Browse Algebra problems in the Studdy Learning Bank!

Problem 5601

Find the equation of a line passing through (2,4) and perpendicular to $y = \frac{1}{6}x + 3$ in slope-intercept form.

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Problem 5602

Find the roots and their multiplicities of the function $f(t) = (t-3)(-6t+7)^7(t-6)^3$ .

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Problem 5603

Find the values of the integers $A$ and $B$ in the simplified expression $\frac{A x^{2}}{x y-B y}$ for $\frac{4 x y}{x-2} \cdot \frac{x^{2}}{y^{2} x}$ .

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Problem 5604

Simplify the expression $\frac{7}{2-6 \sqrt{2}}$ .

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Problem 5605

Solve the equation $0.5 x = 16$ for $x$ using the division property of equality.

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Problem 5606

Evaluate the expression $\left(3^{2}\right)^{4}$ and select the correct answer. A) $(3 \times 3)(3 \times 3 \times 3 \times 3)$ B) $(3 \times 3 \times 3 \times 3 \times 3 \times 3)$ C) $(3 \times 3)(3 \times 3)(3 \times 3)(3 \times 3)$ D) $(3 \times 3 \times 3 \times 3)(3 \times 3 \times 3 \times 3)$

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Problem 5607

Find the unknown value in the proportions: (a) $a: 6=7: 2$ and (b) $5: 4=b: 20$ .

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Problem 5608

Find the value of $(\sqrt{a})^{2}$ for any nonnegative real number $a$ .

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Problem 5609

Divide the expression $\frac{v^{2}-9}{3 v}+\frac{v^{2}+6 v+9}{6 v}$ .

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Problem 5610

Solve the quadratic equation $3x^2 + 8x - 1 = 0$ and select the correct solution set.

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Problem 5611

Solve for the variable $v$ given the equation $25.6=\frac{v}{2}$ .

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Problem 5612

Find the total number of people in the senior center dining room if 3/5 of them are men and there are 93 men.
Let $p$ be the total number of people.
Equation: $p = \frac{93}{\frac{3}{5}}$

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Problem 5613

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

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Problem 5614

Expand and simplify polynomial expressions, including binomial squares, products, and factorials. Determine equivalence of expanded polynomial expressions.
$2 x(3 x-5 x^{2}+4 y)$ $(x+4)^{2}$ $(3 x-4)(2 x+5)$ $(x+1)(x^{2}+2 x-3)$ $4 x(x+5)(x-5)$ $-2 a(a+4)^{2}$ $(x+2)(x-5)(x-2)$ $(2 x+1)(3 x-5)(4-x)$ $(9 a-5)^{3}$ $(a-b+c-d)(a+b-c-d)$

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Problem 5615

Find the positive value of $p$ that satisfies the equation $\sqrt{4p^2 + 28} - 8 = 0$ .

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Problem 5616

Solve for $y$ in the equation $5 y^{\frac{2}{3}} + 7 = 27$ .

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Problem 5617

Solve the linear equation $3x + 5 = 9x + 8$ for the unknown variable $x$ .

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Problem 5618

Determine if all numbers are solutions to the inequality $\frac{60}{9} > 3 \times 5$ .

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Problem 5619

Find the sum of two linear functions $h(n) = 2n - 4$ and $g(n) = n - 2$ .

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Problem 5620

Solve the quadratic equation $-7x^2 - 2x + 6 = 0$ and find its roots.

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Problem 5621

Find inverse function $f^{-1}(x)$ of $f(x)=3x+4$ , then verify $f(f^{-1}(x))=x$ and $f^{-1}(f(x))=x$ .

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Problem 5622

Solve for $x$ given the equation $4x = 4.56$ .

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Problem 5623

Simplify the expression: $\frac{1-2 x}{1+x} * \frac{-7-7 x}{2 x-1}$ .

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Problem 5624

Solve for $w$ in the formula $v = \frac{1}{3} w b$ .

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Problem 5625

Simplify the expression $(b^{12})^{3}$ and write the answer as a power.

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Problem 5626

Solve for $n$ if $P(n, 2)=1482$ . Alicia's formula is $n^{2}-n-1482=0$ . Explain how she created the formula and use it to solve for $n$ .

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Problem 5627

Express quadratic functions in standard form, find y-intercept. a) $f(x)=3x(x-4)$ , c) $f(x)=2(x-4)(3x+2)$ , b) $f(x)=(x-5)(x+7)$ , d) $f(x)=(3x-4)(2x+5)$ .

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Problem 5628

Find the value of $p$ that satisfies the equation $\frac{6p+4}{6}=\frac{4p-8}{3}$ .

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Problem 5629

Analyze exponential growth/decay functions: $y=(\frac{3}{2})^{x}$ , $y=-4(0.5)^{x}$ , $y=4(0.25)^{x}$ , $y=-2(2)^{x}$ . Determine growth/decay, y-intercept, asymptote.

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Problem 5630

Find the inverse of the one-to-one functions $g$ and $h$ , where $g=\{(1,3),(3,-1),(4,-7),(6,8),(7,6)\}$ and $h(x)=\frac{x-13}{5}$ . Determine $g^{-1}(6)$ , $h^{-1}(x)$ , and $\left(h \circ h^{-1}\right)(-4)$ .

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Problem 5631

Translate the phrase "42 decreased by twice Vanessa's age" into an algebraic expression using the variable $v$ to represent Vanessa's age.

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Problem 5632

Solve for $y$ in the equation $-63=-2 y^{2}+9$ , expressing the answer as an integer or in simplest radical form.

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Problem 5633

Solve the linear equation $4b + 6 = 2 - b + 4$ and select the correct solution.

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Problem 5634

Solve the linear inequality $18 < 4m - 15$ for the variable $m$ .

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Problem 5635

Find the equation that represents "three minus the difference of a number and one equals one-half of the difference of three times the same number and four".
$3 - (n - 1) = \frac{1}{2}(3n - 4)$

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Problem 5636

Solve the equation $5^{\frac{x}{3}}=4$ . The exact solution is $x=\log_5(4)$ . The approximate solution, rounded to 4 decimal places, is $x=3.0910$ .

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Problem 5637

Find the error in Jane's solution of the quadratic equation $x^2 - 5x - 24 = 0$ using the quadratic formula.

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Problem 5638

Find the range of $x$ values where the function $f(x) = x^3 + 3x^2 - 9x + 7$ is increasing.

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Problem 5639

Solve the linear equation $6x + 6 = 0$ for the unknown variable $x$ .

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Problem 5640

Find a recursive formula for the number of seats in each row of a movie theater, where the explicit formula is $a_{n}=6+6 n$ and $n$ represents the row number.

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Problem 5641

Find the value of $x$ in the system of linear equations $15x + 7y = 4$ , $-5x - 7y = 2$ , and $10x = 2$ . Enter the answer as a simplified fraction.

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Problem 5642

Plot the quadratic equation $y = x^{2} + 10x + 21$ and find its roots using the graph.

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Problem 5643

Evaluate the factorial ratio $\frac{16 !}{13 !}$ . The solution is $\square$ .

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Problem 5644

Find the value of $n$ that satisfies the equation $n \times \frac{3}{4} = \frac{3}{16}$ .

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Problem 5645

Graph the set of all $(x, y)$ satisfying $x + 2y > 2$ .

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Problem 5646

Find the degree of the polynomial equation $2 x^{5} - 6 x^{4} = 0$ .

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Problem 5647

Solve for h in the equation $7x + 4 = 7x + h$ to find the value of h that results in zero solutions.

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Problem 5648

Solve for $f$ by completing the square: $2f^2 - 56f + 34 = 0$ . Express your answers as integers, simplified fractions, or rounded decimals.

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Problem 5649

Divide $4x^3 - 16x^2 + 18x - 28$ by $-x + 3$ using long division. Find the quotient and remainder.

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Problem 5650

Solve for $x$ in the inequality $3x - 7 > 7x + 9$ and graph the solution.

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Problem 5651

Find the number $x$ such that $x + 5/x = 6$ .

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Problem 5652

Solve for y: $\sqrt{y+4}-4=0$

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Problem 5653

Find the gradient of the line segment connecting the points $C(-5,6)$ and $D(2,-1)$ .

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Problem 5654

Evaluate the expression $x^{2} + 4y \div 2w + 3z$ when $w=1, x=4, y=7, z=0$ .

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Problem 5655

Demarco substitutes a value for $x$ in $\frac{1}{2} x=4$ . How can Demarco determine if the value is a solution?

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Problem 5656

Multiply and simplify the expression $6 x y^{3} z \cdot 3 x^{2} y x^{2}$ .

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Problem 5657

Solve the rational equation $\frac{4}{x+4}-\frac{2}{x-1}=\frac{4}{x^{2}+3x-4}$ .

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Problem 5658

Solve for the integer value(s) of $n$ in the equation $-62=-8 n^{2}+10$ .

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Problem 5659

Simplify $3u + 3u = 42$ to find the value of $u$ .

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Problem 5660

Solve $x^{2}+28x=5$ by completing the square. Select the correct answer: A) $x=14 \pm \sqrt{191}$ B) $x=-14 \pm \sqrt{191}$ C) $x=-14 \pm \sqrt{201}$ D) $x=14 \pm \sqrt{201}$

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Problem 5661

Simplify the equation $2(3v+4)=26$ to find the value of $v$ .

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Problem 5662

Find the least common denominator (LCD) of the rational expressions $\frac{x}{x^{2}-4}, \frac{3}{x}, \frac{9}{8-4x}$ . The LCD is $\frac{(x^{2}-4)x(8-4x)}{x(8-4x)}$ .

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Problem 5663

Solve for y, where 6 is greater than or equal to (y/8) - 4.

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Problem 5664

Solve the system of linear equations $4x - y = 11$ and $x + y = 4$ using the elimination method. The system has no solution.

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Problem 5665

Find the solutions to the equation $4x+21=-\left(\frac{1}{3}\right)^{x+4}+6$ .

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Problem 5666

Compare the doubling times using approximate and exact formulas. Find the population after 30 years if a nation of 100 million grows at $9\%$ per year.
The approximate doubling time is $\frac{\ln(2)}{\ln(1.09)} \approx \square$ years and the exact doubling time is $\frac{\ln(2)}{\ln(1.09)} \approx \square$ years.

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Problem 5667

Solve for the value of $f$ that satisfies the inequality $-21 > 13 - 17f$ .

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Problem 5668

Simplify the expression $25 a^{2} - 4 b^{2}$ to find the preferred form.

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Problem 5669

Solve the equation $2x=26$ . Which operation should be performed to isolate $x$ ?

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Problem 5670

Find the quadratic function equation from the given table of $(x, y)$ values: $y = a(x - b)^2 + c$

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Problem 5671

Solve the system of linear equations: $50x - 5y = -75$ , $y = 2$ , $y = 2x$ .

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Problem 5672

Subtract the two polynomials: $\left(3 x^{5}-2 x^{4}-5\right)-\left(2 x^{4}+x^{2}-10\right)$ .

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Problem 5673

Find the value of $m$ and evaluate $x+14$ when $x=8$ .

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Problem 5674

Camelle needs to order 4 practice jerseys for each of $y$ players. How many total practice jerseys does she need to order?

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Problem 5675

Find the value of $(-2)^{4}(-2)^{-1}$ .

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Problem 5676

Solve for $w$ in the equation $\frac{w}{3}-14=26$ .

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Problem 5677

Find an equation with zeros at -3 and 13, passing through (4,21). Express in factored form $y=a(x-(-3))(x-13)$ and general form $y=a x^{2}+b x+c$ .

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Problem 5678

Solve for $x$ and express your answers as exact roots: (a) $(x-3)^2 = 4$ , (b) $(x+2)^2 = 9$ .

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Problem 5679

Find the quadratic function with zeros at $x=0$ and $x=4$ that passes through the point $(-1,-10)$ .

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Problem 5680

Solve for $v$ in the equation $63=5v-17$ .

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Problem 5681

What does $k$ represent in $\mathbf{y}=\mathbf{k x}$ ? Constant of proportionality.

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Problem 5682

Identify the graph of $f(x)=x^{2}-25$ . Label the vertex, axis of symmetry, and x-intercepts. Find the domain (all real numbers) and range.

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Problem 5683

Simplify $x^{5}y^{3}(-9y^{3})$

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Problem 5684

Solve the system of linear equations $x-2y=6, 2x+5y=3$ and classify it. Solve the system $y=2x-6, 4x-2y=12$ and classify it.

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Problem 5685

If $f^{-1}$ is the inverse of $f$ , then $f$ and $f^{-1}$ graphs are symmetric about $y=x$ .

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Problem 5686

Simplify the expression $7(3x + 3) - 5$ .

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Problem 5687

Find the solution to $-4|-2 x+6|=-24$ . The possible solutions are $x=0$ or $x=-6$ .

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Problem 5688

Find values of $x$ satisfying $2|x+5.3|=4.2$ . $x$ can be -3.2 or 7.4.

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Problem 5689

Find the amounts of two Italian dressings (6% and 12% vinegar) to make 330 mL of 11% vinegar dressing.

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Problem 5690

Solve for the value of $x$ that satisfies the equation $2(4x + 7) = 62$ .

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Problem 5691

Graph the exponential function $g(x) = \frac{1}{4}(5)^{x}$ . Plot 5 points on the graph and use the graph-a-function tool.

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Problem 5692

Determine which choice, if any, uses deductive reasoning to show that the sum of 3 even integers is even.
$2x + 2y + 2z = 2(x + y + z)$

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Problem 5693

Solve radical equations using isolation, squaring, and checking for extraneous solutions. Practice: $\sqrt{6 x+9}+2=11$ , $\sqrt{x-3}+3=x$ .

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Problem 5694

Solve the two-step equation $-0.45 x+0.33=-0.66$ . What is the solution?

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Problem 5695

Find the real roots of each quadratic equation. If no real roots, use a graph to explain. a) $0=x^{2}-4x+3$ b) $0=2x^{2}-7x-15$ c) $0=-x^{2}-2x+3$

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Problem 5696

Find the equation with the correct sign on the product of the numbers.
A. $17 \cdot 3=-51$ B. $(-11) 9=99$ C. $25(-5)=125$ D. $(-12)(-12)=144$

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Problem 5697

Simplify the expression $(x-3y)-(3x+3y)$ .

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Problem 5698

Convert the equation from vertex form to standard form: $y = (x + 4)^{2} - 12$

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Problem 5699

Solve for $x$ in the equation $x - (-6) = 15$ .

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Problem 5700

Find the equation that matches "38 minus a number is 19".
A. $38-n=19$ B. $\frac{38}{n}=19$ C. $\frac{n}{19}=38$ D. $n-38=19$

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Algebra

Problem 5601

Find the equation of a line passing through (2,4) and perpendicular to y=16x+3y = \frac{1}{6}x + 3y=61​x+3 in slope-intercept form.

Problem 5602

Find the roots and their multiplicities of the function f(t)=(t−3)(−6t+7)7(t−6)3f(t) = (t-3)(-6t+7)^7(t-6)^3f(t)=(t−3)(−6t+7)7(t−6)3.

Problem 5603

Find the values of the integers AAA and BBB in the simplified expression Ax2xy−By\frac{A x^{2}}{x y-B y}xy−ByAx2​ for 4xyx−2⋅x2y2x\frac{4 x y}{x-2} \cdot \frac{x^{2}}{y^{2} x}x−24xy​⋅y2xx2​.

Problem 5604

Simplify the expression 72−62\frac{7}{2-6 \sqrt{2}}2−62​7​.

Problem 5605

Solve the equation 0.5x=160.5 x = 160.5x=16 for xxx using the division property of equality.

Problem 5606

Problem 5607

Find the unknown value in the proportions: (a) a:6=7:2a: 6=7: 2a:6=7:2 and (b) 5:4=b:205: 4=b: 205:4=b:20.

Problem 5608

Find the value of (a)2(\sqrt{a})^{2}(a​)2 for any nonnegative real number aaa.

Problem 5609

Divide the expression v2−93v+v2+6v+96v\frac{v^{2}-9}{3 v}+\frac{v^{2}+6 v+9}{6 v}3vv2−9​+6vv2+6v+9​.

Problem 5610

Solve the quadratic equation 3x2+8x−1=03x^2 + 8x - 1 = 03x2+8x−1=0 and select the correct solution set.

Problem 5611

Solve for the variable vvv given the equation 25.6=v225.6=\frac{v}{2}25.6=2v​.

Problem 5612

Find the total number of people in the senior center dining room if 3/5 of them are men and there are 93 men.Let ppp be the total number of people.Equation: p=9335p = \frac{93}{\frac{3}{5}}p=53​93​

Problem 5613

Solve for www in the equation −5+w=7-5+w=7−5+w=7.

Problem 5614

Problem 5615

Find the positive value of ppp that satisfies the equation 4p2+28−8=0\sqrt{4p^2 + 28} - 8 = 04p2+28​−8=0.

Problem 5616

Solve for yyy in the equation 5y23+7=275 y^{\frac{2}{3}} + 7 = 275y32​+7=27.

Problem 5617

Solve the linear equation 3x+5=9x+83x + 5 = 9x + 83x+5=9x+8 for the unknown variable xxx.

Problem 5618

Determine if all numbers are solutions to the inequality 609>3×5\frac{60}{9} > 3 \times 5960​>3×5.

Problem 5619

Find the sum of two linear functions h(n)=2n−4h(n) = 2n - 4h(n)=2n−4 and g(n)=n−2g(n) = n - 2g(n)=n−2.

Problem 5620

Solve the quadratic equation −7x2−2x+6=0-7x^2 - 2x + 6 = 0−7x2−2x+6=0 and find its roots.

Problem 5621

Find inverse function f−1(x)f^{-1}(x)f−1(x) of f(x)=3x+4f(x)=3x+4f(x)=3x+4, then verify f(f−1(x))=xf(f^{-1}(x))=xf(f−1(x))=x and f−1(f(x))=xf^{-1}(f(x))=xf−1(f(x))=x.

Problem 5622

Solve for xxx given the equation 4x=4.564x = 4.564x=4.56.

Problem 5623

Simplify the expression: 1−2x1+x∗−7−7x2x−1\frac{1-2 x}{1+x} * \frac{-7-7 x}{2 x-1}1+x1−2x​∗2x−1−7−7x​.

Problem 5624

Solve for www in the formula v=13wbv = \frac{1}{3} w bv=31​wb.

Problem 5625

Simplify the expression (b12)3(b^{12})^{3}(b12)3 and write the answer as a power.

Problem 5626

Solve for nnn if P(n,2)=1482P(n, 2)=1482P(n,2)=1482. Alicia's formula is n2−n−1482=0n^{2}-n-1482=0n2−n−1482=0. Explain how she created the formula and use it to solve for nnn.

Problem 5627

Express quadratic functions in standard form, find y-intercept. a) f(x)=3x(x−4)f(x)=3x(x-4)f(x)=3x(x−4), c) f(x)=2(x−4)(3x+2)f(x)=2(x-4)(3x+2)f(x)=2(x−4)(3x+2), b) f(x)=(x−5)(x+7)f(x)=(x-5)(x+7)f(x)=(x−5)(x+7), d) f(x)=(3x−4)(2x+5)f(x)=(3x-4)(2x+5)f(x)=(3x−4)(2x+5).

Problem 5628

Find the value of ppp that satisfies the equation 6p+46=4p−83\frac{6p+4}{6}=\frac{4p-8}{3}66p+4​=34p−8​.

Problem 5629

Analyze exponential growth/decay functions: y=(32)xy=(\frac{3}{2})^{x}y=(23​)x, y=−4(0.5)xy=-4(0.5)^{x}y=−4(0.5)x, y=4(0.25)xy=4(0.25)^{x}y=4(0.25)x, y=−2(2)xy=-2(2)^{x}y=−2(2)x. Determine growth/decay, y-intercept, asymptote.

Problem 5630

Problem 5631

Translate the phrase "42 decreased by twice Vanessa's age" into an algebraic expression using the variable vvv to represent Vanessa's age.

Problem 5632

Solve for yyy in the equation −63=−2y2+9-63=-2 y^{2}+9−63=−2y2+9, expressing the answer as an integer or in simplest radical form.

Problem 5633

Solve the linear equation 4b+6=2−b+44b + 6 = 2 - b + 44b+6=2−b+4 and select the correct solution.

Problem 5634

Solve the linear inequality 18<4m−1518 < 4m - 1518<4m−15 for the variable mmm.

Problem 5635

Find the equation that represents "three minus the difference of a number and one equals one-half of the difference of three times the same number and four".3−(n−1)=12(3n−4)3 - (n - 1) = \frac{1}{2}(3n - 4)3−(n−1)=21​(3n−4)

Problem 5636

Solve the equation 5x3=45^{\frac{x}{3}}=453x​=4. The exact solution is x=log⁡5(4)x=\log_5(4)x=log5​(4). The approximate solution, rounded to 4 decimal places, is x=3.0910x=3.0910x=3.0910.

Problem 5637

Find the error in Jane's solution of the quadratic equation x2−5x−24=0x^2 - 5x - 24 = 0x2−5x−24=0 using the quadratic formula.

Problem 5638

Find the range of xxx values where the function f(x)=x3+3x2−9x+7f(x) = x^3 + 3x^2 - 9x + 7f(x)=x3+3x2−9x+7 is increasing.

Problem 5639

Solve the linear equation 6x+6=06x + 6 = 06x+6=0 for the unknown variable xxx.

Problem 5640

Find a recursive formula for the number of seats in each row of a movie theater, where the explicit formula is an=6+6na_{n}=6+6 nan​=6+6n and nnn represents the row number.

Problem 5641

Find the value of xxx in the system of linear equations 15x+7y=415x + 7y = 415x+7y=4, −5x−7y=2-5x - 7y = 2−5x−7y=2, and 10x=210x = 210x=2. Enter the answer as a simplified fraction.

Find the equation of a line passing through (2,4) and perpendicular to $y = \frac{1}{6}x + 3$ in slope-intercept form.

Find the roots and their multiplicities of the function $f(t) = (t-3)(-6t+7)^7(t-6)^3$ .

Find the values of the integers $A$ and $B$ in the simplified expression $\frac{A x^{2}}{x y-B y}$ for $\frac{4 x y}{x-2} \cdot \frac{x^{2}}{y^{2} x}$ .

Simplify the expression $\frac{7}{2-6 \sqrt{2}}$ .

Solve the equation $0.5 x = 16$ for $x$ using the division property of equality.

Find the unknown value in the proportions: (a) $a: 6=7: 2$ and (b) $5: 4=b: 20$ .

Find the value of $(\sqrt{a})^{2}$ for any nonnegative real number $a$ .

Divide the expression $\frac{v^{2}-9}{3 v}+\frac{v^{2}+6 v+9}{6 v}$ .

Solve the quadratic equation $3x^2 + 8x - 1 = 0$ and select the correct solution set.

Solve for the variable $v$ given the equation $25.6=\frac{v}{2}$ .

Find the total number of people in the senior center dining room if 3/5 of them are men and there are 93 men.
Let $p$ be the total number of people.
Equation: $p = \frac{93}{\frac{3}{5}}$

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

Find the positive value of $p$ that satisfies the equation $\sqrt{4p^2 + 28} - 8 = 0$ .

Solve for $y$ in the equation $5 y^{\frac{2}{3}} + 7 = 27$ .

Solve the linear equation $3x + 5 = 9x + 8$ for the unknown variable $x$ .

Determine if all numbers are solutions to the inequality $\frac{60}{9} > 3 \times 5$ .

Find the sum of two linear functions $h(n) = 2n - 4$ and $g(n) = n - 2$ .

Solve the quadratic equation $-7x^2 - 2x + 6 = 0$ and find its roots.

Find inverse function $f^{-1}(x)$ of $f(x)=3x+4$ , then verify $f(f^{-1}(x))=x$ and $f^{-1}(f(x))=x$ .

Solve for $x$ given the equation $4x = 4.56$ .

Simplify the expression: $\frac{1-2 x}{1+x} * \frac{-7-7 x}{2 x-1}$ .

Solve for $w$ in the formula $v = \frac{1}{3} w b$ .

Simplify the expression $(b^{12})^{3}$ and write the answer as a power.

Solve for $n$ if $P(n, 2)=1482$ . Alicia's formula is $n^{2}-n-1482=0$ . Explain how she created the formula and use it to solve for $n$ .

Express quadratic functions in standard form, find y-intercept. a) $f(x)=3x(x-4)$ , c) $f(x)=2(x-4)(3x+2)$ , b) $f(x)=(x-5)(x+7)$ , d) $f(x)=(3x-4)(2x+5)$ .

Find the value of $p$ that satisfies the equation $\frac{6p+4}{6}=\frac{4p-8}{3}$ .

Analyze exponential growth/decay functions: $y=(\frac{3}{2})^{x}$ , $y=-4(0.5)^{x}$ , $y=4(0.25)^{x}$ , $y=-2(2)^{x}$ . Determine growth/decay, y-intercept, asymptote.

Translate the phrase "42 decreased by twice Vanessa's age" into an algebraic expression using the variable $v$ to represent Vanessa's age.

Solve for $y$ in the equation $-63=-2 y^{2}+9$ , expressing the answer as an integer or in simplest radical form.

Solve the linear equation $4b + 6 = 2 - b + 4$ and select the correct solution.

Solve the linear inequality $18 < 4m - 15$ for the variable $m$ .

Find the equation that represents "three minus the difference of a number and one equals one-half of the difference of three times the same number and four".
$3 - (n - 1) = \frac{1}{2}(3n - 4)$

Solve the equation $5^{\frac{x}{3}}=4$ . The exact solution is $x=\log_5(4)$ . The approximate solution, rounded to 4 decimal places, is $x=3.0910$ .

Find the error in Jane's solution of the quadratic equation $x^2 - 5x - 24 = 0$ using the quadratic formula.

Find the range of $x$ values where the function $f(x) = x^3 + 3x^2 - 9x + 7$ is increasing.

Solve the linear equation $6x + 6 = 0$ for the unknown variable $x$ .

Find a recursive formula for the number of seats in each row of a movie theater, where the explicit formula is $a_{n}=6+6 n$ and $n$ represents the row number.

Find the value of $x$ in the system of linear equations $15x + 7y = 4$ , $-5x - 7y = 2$ , and $10x = 2$ . Enter the answer as a simplified fraction.

Plot the quadratic equation $y = x^{2} + 10x + 21$ and find its roots using the graph.

Evaluate the factorial ratio $\frac{16 !}{13 !}$ . The solution is $\square$ .

Find the value of $n$ that satisfies the equation $n \times \frac{3}{4} = \frac{3}{16}$ .

Graph the set of all $(x, y)$ satisfying $x + 2y > 2$ .

Find the degree of the polynomial equation $2 x^{5} - 6 x^{4} = 0$ .

Solve for h in the equation $7x + 4 = 7x + h$ to find the value of h that results in zero solutions.

Solve for $f$ by completing the square: $2f^2 - 56f + 34 = 0$ . Express your answers as integers, simplified fractions, or rounded decimals.

Divide $4x^3 - 16x^2 + 18x - 28$ by $-x + 3$ using long division. Find the quotient and remainder.

Solve for $x$ in the inequality $3x - 7 > 7x + 9$ and graph the solution.

Find the number $x$ such that $x + 5/x = 6$ .

Solve for y: $\sqrt{y+4}-4=0$

Find the gradient of the line segment connecting the points $C(-5,6)$ and $D(2,-1)$ .

Evaluate the expression $x^{2} + 4y \div 2w + 3z$ when $w=1, x=4, y=7, z=0$ .

Demarco substitutes a value for $x$ in $\frac{1}{2} x=4$ . How can Demarco determine if the value is a solution?

Multiply and simplify the expression $6 x y^{3} z \cdot 3 x^{2} y x^{2}$ .

Solve the rational equation $\frac{4}{x+4}-\frac{2}{x-1}=\frac{4}{x^{2}+3x-4}$ .

Solve for the integer value(s) of $n$ in the equation $-62=-8 n^{2}+10$ .

Simplify $3u + 3u = 42$ to find the value of $u$ .

Solve $x^{2}+28x=5$ by completing the square. Select the correct answer: A) $x=14 \pm \sqrt{191}$ B) $x=-14 \pm \sqrt{191}$ C) $x=-14 \pm \sqrt{201}$ D) $x=14 \pm \sqrt{201}$

Simplify the equation $2(3v+4)=26$ to find the value of $v$ .

Find the least common denominator (LCD) of the rational expressions $\frac{x}{x^{2}-4}, \frac{3}{x}, \frac{9}{8-4x}$ . The LCD is $\frac{(x^{2}-4)x(8-4x)}{x(8-4x)}$ .

Solve the system of linear equations $4x - y = 11$ and $x + y = 4$ using the elimination method. The system has no solution.

Find the solutions to the equation $4x+21=-\left(\frac{1}{3}\right)^{x+4}+6$ .

Solve for the value of $f$ that satisfies the inequality $-21 > 13 - 17f$ .

Simplify the expression $25 a^{2} - 4 b^{2}$ to find the preferred form.

Solve the equation $2x=26$ . Which operation should be performed to isolate $x$ ?

Find the quadratic function equation from the given table of $(x, y)$ values: $y = a(x - b)^2 + c$

Solve the system of linear equations: $50x - 5y = -75$ , $y = 2$ , $y = 2x$ .

Subtract the two polynomials: $\left(3 x^{5}-2 x^{4}-5\right)-\left(2 x^{4}+x^{2}-10\right)$ .

Find the value of $m$ and evaluate $x+14$ when $x=8$ .

Camelle needs to order 4 practice jerseys for each of $y$ players. How many total practice jerseys does she need to order?