Browse Math problems in the Studdy Learning Bank!

Problem 2501

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

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Problem 2502

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 2503

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 2504

Find the derivative $g'(u)$ of $g(u) = \int_{3}^{u} \frac{-2}{x+x^{2}} dx$ using the Fundamental Theorem of Calculus.

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Problem 2505

Vergleiche das Volumen eines Quaders mit $a=4 \mathrm{~cm}$ , $b=2,5 \mathrm{~cm}$ , $c=6 \mathrm{~cm}$ und eines Würfels mit $a=4 \mathrm{~cm}$ .

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Problem 2506

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 2507

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

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Problem 2508

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 2509

Find the transition matrix from basis $F$ to basis $E$ where $E=[(1,2)^{T},(3,7)^{T}]$ and $F=[(1,-2)^{T},(3,-5)^{T}]$ in $\mathbb{R}^{2}$ .

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Problem 2510

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

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Problem 2511

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 2512

Find the value of the expression $h-7$ when $h=21$ .

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Problem 2513

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 2514

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

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Problem 2515

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

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Problem 2516

Simplify the expression $2 \cdot 4^{\frac{1}{2}}$ to an integer or simplified fraction.

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Problem 2517

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

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Problem 2518

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

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Problem 2519

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

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Problem 2520

Rewrite $f(x) = \log_a x$ to show $-f(x) = \log_{1/a} x$ . Let $y = f(x)$ , then $y = \log_a x$ . Rewrite the left side of the equation using logarithm properties to show $-f(x) = \log_{1/a} x$ .

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Problem 2521

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

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Problem 2522

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

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Problem 2523

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

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Problem 2524

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

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Problem 2525

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

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Problem 2526

Find the maximum number of graduated cylinders a scientist can purchase for $\$ 500$ , given the cost is $\$ 12.10$ each for 1 to 3, $\$ 11.07$ each for 4-47, and $\$ 10.20$ each for 48 or more.

See Solution

Problem 2527

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

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Problem 2528

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

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Problem 2529

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 2530

Find the sales tax and total cost of an item given its selling price and sales tax rate. Selling Price: $\$ 40.00$ , Sales Tax Rate: $4 \%$ , Sales Tax: ?

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Problem 2531

Calculate the area of a circle with $r=6\,\mathrm{cm}$ using $\pi=3$ .

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Problem 2532

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 2533

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

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Problem 2534

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

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Problem 2535

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 2536

Find the closest value to $4,367 \div 0.004$ .

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Problem 2537

Find the Maclaurin series expansions up to 5th degree for $y=\sin x \cos x$ , $y=\ln(x+1)$ , and $y=x \cos x$ .

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Problem 2538

Find the fraction of a rectangle divided into 10 equal boxes, where 6 boxes are shaded.

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Problem 2539

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

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Problem 2540

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

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Problem 2541

Complementary angles $a$ and $b$ have measures $42^{\circ}$ and $x^{\circ}$ . Which equation represents $a + b = 90^{\circ}$ ?

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Problem 2542

Find the value of the expression $-3 \times 8 - 52 - 19$ .

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Problem 2543

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 2544

Find Long Light Corporation's operating profit given gross profit of $1,200,000$ , operating expenses of $360,000$ , interest expenses of $125,000$ , tax rate of $21\%$ , and preferred stock dividends of $62,000$ with $15,000$ common stock shares outstanding.

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Problem 2545

Calculate the annual payment for a $\$ 140000$ car loan with a 5-year term and $12\%$ annual interest rate.

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Problem 2546

Simplify the expression $5 \cdot 0$ .

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Problem 2547

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 2548

What is the formula to find a weighted mean? $\frac{\Sigma w \cdot x}{\Sigma w}$

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Problem 2549

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

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Problem 2550

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

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Problem 2551

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 2552

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

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Problem 2553

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

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Problem 2554

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

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Problem 2555

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

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Problem 2556

Find the total amounts of nitrogen ( $N$ ), phosphoric acid ( $P_2O_5$ ), and potash ( $K_2O$ ) in a mixture of 200 pounds of Vigoro and 500 pounds of Parker's fertilizers.

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Problem 2557

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

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Problem 2558

Find the length of side $p$ in $\triangle \mathrm{PQR}$ given $r=38 \mathrm{~cm}, m \angle \mathrm{P}=49^{\circ}, m \angle \mathrm{Q}=127^{\circ}$ .

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Problem 2559

Solve the indefinite integral of $\cot^{-1}x$ by selecting the correct antiderivative.

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Problem 2560

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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Problem 2561

Find the range of $f(x) = \frac{1}{\sqrt{|x^2 - 4|}}$ .

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Problem 2562

Solve the equation $x+1=11$ and find all real solutions.

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Problem 2563

Divide the polynomial $\left(x^{2}-4\right)$ by $(x-2)$ using factoring.

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Problem 2564

Solve the linear equation $2(5x+4) = 4(x+3) + 4 + 2x$ and select the correct solution.

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Problem 2565

Find $a$ and $b$ such that $P(x) = (2a - b)x^2 + (b - 6)x + a - 3$ is the zero polynomial.

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Problem 2566

Determine if the equation $y^{2}=3x-2$ represents a function.

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Problem 2567

Find the value of the expression $\frac{6^{\frac{5}{2}}}{6}$ .

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Problem 2568

Find the derivative of the function $y=\frac{\sqrt{x}-5}{\sqrt{x}+6}$ .

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Problem 2569

Solve the linear system $Ax=b$ where $A$ is a $3\times 3$ matrix, $x=\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}$ , and $b=\begin{bmatrix}5\\0\\-5\end{bmatrix}$ . If $A^{-1}=\begin{bmatrix}1&4&-1\\2&-3&2\\0&5&-4\end{bmatrix}$ , then $x_3=$

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Problem 2570

Find the height of a building in New York, given that the angle of elevation to its top is 5 degrees and the distance from its base is 1 mile. Round the height to the nearest tenth. Hint: 1 mile = $5280$ feet. The answer is in feet.

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Problem 2571

Find the value of $f(-2)$ given $f(x)=4x^3+7x$ .

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Problem 2572

Solve for $w$ in the quadratic equation $4 w^{2} = -11 w - 6$ . If there are multiple solutions, list them separately.

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Problem 2573

Simplify the expression $6 \cos \left(\frac{\pi}{2}-x\right) \sec x$ using fundamental identities. Multiple correct forms.

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Problem 2574

Find the volume of a solid with a triangular base and semicircular cross-sections perpendicular to the $x$ -axis. The triangle has vertices at $(0,0), (2,0), (0,2)$ .
Select one: $V=\int_{0}^{2} \frac{\pi}{8}(2-x)^{2} d x$ $V=\int_{0}^{2} \frac{\pi}{4}(x-2)^{2} d x$

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Problem 2575

Find the expression equivalent to $5.8 \div 1.15$ .

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Problem 2576

Find the value of $c$ given the equation $-0.1 = -10c$ .

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Problem 2577

Graph the linear function $y = -2x$ .

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Problem 2578

Describe the linear relationship between $x$ and $y$ . Write the equation $x + 12 = y$ . Find the flower's height after 9 days.

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Problem 2579

Expand the expression $(2x+6)(2x+5)$ and express the result as a trinomial.

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Problem 2580

Solve the quadratic equation $b(b-1) = 2 + b^{2}$ for $b$ .

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Problem 2581

Find the possible values of $x$ and $y$ for two distinct points, $(5, -2)$ and $(x, y)$ , to represent a function.

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Problem 2582

Redefine the problem: Skateboard shop gets 92 wheels, puts 4 per board. Write a function $g(x)$ to describe the number of wheels left after assembling $x$ boards.

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Problem 2583

Solve the equation $8|\ln x|-16=0$ . The solution set is $\{e^{2}, e^{-2}\}$ .

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Problem 2584

Find the value of $x$ in the equation $y^{12} = y^{2x}$ .

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Problem 2585

Rewrite the equation $y = \frac{9}{4x^5}$ to not be a fraction.

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Problem 2586

Calculate $8 \times 10^{18} \div 4 \times 10^{3}$ and express the result in standard form.

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Problem 2587

Trouver l'ordonnée à l'origine de la fonction $y=5^{x}$ .

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Problem 2588

Solve the equation $32-32x = (6x+4)(x-1)$ by factoring. The solution set is $\{-4, 1\}$ .

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Problem 2589

Find the integral of $2f(x) + g(x)$ from 4 to 9 given $\int_{4}^{9} f(x) dx=1$ and $\int_{9}^{4} g(x) dx=5$ .

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Problem 2590

Solve the exponential equation $e^{-2x} = 18$ for the value of $x$ .

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Problem 2591

Solve for $u$ in the equation $9=u-8$ .

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Problem 2592

Convert the decimal number $27.35$ to a mixed number in simplest form.

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Problem 2593

Identify the independent and dependent variables in the relationship between paycheck and work hours for an hourly wage job. $Paycheck$ is the $dependent$ variable and $number\ of\ hours\ of\ work$ is the $independent$ variable.

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Problem 2594

Find the equation equivalent to $2x + 180 = 2x^2$ . Options: $2x^2 + 2x + 180 = 0$ , $2x^2 - 2x + 180 = 0$ , $2x^2 + 2x - 180 = 0$ , $2x^2 - 2x - 180 = 0$ .

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Problem 2595

Find the other factor in the denominator when $x = -3$ is a restricted value for $f(x) = \frac{\text{anything}}{\text{not zero}}$ .

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Problem 2596

Hani maximizes utility with goods $X$ and $Y$ given prices $\$ 5$ and $\$ 8$ and income $\$ 120$ . What are the optimal units of $X$ and $Y$ ?

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Problem 2597

Solve for $w$ where $\frac{3}{9}=\frac{w}{12}$ . Simplify the solution $w$ as much as possible.

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Problem 2598

Solve $\frac{2}{3} \div \frac{4}{5}$ . SELECT ALL THAT APPLY: $\frac{5}{6}$ , $\frac{8}{15}$ , $\frac{12}{10}$ , $\frac{10}{12}$ , $1 \frac{5}{6}$ .

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Problem 2599

Determine why the equation $y=-x^{2}+1$ does not represent a line.

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Problem 2600

Solve the system of linear equations $y=5$ and $-3x+4y=8$ .

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Math

Problem 2501

Solve the linear system 17x+17y=1517x + 17y = 1517x+17y=15 for integers, proper fractions, and improper fractions.

Problem 2502

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£ 21£21.

Problem 2503

Solve x+14=35x + 14 = 35x+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?

Problem 2504

Find the derivative g′(u)g'(u)g′(u) of g(u)=∫3u−2x+x2dxg(u) = \int_{3}^{u} \frac{-2}{x+x^{2}} dxg(u)=∫3u​x+x2−2​dx using the Fundamental Theorem of Calculus.

Problem 2505

Vergleiche das Volumen eines Quaders mit a=4 cma=4 \mathrm{~cm}a=4 cm, b=2,5 cmb=2,5 \mathrm{~cm}b=2,5 cm, c=6 cmc=6 \mathrm{~cm}c=6 cm und eines Würfels mit a=4 cma=4 \mathrm{~cm}a=4 cm.

Problem 2506

Find real numbers aaa and bbb such that (a+1)+(b−2)i=4+6i(a+1)+(b-2)i=4+6i(a+1)+(b−2)i=4+6i, where a=□a=\squarea=□ and b=□b=\squareb=□.

Problem 2507

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

Problem 2508

Problem 2509

Find the transition matrix from basis FFF to basis EEE where E=[(1,2)T,(3,7)T]E=[(1,2)^{T},(3,7)^{T}]E=[(1,2)T,(3,7)T] and F=[(1,−2)T,(3,−5)T]F=[(1,-2)^{T},(3,-5)^{T}]F=[(1,−2)T,(3,−5)T] in R2\mathbb{R}^{2}R2.

Problem 2510

Find the value of yyy given the linear equation 2x+5y=102x + 5y = 102x+5y=10.

Problem 2511

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

Problem 2512

Find the value of the expression h−7h-7h−7 when h=21h=21h=21.

Problem 2513

Problem 2514

Solve for www in the equation 5=−1w−65=-\frac{1}{w-6}5=−w−61​. Simplify the solution w=w=w=.

Problem 2515

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

Problem 2516

Simplify the expression 2⋅4122 \cdot 4^{\frac{1}{2}}2⋅421​ to an integer or simplified fraction.

Problem 2517

Identify variables in expression 11r+5hr+πh11 r + 5 h r + \pi h11r+5hr+πh. Select all correct answers: rrr, hhh, π\piπ.

Problem 2518

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

Problem 2519

Find LLL given the equation 5LW=V5 L W = V5LW=V.

Problem 2520

Problem 2521

Find the value of 3+5x3+5x3+5x when x=3x=3x=3.

Problem 2522

Simplify the expression 3−3÷3−4⋅9−23^{-3} \div 3^{-4} \cdot 9^{-2}3−3÷3−4⋅9−2 into an integer or simplified fraction.

Problem 2523

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

Problem 2524

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

Problem 2525

Solve for zzz in the equation 5(z+2)=155(z+2)=155(z+2)=15.

Problem 2526

Find the maximum number of graduated cylinders a scientist can purchase for $500\$ 500$500, given the cost is $12.10\$ 12.10$12.10 each for 1 to 3, $11.07\$ 11.07$11.07 each for 4-47, and $10.20\$ 10.20$10.20 each for 48 or more.

Problem 2527

Solve the exponential equation 9x=139^{x}=\frac{1}{\sqrt{3}}9x=3​1​ for the value of xxx.

Problem 2528

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

Problem 2529

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

Problem 2530

Find the sales tax and total cost of an item given its selling price and sales tax rate. Selling Price: $40.00\$ 40.00$40.00, Sales Tax Rate: 4%4 \%4%, Sales Tax: ?

Problem 2531

Calculate the area of a circle with r=6 cmr=6\,\mathrm{cm}r=6cm using π=3\pi=3π=3.

Problem 2532

Identify the horizontal and vertical shifts for the exponential function f(x)=12⋅(3)x+1+4f(x) = \frac{1}{2} \cdot (3)^{x+1} + 4f(x)=21​⋅(3)x+1+4.

Problem 2533

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

Problem 2534

Evaluate the cube root of x6x^{6}x6 when x=2x=2x=2.

Problem 2535

Find the linear operator from P3P_3P3​ to P4P_4P4​ where L(p(x))=x2p′′(x)+p′(x)+p(0)L(p(x)) = x^2 p''(x) + p'(x) + p(0)L(p(x))=x2p′′(x)+p′(x)+p(0).

Problem 2536

Find the closest value to 4,367÷0.0044,367 \div 0.0044,367÷0.004.

Problem 2537

Find the Maclaurin series expansions up to 5th degree for y=sin⁡xcos⁡xy=\sin x \cos xy=sinxcosx, y=ln⁡(x+1)y=\ln(x+1)y=ln(x+1), and y=xcos⁡xy=x \cos xy=xcosx.

Problem 2538

Find the fraction of a rectangle divided into 10 equal boxes, where 6 boxes are shaded.

Problem 2539

Find the value of nnn when 8n−2=6n+68n - 2 = 6n + 68n−2=6n+6.

Problem 2540

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

Problem 2541

Complementary angles aaa and bbb have measures 42∘42^{\circ}42∘ and x∘x^{\circ}x∘. Which equation represents a+b=90∘a + b = 90^{\circ}a+b=90∘?

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 the derivative $g'(u)$ of $g(u) = \int_{3}^{u} \frac{-2}{x+x^{2}} dx$ using the Fundamental Theorem of Calculus.

Vergleiche das Volumen eines Quaders mit $a=4 \mathrm{~cm}$ , $b=2,5 \mathrm{~cm}$ , $c=6 \mathrm{~cm}$ und eines Würfels mit $a=4 \mathrm{~cm}$ .

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 transition matrix from basis $F$ to basis $E$ where $E=[(1,2)^{T},(3,7)^{T}]$ and $F=[(1,-2)^{T},(3,-5)^{T}]$ in $\mathbb{R}^{2}$ .

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.

Find the value of the expression $h-7$ when $h=21$ .

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.

Simplify the expression $2 \cdot 4^{\frac{1}{2}}$ to an integer or simplified fraction.

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 $2(\square-4x)+\square(3x-1)=2(2x+3)$ .

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

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

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

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

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

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

Find the maximum number of graduated cylinders a scientist can purchase for $\$ 500$ , given the cost is $\$ 12.10$ each for 1 to 3, $\$ 11.07$ each for 4-47, and $\$ 10.20$ each for 48 or more.

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

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

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

Find the sales tax and total cost of an item given its selling price and sales tax rate. Selling Price: $\$ 40.00$ , Sales Tax Rate: $4 \%$ , Sales Tax: ?

Calculate the area of a circle with $r=6\,\mathrm{cm}$ using $\pi=3$ .

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

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

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

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

Find the closest value to $4,367 \div 0.004$ .

Find the Maclaurin series expansions up to 5th degree for $y=\sin x \cos x$ , $y=\ln(x+1)$ , and $y=x \cos x$ .

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

Complementary angles $a$ and $b$ have measures $42^{\circ}$ and $x^{\circ}$ . Which equation represents $a + b = 90^{\circ}$ ?

Find the value of the expression $-3 \times 8 - 52 - 19$ .

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

Calculate the annual payment for a $\$ 140000$ car loan with a 5-year term and $12\%$ annual interest rate.

Simplify the expression $5 \cdot 0$ .

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

What is the formula to find a weighted mean? $\frac{\Sigma w \cdot x}{\Sigma w}$

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

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

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

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

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

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

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

Find the total amounts of nitrogen ( $N$ ), phosphoric acid ( $P_2O_5$ ), and potash ( $K_2O$ ) in a mixture of 200 pounds of Vigoro and 500 pounds of Parker's fertilizers.

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

Find the length of side $p$ in $\triangle \mathrm{PQR}$ given $r=38 \mathrm{~cm}, m \angle \mathrm{P}=49^{\circ}, m \angle \mathrm{Q}=127^{\circ}$ .

Solve the indefinite integral of $\cot^{-1}x$ by selecting the correct antiderivative.

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 $x=7/2+y$ .

Find the range of $f(x) = \frac{1}{\sqrt{|x^2 - 4|}}$ .

Solve the equation $x+1=11$ and find all real solutions.

Divide the polynomial $\left(x^{2}-4\right)$ by $(x-2)$ using factoring.

Solve the linear equation $2(5x+4) = 4(x+3) + 4 + 2x$ and select the correct solution.

Find $a$ and $b$ such that $P(x) = (2a - b)x^2 + (b - 6)x + a - 3$ is the zero polynomial.

Determine if the equation $y^{2}=3x-2$ represents a function.

Find the value of the expression $\frac{6^{\frac{5}{2}}}{6}$ .

Find the derivative of the function $y=\frac{\sqrt{x}-5}{\sqrt{x}+6}$ .

Find the height of a building in New York, given that the angle of elevation to its top is 5 degrees and the distance from its base is 1 mile. Round the height to the nearest tenth. Hint: 1 mile = $5280$ feet. The answer is in feet.

Find the value of $f(-2)$ given $f(x)=4x^3+7x$ .

Solve for $w$ in the quadratic equation $4 w^{2} = -11 w - 6$ . If there are multiple solutions, list them separately.

Simplify the expression $6 \cos \left(\frac{\pi}{2}-x\right) \sec x$ using fundamental identities. Multiple correct forms.