Browse Algebra problems in the Studdy Learning Bank!

Problem 1501

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 1502

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

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Problem 1503

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

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Problem 1504

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

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Problem 1505

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

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Problem 1506

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

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Problem 1507

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

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Problem 1508

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

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Problem 1509

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

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Problem 1510

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

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Problem 1511

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

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Problem 1512

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

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Problem 1513

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

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Problem 1514

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 1515

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

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Problem 1516

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

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Problem 1517

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

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Problem 1518

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

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Problem 1519

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 1520

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

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Problem 1521

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

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Problem 1522

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 1523

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

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Problem 1524

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

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Problem 1525

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 1526

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

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Problem 1527

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

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Problem 1528

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

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Problem 1529

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

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Problem 1530

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 1531

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 1532

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

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Problem 1533

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

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Problem 1534

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. $-\frac{1}{6}x - 4 = -1$

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Problem 1535

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

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Problem 1536

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

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Problem 1537

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

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Problem 1538

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

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Problem 1539

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

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Problem 1540

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 1541

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 1542

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

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Problem 1543

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 1544

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

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Problem 1545

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

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Problem 1546

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 1547

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

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Problem 1548

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

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Problem 1549

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 1550

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

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Problem 1551

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

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Problem 1552

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.

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Problem 1553

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

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Problem 1554

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

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Problem 1555

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

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Problem 1556

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

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Problem 1557

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

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Problem 1558

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

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Problem 1559

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

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Problem 1560

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

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Problem 1561

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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Problem 1562

Solve the linear system $17x + 17y = 15$ for integers, proper fractions, and improper fractions.

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Problem 1563

Find the cost of a cake given that the cost of a cake is twice that of a cup of tea, and 1 cake and 5 cups of tea cost $£ 21$ .

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Problem 1564

Solve $x + 14 = 35$ using mental math. What is the sum of 14 and 35? What number plus 14 equals 35? What number minus 14 equals 35?

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Problem 1565

Find real numbers $a$ and $b$ such that $(a+1)+(b-2)i=4+6i$ , where $a=\square$ and $b=\square$ .

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Problem 1566

Expand the expression $(a+2b)(4a+b)$ .

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Problem 1567

Identify the polynomial function from the given options: $f(x)=x^{2}+4 x-\frac{7}{x}$ , $f(x)=3 x^{3}-2 x^{2}+\sqrt{x}$ , $f(x)=-5 x^{-4}-3^{2}$ , $f(x)=2 x^{2}-\sqrt{7}$ , $f(x)=\frac{x+3}{2 x-6}$ .

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Problem 1568

Find the value of $y$ given the linear equation $2x + 5y = 10$ .

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Problem 1569

Find the inequality for the number of copies you can make with $\$ 3.00$ if each copy costs $\$ 0.45$ , using $x$ as the variable.

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Problem 1570

David has completed 2 oil changes and can do 1 every 2 hours. Ezra can do 3 oil changes per hour. Find the number of oil changes each has completed after a given time.
Let $x$ be the time in hours and $y_1$ and $y_2$ be the number of oil changes completed by David and Ezra, respectively.
$y_1 = 2 + \frac{x}{2}$ $y_2 = 3x$

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Problem 1571

Solve for $w$ in the equation $5=-\frac{1}{w-6}$ . Simplify the solution $w=$ .

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Problem 1572

Expand the binomial expression $(x+h)^{5}$ using the binomial formula.

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Problem 1573

Identify variables in expression $11 r + 5 h r + \pi h$ . Select all correct answers: $r$ , $h$ , $\pi$ .

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Problem 1574

Find the values to complete the equation $2(\square-4x)+\square(3x-1)=2(2x+3)$ .

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Problem 1575

Find $L$ given the equation $5 L W = V$ .

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Problem 1576

Find the value of $3+5x$ when $x=3$ .

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Problem 1577

Simplify the expression $3^{-3} \div 3^{-4} \cdot 9^{-2}$ into an integer or simplified fraction.

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Problem 1578

Solve the inequality $f + 5 \geq 8$ for the variable $f$ .

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Problem 1579

Determine if the function $f(x) = |x| + 2$ is odd, even, or neither.

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Problem 1580

Solve for $z$ in the equation $5(z+2)=15$ .

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Problem 1581

Solve the exponential equation $9^{x}=\frac{1}{\sqrt{3}}$ for the value of $x$ .

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Problem 1582

If $y$ varies directly with $x$ , and $y=12$ when $x=6$ , find $y$ when $x=3$ .

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Problem 1583

Find the value of $h(6)$ given $f(x)=x-5$ , $g(x)=-3x$ , and $h(x)=2f(x+3)+3g(x-3)$ .

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Problem 1584

Identify the horizontal and vertical shifts for the exponential function $f(x) = \frac{1}{2} \cdot (3)^{x+1} + 4$ .

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Problem 1585

Find the value of $k$ when $t=-7$ for the linear equation $k=10t-19$ .

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Problem 1586

Evaluate the cube root of $x^{6}$ when $x=2$ .

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Problem 1587

Find the linear operator from $P_3$ to $P_4$ where $L(p(x)) = x^2 p''(x) + p'(x) + p(0)$ .

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Problem 1588

Find the value of $n$ when $8n - 2 = 6n + 6$ .

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Problem 1589

Find two positive numbers with given sum that maximize their product. 59. Sum is 110. 60. Sum is 66.

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Problem 1590

Find the leftmost $x$ value by completing the square for $2x^2 + 8x + 6$ . Round your answer to the nearest 0.001.

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Problem 1591

Write each expression in the form $a + b\sqrt{7}$ . (1) $\frac{3}{\sqrt{7}}$ , (2) $\frac{5 + \sqrt{7}}{3 - \sqrt{7}}$ .

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Problem 1592

Find the roots of the quadratic equation $\mathbf{(2x-4)(x+3)=0}$ from the given factored polynomial.

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Problem 1593

Simplify $\log_3 (24) - \log_3 (8)$

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Problem 1594

Solve the system of linear equations $4x - 7y = z$ and $x = \frac{z + 7y}{4}$ for $x$ , $y$ , and $z$ .

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Problem 1595

Solve $2 d-g^{3}=A h$ for $A$ , accounting for capitalization.

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Problem 1596

Expand the expression $(x-8)(x+2)$ using the FOIL method.

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Problem 1597

Solve for $a$ where $9a=15$ . Simplify the solution for $a$ .

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Problem 1598

Find the value of $y$ given the equation $C = (y - 8)h$ .

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Problem 1599

Find the expression for 3 subtracted from $5x$ .

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Problem 1600

Solve for x in the equation $7=2(x+y)$ . The solutions are $x=7/2-y$ , $x=2/7+y$ , $x=2/7-y$ , and $x=7/2+y$ .

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Algebra

Problem 1501

Problem 1502

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

Problem 1503

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 1504

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

Problem 1505

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

Problem 1506

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 1507

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 1508

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 1509

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

Problem 1510

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

Problem 1511

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 1512

Express www as the sum of 158 and 128.

Problem 1513

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

Problem 1514

Problem 1515

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 1516

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

Problem 1517

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

Problem 1518

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 1519

19. (1 point) For the equation 2x+3=132x + 3 = 132x+3=13, which operation should you undo first?20. (2 points) Solve the equation y−17=82y - 17 = 82y−17=82. (SHOW YOUR WORK)

Problem 1520

Find the inverse of the quadratic function f(x)=x2+6x+15f(x) = x^2 + 6x + 15f(x)=x2+6x+15 by completing the square.

Problem 1521

Solve for xxx in the equation ∣x∣6=4\frac{|x|}{6}=46∣x∣​=4. Write both solutions as equations.

Problem 1522

Compute the values of a periodic function g(x)=x+1x2−x+4g(x)=\frac{x+1}{x^{2}-x+4}g(x)=x2−x+4x+1​ with period 7 on the interval [−2,5)[-2,5)[−2,5). Find all roots of g(x)g(x)g(x).

Problem 1523

Find all values of xxx that solve the equation 2x2−13x+36=152x^2 - 13x + 36 = 152x2−13x+36=15.

Problem 1524

Solve for xxx: x−12=52x - 12 = 52x−12=52. x=64x = 64x=64.

Problem 1525

Taylor uses Intermediate Value Theorem to solve x3−3x2−9=Kx^3 - 3x^2 - 9 = Kx3−3x2−9=K over [3,9][3, 9][3,9]. What is the possible value of KKK?

Problem 1526

Calculate e2ln⁡3−3e^{2 \ln 3} - 3e2ln3−3 and provide the numerical result.

Problem 1527

Simplify the inequality x−2+6x≠6+8xx-2+6 x \neq 6+8 xx−2+6x=6+8x and solve for xxx.

Problem 1528

Solve for uuu in the equation 5(u+3)=8u+245(u+3)=8u+245(u+3)=8u+24. Simplify the solution.

Problem 1529

Factor the expression z4−16z^{4} - 16z4−16. If the expression is prime, enter PRIME.

Problem 1530

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

Problem 1531

Find the two values of xxx that satisfy the quadratic equation 5.15x2+2.03x−1.69=05.15 x^{2} + 2.03 x - 1.69 = 05.15x2+2.03x−1.69=0.

Problem 1532

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

Problem 1533

Write an equation to solve for yyy in terms of xxx given that 2y=5x2y = 5x2y=5x.

Problem 1534

Solve for the variable in each equation. Write final solution as an equation.1. −8t+4=−60-8t + 4 = -60−8t+4=−602. 3=6−3z3 = 6 - 3z3=6−3z3. 65d+1=−11\frac{6}{5}d + 1 = -1156​d+1=−114. −16x−4=−1-\frac{1}{6}x - 4 = -1−61​x−4=−1

Problem 1535

Find the value of yyy in the linear equation 2x+3y=122x + 3y = 122x+3y=12.

Problem 1536

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

Problem 1537

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

Problem 1538

Solve the linear equation −23(15x+3)=−3x−9-\frac{2}{3}(15 x+3)=-3 x-9−32​(15x+3)=−3x−9 for the unknown variable xxx.

Problem 1539

Find the inverse function f−1(x)f^{-1}(x)f−1(x) for the rational function f(x)=7−5x5x+2f(x) = \frac{7-5x}{5x+2}f(x)=5x+27−5x​.

Problem 1540

Find the values of xxx and yyy that satisfy the system of equations x=7yx=7yx=7y and y3=xy^{3}=xy3=x with y≥0y \geq 0y≥0.

Problem 1541

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

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

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

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

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

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

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

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

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

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

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

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

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".

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

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

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

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.

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.

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

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 $5.15 x^{2} + 2.03 x - 1.69 = 0$ .

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

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

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. $-\frac{1}{6}x - 4 = -1$

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

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

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

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

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

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

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 $w$ in the equation $w + 7 = 5$ .

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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.

Solve the linear system $17x + 17y = 15$ for integers, proper fractions, and improper fractions.

Find the cost of a cake given that the cost of a cake is twice that of a cup of tea, and 1 cake and 5 cups of tea cost $£ 21$ .

Solve $x + 14 = 35$ using mental math. What is the sum of 14 and 35? What number plus 14 equals 35? What number minus 14 equals 35?

Find real numbers $a$ and $b$ such that $(a+1)+(b-2)i=4+6i$ , where $a=\square$ and $b=\square$ .

Expand the expression $(a+2b)(4a+b)$ .

Find the value of $y$ given the linear equation $2x + 5y = 10$ .

Find the inequality for the number of copies you can make with $\$ 3.00$ if each copy costs $\$ 0.45$ , using $x$ as the variable.

Solve for $w$ in the equation $5=-\frac{1}{w-6}$ . Simplify the solution $w=$ .

Expand the binomial expression $(x+h)^{5}$ using the binomial formula.

Identify variables in expression $11 r + 5 h r + \pi h$ . Select all correct answers: $r$ , $h$ , $\pi$ .

Find the values to complete the equation $2(\square-4x)+\square(3x-1)=2(2x+3)$ .