting left 4 units, up 7 units, and stretching vertically by -8.

Find the end behavior of the polynomial $P(x)=3 x^{3}-x^{2}+5 x+1$ .

Grade 7 students plan to sell 100-150 hot dogs.
a) How many packs of 12 wieners and 8 buns to avoid leftovers? Justify. b) How many packs for over 300 hot dogs?

Simplify: $\frac{2 x}{y^{2}}+\frac{3 x}{2 y}-\frac{4 x}{5}$ . What is the simplest form?

Solve the equation $(x+4)^{2}-4=36$ . Find all possible values for $x$ .

Find the new equation of $y=f(x)$ after translating left 5 units, up 2 units, and stretching horizontally by 3.

Which radical expression simplifies to include absolute value? Options: $\sqrt[3]{64 x^{3}}$ , $\sqrt[3]{-125 x^{3}}$ , $\sqrt[4]{81 x}$ , $\sqrt[4]{16 x^{4}}$ .

Find the value of $b$ in the equation $5=\log _{b}(32)$ .

Simplify: $\frac{\sqrt{6 x^{3}}}{\sqrt{3 x}} \cdot \sqrt{8 x^{2}}$ and find the result among these: $16 x^{4}$ , $\sqrt{16 x^{4}}$ , $4 x \sqrt{x^{3}}$ , $4 x^{2}$ .

Graph the function $g(x)=|x|+2$ based on the graph of $f(x)=|x|$ .

Reflect the graph of $f(x)=x^{3}$ about the $x$ -axis, shift it down 9 and right 2. Find $g(x)$ .

Solve for $x$ : $x^{2}-8x=24$ . Find the values of $x$ .

How much will \ $12,000 grow in 5 years at 2% interest compounded semiannually? Use$ A=P\left(1+\frac{r}{m}\right)^{mt}$.

Determine the slope and $y$ -intercept of the line given by the equation $2x + 5y = 21$ .

Find the solution for the inequality: $-8 < -6 - f$ . Choose from: $f=9$ , $f=11$ , $f=-9$ , $f=6$ .

Find the line equation with slope $m$ through point (4,4). Answer in slope-intercept form: $m=-\frac{2}{3}$ .

Solve for $b$ in the equation $T=\frac{b-d}{k}$ .

Graph the function $g$ by reflecting $f(x)=x^{2}$ about the $x$ -axis, then shifting up 2 and left 4. Find $g(x)$ .

Find $\log_{8} 1,000$ using $\ln 8 \approx 2.08$ and $\ln 1,000 \approx 6.91$ .

What does $\ln(10)$ equal among these: $\log(10)$ , $\log_{10}(e)$ , $\log_{e}(10)$ , $10 \cdot \ln(e)$ ?

Divide the polynomials $P(x)=-x^{3}-2x+6$ by $D(x)=x+1$ using synthetic or long division. Express $P$ as $P(x)=D(x) \bullet Q(x)+R(x)$ .

Solve: $\log 8 x - \log 2 = \log 16$ for $x$ . Options: $1$ , $4$ , $\frac{9}{4}$ , $\frac{\log 16 + \log 2}{\log 8}$ .

Find the solutions to the inequality $-122 \leq -12 p$ . Choose from: $p=-3$ , $p=-7$ , $p=-4$ , $p=5$ .

Describe how to generate the next terms in the pattern: A: $5, 8, 11, 14, 17, \ldots$

Solve for $m$ in the equation $y=mx+b$ .

Find the average cost per item for manufacturing 90 items if $C=600+30x$ .

Graph the cost equation $c = 10 + \frac{1}{4} m$ and estimate $c$ for $m = 36$ .

Solve for $y$ : $3(2y + 4) = 4(2y - \frac{1}{2})$ . What is the value of $y$ ?

Solve the equation $x-9=23$ . What is the value of $x$ ? Options: $32$ , $-14$ , $14$ , $-32$ .

Find the snow depth, $d$ , on January 30 using the equation $d=-2t+64$ , where $t$ is days since Dec 31.

Solve the equation $x - 9 = 23$ . What is the value of $x$ ?

Which steps solve $\frac{3 x}{4}=\frac{7}{3}$ ? Find the solution for $x$ .

Find the sales in 1989 using the formula $S=70 x+500$ , where $x=0$ is 1982.

Find the mass of a gold sample (density 19.3 g/cm³) with a volume of 2.5 cm³ using $d=\frac{m}{v}$ . Mass: g

Find $x$ in the equation: $2x - 11 = 7x + 16$ . Options: $3$ , $-5 \frac{2}{5}$ , $-1$ , $\frac{5}{9}$ .

Solve for $y$ in the equation $Ax + By = C$ using $x$ , $A$ , $B$ , and $C$ .

Find the hours when total costs of ski rentals from Shop A ( $3 + 9h$ ) and Shop B ( $9 + 6h$ ) are equal.

Find the width $w$ of a rectangular enclosure with area $\geq 2700 \mathrm{yd}^{2}$ and perimeter $240 \mathrm{yd}$ .

Identify the rule for generating terms in these sequences: a. Pattern A: 5, 8, 11, 14, 17, ... b. Pattern B: $\frac{1}{2}, 1, 2, 4, 8, ...$

Check if Rebecca's five pairs of like terms are correct and fix any mistakes: $2.5 w$ and $-8 w$ , $\frac{1}{2}$ and $\frac{1}{2}$ , 38 and -15, $-7 c^{2}$ and $c^{2}$ , $5 a$ and $5 b$ .

What score does Paul need on his third test to average at least $80$ if he scored 83 and 75 on the first two tests?

Solve the equation $\frac{x+1-1}{3}=2-1$ .

Solve the equation $\frac{x+1-1}{3} = 2-1$ . What mistake was made? Correctly solve for $x$ .

Find the minimum number of backpacks $x$ to sell for profit where $C=98x+7,809$ and $R=190x$ . Choices: A. 718,428 B. \$2,248,992 C. 85 D. 29

Solve the inequality: $x^{2}+2 x \geq 8$ .

A plane flies at 200 mph for 225 miles ± 50 miles. Find the min and max travel time in hours. At least $h$ and at most $h$ .

Prove or disprove that there are no positive integers $a, b, c$ and integer $n>2$ such that $a^{n}+b^{n}=c^{n}$ .

Find the number of units $t$ to sell for profit if cost is $C=3t^{2}+7t$ and revenue is $R=4t^{2}+t$ .

There are 48 trails in total, with $37.5\%$ being beginner trails. Find the number of expert trails.

Combine the terms in the expression: $4 r + 9 r - 11 r + 7 r$ .

Is $q=-20$ a solution to the inequality $-5>\frac{q}{20}$ ? Answer yes or no.

Simplify: $-26 r + 7 r - 15 p - 7 p$ .

Is $b=-3$ a solution for the inequality $-6+b>-2$ ? Answer yes or no.

Find the solutions to the inequality $14 < 7 + t$ . Choose all that apply: $t=8$ , $t=7$ , $t=5$ , $t=10$ .

Evaluate $\frac{3 a+1}{b+\frac{c}{a}}$ for $a=3$ , $b=\frac{2}{3}$ , and $c=4$ .

Find the quotient and remainder of $2 x^{2}-5 x+3$ divided by $x-3$ using synthetic division.

Find the solutions for the inequality $-12 + 10g > -72$ . Which values of $g$ are valid? Options: $g=9$ , $g=-12$ , $g=11$ , $g=-5$ .

Is $t=-8$ a solution to the inequality $-52 \geq 6 t - 5$ ? Answer yes or no.

Identify the equation that is not equivalent to $c x-a=b$ : 1) $c x-a+b=2 b$ 2) $c x-a+b=0$ 3) $2 c x-2 a=2 b$ 4) $b+a=c x$

Find the number of solutions $N$ for $3(x-a)=3x-6$ . Which statements about $a$ and $N$ are correct?

Find the quotient and remainder of $x^{3}+2x+1$ divided by $x^{2}-x+3$ using long division.

Solve for $d$ in the equation $72 \cdot 5 d =$ .

Find the equivalent expression for $\left(\frac{1}{z^{3 / 5}}\right)^{-1 / 5}$ . A. $z^{3 / 25}$ B. $z^{-3 / 25}$ C. $z^{-2 / 5}$ D. $z^{2 / 5}$

a) $\log _{x} 49=2$

$-6=\frac{5 x-27}{-3}$
Simplify your answer as much as possible. $x=$

Solve for $x$ . $\frac{x+41}{6}=5$
Simplify your answer as much as possible. $x=$

9.) Consider the line $y=-8 x+2$ . (a) Find the equation of the line that is perpendicular to this line and passes through the point $(-4,5)$ . (b) Find the equation of the line that is parallel to this line and passes through the point( $4,5)$ .

d) $\log (x y)+\log \frac{y}{x}$