Browse Math problems in the Studdy Learning Bank!

Problem 3501

Convert 823 to base-5 notation. $823=\square_{\text{five}}$

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Problem 3502

Evaluate the integral $\int \cos 3x \cos 3x dx$ and select the correct solution from the given options.

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Problem 3503

Find the value of $y$ if the difference between $y$ and one-third is $-\frac{1}{6}$ .

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Problem 3504

Find the derivative of $3^x$ with respect to $x$ . Type $\ln(x)$ for the natural logarithm function.

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Problem 3505

Solve for vector $\mathbf{n}$ given the equation $56=8n$ .

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Problem 3506

Determine the range of a 7265-foot vehicular tunnel's length, given the concept of accuracy and significant digits. The range is from $7264$ to $7266$ feet.

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Problem 3507

Graph the values of $x$ where $x \leq 2$ or $x \geq 7$ .

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Problem 3508

Erbium isotope with 12-hour half-life, initial 22g. Find: a) $A(t)$ function, b) decay rate $A'(t)$ , c) decay rate at 11 hours.
a) $A(t) = 22e^{-0.0577t}$ grams b) $A'(t) = -1.2694e^{-0.0577t}$ grams/hour c) $A'(11) = 0.2069$ grams/hour

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Problem 3509

Calculate the integral $\int 2 \sqrt[3]{x} \, dx$ and express the result in simplest form.

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Problem 3510

Solve for $u$ where $\frac{5}{8} u=40$ . Simplify the solution $u$ .

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Problem 3511

Evaluate the expression $\sin x \csc (-x)$ .

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Problem 3512

Calculate the integral of $-2 x^{-2} + 2 - 4 x$ and simplify the result.

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Problem 3513

Identify the vertical line from the given set of lines: $x=4$ , $y=2x+3$ , $3x-2y=6$ , $2x+3y=9$ , $y=-5$ .

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Problem 3514

Determine which of the given linear systems is consistent: $x+2y=5, 2x+y=4$ or $3x+3y=9, 2x+2y=5$ or $x+y=3, 2x+2y=4$ or $x+y=1, 3x+3y=8$ or $x+y=5, 2x+2y=6$ or none.

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Problem 3515

Find an equation relating the number of pens $a$ in the first box and the number of pens $c$ in the third box, given $a=b+9$ and $b=c-2$ .

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Problem 3516

Solve for $\mathrm{K}$ given $3(j-h)=k$ , $j=13$ , and $h=2$ .

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Problem 3517

Find the solution set of the inequality $-6x + 18 < -36x - 12$ .

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Problem 3518

Solve for $n$ in the equation $12 = n - 9$ .

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Problem 3519

Find the exact values of $\sin \theta$ and $\csc \theta$ given $\tan \theta = 8/15$ and $\cos \theta < 0$ .

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Problem 3520

Solve for $y$ given the system of linear equations $10x - 9y = 74$ and $x = 2$ .

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Problem 3521

Write an equation where the variable $n$ represents the number of cookies. The equation should express that twice the number of cookies minus four is equal to six.

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Problem 3522

What fraction of students in a class of 258 passed a term test if 16 students failed? Express the answer in lowest terms.
$\frac{242}{258}$

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Problem 3523

Find $\tan (\theta)$ for a triangle with $h=60$ and $\ell=12$ , where $\ell$ is the opposite and $h$ is the hypotenuse.

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Problem 3524

Solve the system of linear equations and find the solution set. Round to nearest hundredth. $\left\{\begin{array}{l} 2y + 7x = 11 \\ 3y = -16x + 10 \end{array}\right.$ A. Infinite solutions B. $(-1.18, 9.64)$ C. $(-0.25, 4.64)$ D. No solution

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Problem 3525

Solve for the value of $v$ given the equation $11.1 \cdot 0.2=v$ .

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Problem 3526

Find the number of terms and constants in the expression $4 x^{2} - 2 x^{2} + 9 x - 2$ .

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Problem 3527

Find $\cos A$ , $\tan A$ , and $\sin A$ for a right triangle with side lengths 8, 15, and 17.

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Problem 3528

Find the number $x$ such that $6x + 8 = 68$ .

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Problem 3529

Find the cube root of 216.

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Problem 3530

Solve for $v$ in the equation $6 = -\frac{8}{v}$ .

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Problem 3531

Find the value of $m$ given the equations $-1.23m = -0.492$ and $m = 0.738, 0.60516, 0.4$ .

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Problem 3532

Solve the equation $8-6y=7-7y$ using the addition property of equality. The solution set is $\{1/13\}$ .

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Problem 3533

Find the product of the binomial expression $(3h+2)(3h-2)$ .

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Problem 3534

Find two polynomials of degree 4 with 3 terms, one with degree 1 and coefficient -5, and y-intercept at 10.

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Problem 3535

Find the expression that correctly describes a swimmer diving 300 feet, swimming up 150 feet, and then swimming down 50 feet. The correct expression is $-300 + 150 + (-50)$ .

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Problem 3536

Solve $5|{-8 x - 9}| = 20$ and write the fractional solutions separated by a comma.

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Problem 3537

Find the equation with the correct sign on the product: $(-8)(-8)=-64$ or $(-18)4=-72$ or $45(-4)=180$ or $13 \cdot 3=-39$ ?

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Problem 3538

Find the derivative of $y = \cos^{-1}(\sin(x))$ .

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Problem 3539

Jill's mom bought a generator that holds 6.6 gallons of gas and consumes 0.75 gallons/hour. Write a linear function $h(x) = mx + b$ to model the remaining gas after $x$ hours.

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Problem 3540

Find the center of the hyperbola given by the equation $\frac{y^{2}}{25}-\frac{x^{2}}{36}=1$ .

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Problem 3541

Solve the equation $10=z+6$ .

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Problem 3542

Find the limit of $\frac{\tan(2x)}{x\cos(x)}$ as $x$ approaches 0.

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Problem 3543

Find the values of $a$ , $b$ , and $c$ that make the equation $(2x-1)(3x+4) = ax^2 + bx + c$ true.

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Problem 3544

Find the ordered pair $(x, y)$ such that $f(x) = y$ and $f(5) = 4$ .

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Problem 3545

Solve for $b$ where $|b| + 4 = 87$ . Write the solution as an integer or simplified fraction.

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Problem 3546

Solve for x when 8(x+1) = 7(x+8). The number is $\frac{8}{3}$ .

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Problem 3547

Calculate the percent grade and angle of elevation for a highway with a vertical rise of $140$ feet over $2000$ feet of horizontal distance.

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Problem 3548

Simplify the rational expression $\frac{56 x^{2}+29 x+3}{48 x^{2}+58 x+15}$ and specify any variable restrictions.

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Problem 3549

Solve the equation in one step by dividing both sides by 1.1: $\frac{t}{1.1}=8.8$

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Problem 3550

Solve for $x$ in the equation $5 \ln x = -15$ . Select the correct choice: A. $x = e^{-3}$ , or B. The solution is not a real number.

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Problem 3551

Choose the formula that describes the inverse relationship between $T$ and $r$ . Options: A. $r=kT$ , B. $T=krz$ , C. $T=\frac{k}{r}$ , D. $T=kr$ .

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Problem 3552

Solve for $t$ in the equation $t + 3.21 = 5.1$ . Show your work.

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Problem 3553

Solve the equation $\frac{7}{5 x+3}-\frac{1}{x-6}=0$ for the variable $x$ .

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Problem 3554

Solve for $t$ where $|t| + 1 = 17$ . Write the solution as an integer or simplified fraction.

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Problem 3555

Find the angle whose cosine is $-\sqrt{2}/2$ .

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Problem 3556

Find the value of $k$ if the solutions to $\frac{1}{3}x^2 - 5 = 16$ are $\pm 3\sqrt{k}$ .

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Problem 3557

Solve for the value of $a$ given the equation $b = a - 15$ .

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Problem 3558

Lili a mangé quelle fraction du pâté entier si elle a mangé la moitié de $\frac{3}{8}$ du pâté?

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Problem 3559

Find the characteristic of the graph $y = -3(2)^x$ that is displayed as a constant or coefficient in the equation.

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Problem 3560

Solve for the unknown in the equation $8=8 \sqrt{-15-2n}$ .

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Problem 3561

Two cyclists travel towards each other from towns 152 miles apart. One is $8 \frac{\mathrm{mi}}{\mathrm{h}}$ faster. They meet in 4 hours. Find their rates: $\square \frac{\mathrm{mi}}{\mathrm{h}}$ , $\square \frac{\mathrm{mi}}{\mathrm{h}}$ .

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Problem 3562

Find the missing value in the equation $9 / 11 = ? / 22$ .

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Problem 3563

Find the most common birth weight among 8 babies with weights $4, 5, 5, 3, 5, 4, 5, 4$ kg.

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Problem 3564

Plot $2.25$ and $4.75$ on the number line.

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Problem 3565

Solve for the variable $y$ in the formula $W=X+Xyz$ .

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Problem 3566

Find the length of the kite string if the kite's height is $12 \mathrm{m}$ and the string makes a $30^{\circ}$ angle with the ground.

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Problem 3567

Find the integrating factor for the first-order linear ODE $y' = -y + \cos x$ .

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Problem 3568

Find the critical points of the polynomial function $f(x) = x^4 + 4x^3 - 9$ .

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Problem 3569

Find the area between the cubic curves $y=x^{3}-13x^{2}+30x$ and $y=-x^{3}+13x^{2}-30x$ .

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Problem 3570

Identify the real number property shown in the equation $8+(-8)=0$ .

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Problem 3571

Mateo ate 3/8 of a pizza with 510 calories. Which equation can be used to find the total calories in the pizza? $\frac{3}{8} x=510$

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Problem 3572

The function $f(x)$ satisfies $f(-2) = 4$ . What property of the function must be true?

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Problem 3573

Find the negative square root of $\frac{4}{81}$ . Express the answer as a proper fraction, improper fraction, or whole number.

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Problem 3574

Sketch the graph of $f(x)=-e^{x-3}$ using transformations of $y=e^x$ . Find the domain, range, $y$ -intercept, and horizontal asymptote.

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Problem 3575

Find the absolute value equation for the distance between -3 and $t$ being 5.

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Problem 3576

Find the measure of $\angle X$ to the nearest degree if $\sin X = \frac{4}{9}$ .

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Problem 3577

Simplify the expression $7^{10} - 5 \times 3$ .

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Problem 3578

Divide radical expressions and find the valid range of $x$ . $\sqrt{8 x^{2}} \div \sqrt{2 x}$

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Problem 3579

Solve for the value of $b$ that satisfies the inequality $\frac{b}{4} \leq 5$ .

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Problem 3580

What is the probability that a randomly chosen student from a class of 21 plays basketball or baseball, given that 10 play basketball, 8 play baseball, and 6 play both?

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Problem 3581

Solve for $w$ using the multiplication principle. Find the value of $w$ given the equation $-21.08 = -5.27w$ .

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Problem 3582

Find the true statement about the cotangent function $y=\cot x$ .
A. Zeros are $\frac{n \pi}{2}$ where $n$ is an integer. B. Domain excludes $x$ where $\cos x=0$ . C. Principal cycle is on $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ . D. Infinitely many vertical asymptotes at $x=n \pi$ where $n$ is an integer.

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Problem 3583

Simplify the expression $\frac{x-2}{4 x^{3}} \cdot \frac{x^{2}-1}{x^{2}-x-2}$ .

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Problem 3584

Expand and simplify the expression $(6-\sqrt{5})(2-\sqrt{5})$ .

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Problem 3585

Encuentra la pendiente y la intersección con el eje $y$ de la recta definida por $-4x - 2y = -2$ , luego dibuja su gráfica.

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Problem 3586

Find the derivative of $\sin(g(x))$ evaluated at $x=8$ , given that $g(8)=3$ and $g'(8)=9$ . Round the answer to three decimal places.

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Problem 3587

Find the center of the circle with equation $(x+3)^{2} + y^{2} = 4$ . Provide the simplified ordered pair.

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Problem 3588

Determine the condition for two radical expressions to be considered like terms.

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Problem 3589

Solve for $y$ in the linear equation $-2 = -3y + 9x$ .

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Problem 3590

Solve the given 2x2 linear systems and determine the solution type.
System A: $-x-3y=-6$ , $x+3y+6=0$ System B: $-x-4y=-4$ , $x-4y=-4$

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Problem 3591

Find the rental cost model where $m$ represents miles driven. Options are $C=0.45 m+35$ , $C=4.5 m+35$ , or $C=45 m+35$ .

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Problem 3592

Find the value of $x$ in an isosceles trapezoid $VWXY$ where $VX=3x+85$ and $WY=4x+68$ .

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Problem 3593

Save $300,000 in 25 years with 8% interest. How much to deposit monthly? How much interest earned?

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Problem 3594

Find the value of the variable $u$ in the equation $+5+u=-1$ .

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Problem 3595

Find the range of $g(x) = -8^x$ . (Answer in interval notation)

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Problem 3596

Find the general solution for the differential equation $\frac{d A}{d t}=-7 A$ , where $A(t)=Ce^{-7t}$ .

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Problem 3597

If $\frac{\sqrt{a}}{\sqrt{b}}=x$ , which statement must be true? A. $\sqrt{x}=\frac{a}{b}$ B. $|x|=\frac{a}{b}$ C. $x=\frac{a}{b}$ D. $x^{2}=\frac{a}{b}$

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Problem 3598

Differentiate the function $f(t) = \frac{\sec t}{-1 + \sec t}$ and find the derivative $f'(t)$ .

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Problem 3599

Find the value of $e$ of $x$ and evaluate $-4x+7$ when $x=-1$ .

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Problem 3600

Solve the equation $x^{4} - 81 = 0$ for real values of $x$ .

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Math

Problem 3501

Convert 823 to base-5 notation. 823=□five 823=\square_{\text{five}} 823=□five​

Problem 3502

Evaluate the integral ∫cos⁡3xcos⁡3xdx\int \cos 3x \cos 3x dx∫cos3xcos3xdx and select the correct solution from the given options.

Problem 3503

Find the value of yyy if the difference between yyy and one-third is −16-\frac{1}{6}−61​.

Problem 3504

Find the derivative of 3x3^x3x with respect to xxx. Type ln⁡(x)\ln(x)ln(x) for the natural logarithm function.

Problem 3505

Solve for vector n\mathbf{n}n given the equation 56=8n56=8n56=8n.

Problem 3506

Determine the range of a 7265-foot vehicular tunnel's length, given the concept of accuracy and significant digits. The range is from 726472647264 to 726672667266 feet.

Problem 3507

Graph the values of xxx where x≤2x \leq 2x≤2 or x≥7x \geq 7x≥7.

Problem 3508

Problem 3509

Calculate the integral ∫2x3 dx\int 2 \sqrt[3]{x} \, dx∫23x​dx and express the result in simplest form.

Problem 3510

Solve for uuu where 58u=40\frac{5}{8} u=4085​u=40. Simplify the solution uuu.

Problem 3511

Evaluate the expression sin⁡xcsc⁡(−x)\sin x \csc (-x)sinxcsc(−x).

Problem 3512

Calculate the integral of −2x−2+2−4x-2 x^{-2} + 2 - 4 x−2x−2+2−4x and simplify the result.

Problem 3513

Identify the vertical line from the given set of lines: x=4x=4x=4, y=2x+3y=2x+3y=2x+3, 3x−2y=63x-2y=63x−2y=6, 2x+3y=92x+3y=92x+3y=9, y=−5y=-5y=−5.

Problem 3514

Determine which of the given linear systems is consistent: x+2y=5,2x+y=4x+2y=5, 2x+y=4x+2y=5,2x+y=4 or 3x+3y=9,2x+2y=53x+3y=9, 2x+2y=53x+3y=9,2x+2y=5 or x+y=3,2x+2y=4x+y=3, 2x+2y=4x+y=3,2x+2y=4 or x+y=1,3x+3y=8x+y=1, 3x+3y=8x+y=1,3x+3y=8 or x+y=5,2x+2y=6x+y=5, 2x+2y=6x+y=5,2x+2y=6 or none.

Problem 3515

Find an equation relating the number of pens aaa in the first box and the number of pens ccc in the third box, given a=b+9a=b+9a=b+9 and b=c−2b=c-2b=c−2.

Problem 3516

Solve for K\mathrm{K}K given 3(j−h)=k3(j-h)=k3(j−h)=k, j=13j=13j=13, and h=2h=2h=2.

Problem 3517

Find the solution set of the inequality −6x+18<−36x−12-6x + 18 < -36x - 12−6x+18<−36x−12.

Problem 3518

Solve for nnn in the equation 12=n−912 = n - 912=n−9.

Problem 3519

Find the exact values of sin⁡θ\sin \thetasinθ and csc⁡θ\csc \thetacscθ given tan⁡θ=8/15\tan \theta = 8/15tanθ=8/15 and cos⁡θ<0\cos \theta < 0cosθ<0.

Problem 3520

Solve for yyy given the system of linear equations 10x−9y=7410x - 9y = 7410x−9y=74 and x=2x = 2x=2.

Problem 3521

Write an equation where the variable nnn represents the number of cookies. The equation should express that twice the number of cookies minus four is equal to six.

Problem 3522

What fraction of students in a class of 258 passed a term test if 16 students failed? Express the answer in lowest terms.242258\frac{242}{258}258242​

Problem 3523

Find tan⁡(θ)\tan (\theta)tan(θ) for a triangle with h=60h=60h=60 and ℓ=12\ell=12ℓ=12, where ℓ\ellℓ is the opposite and hhh is the hypotenuse.

Problem 3524

Problem 3525

Solve for the value of vvv given the equation 11.1⋅0.2=v11.1 \cdot 0.2=v11.1⋅0.2=v.

Problem 3526

Find the number of terms and constants in the expression 4x2−2x2+9x−24 x^{2} - 2 x^{2} + 9 x - 24x2−2x2+9x−2.

Problem 3527

Find cos⁡A\cos AcosA, tan⁡A\tan AtanA, and sin⁡A\sin AsinA for a right triangle with side lengths 8, 15, and 17.

Problem 3528

Find the number xxx such that 6x+8=686x + 8 = 686x+8=68.

Problem 3529

Find the cube root of 216.

Problem 3530

Solve for vvv in the equation 6=−8v6 = -\frac{8}{v}6=−v8​.

Problem 3531

Find the value of mmm given the equations −1.23m=−0.492-1.23m = -0.492−1.23m=−0.492 and m=0.738,0.60516,0.4m = 0.738, 0.60516, 0.4m=0.738,0.60516,0.4.

Problem 3532

Solve the equation 8−6y=7−7y8-6y=7-7y8−6y=7−7y using the addition property of equality. The solution set is {1/13}\{1/13\}{1/13}.

Problem 3533

Find the product of the binomial expression (3h+2)(3h−2)(3h+2)(3h-2)(3h+2)(3h−2).

Problem 3534

Find two polynomials of degree 4 with 3 terms, one with degree 1 and coefficient -5, and y-intercept at 10.

Problem 3535

Find the expression that correctly describes a swimmer diving 300 feet, swimming up 150 feet, and then swimming down 50 feet. The correct expression is −300+150+(−50)-300 + 150 + (-50)−300+150+(−50).

Problem 3536

Solve 5∣−8x−9∣=205|{-8 x - 9}| = 205∣−8x−9∣=20 and write the fractional solutions separated by a comma.

Problem 3537

Find the equation with the correct sign on the product: (−8)(−8)=−64(-8)(-8)=-64(−8)(−8)=−64 or (−18)4=−72(-18)4=-72(−18)4=−72 or 45(−4)=18045(-4)=18045(−4)=180 or 13⋅3=−3913 \cdot 3=-3913⋅3=−39?

Problem 3538

Find the derivative of y=cos⁡−1(sin⁡(x))y = \cos^{-1}(\sin(x))y=cos−1(sin(x)).

Problem 3539

Jill's mom bought a generator that holds 6.6 gallons of gas and consumes 0.75 gallons/hour. Write a linear function h(x)=mx+bh(x) = mx + bh(x)=mx+b to model the remaining gas after xxx hours.

Problem 3540

Find the center of the hyperbola given by the equation y225−x236=1\frac{y^{2}}{25}-\frac{x^{2}}{36}=125y2​−36x2​=1.

Problem 3541

Convert 823 to base-5 notation. $823=\square_{\text{five}}$

Evaluate the integral $\int \cos 3x \cos 3x dx$ and select the correct solution from the given options.

Find the value of $y$ if the difference between $y$ and one-third is $-\frac{1}{6}$ .

Find the derivative of $3^x$ with respect to $x$ . Type $\ln(x)$ for the natural logarithm function.

Solve for vector $\mathbf{n}$ given the equation $56=8n$ .

Determine the range of a 7265-foot vehicular tunnel's length, given the concept of accuracy and significant digits. The range is from $7264$ to $7266$ feet.

Graph the values of $x$ where $x \leq 2$ or $x \geq 7$ .

Calculate the integral $\int 2 \sqrt[3]{x} \, dx$ and express the result in simplest form.

Solve for $u$ where $\frac{5}{8} u=40$ . Simplify the solution $u$ .

Evaluate the expression $\sin x \csc (-x)$ .

Calculate the integral of $-2 x^{-2} + 2 - 4 x$ and simplify the result.

Identify the vertical line from the given set of lines: $x=4$ , $y=2x+3$ , $3x-2y=6$ , $2x+3y=9$ , $y=-5$ .

Determine which of the given linear systems is consistent: $x+2y=5, 2x+y=4$ or $3x+3y=9, 2x+2y=5$ or $x+y=3, 2x+2y=4$ or $x+y=1, 3x+3y=8$ or $x+y=5, 2x+2y=6$ or none.

Find an equation relating the number of pens $a$ in the first box and the number of pens $c$ in the third box, given $a=b+9$ and $b=c-2$ .

Solve for $\mathrm{K}$ given $3(j-h)=k$ , $j=13$ , and $h=2$ .

Find the solution set of the inequality $-6x + 18 < -36x - 12$ .

Solve for $n$ in the equation $12 = n - 9$ .

Find the exact values of $\sin \theta$ and $\csc \theta$ given $\tan \theta = 8/15$ and $\cos \theta < 0$ .

Solve for $y$ given the system of linear equations $10x - 9y = 74$ and $x = 2$ .

Write an equation where the variable $n$ represents the number of cookies. The equation should express that twice the number of cookies minus four is equal to six.

What fraction of students in a class of 258 passed a term test if 16 students failed? Express the answer in lowest terms.
$\frac{242}{258}$

Find $\tan (\theta)$ for a triangle with $h=60$ and $\ell=12$ , where $\ell$ is the opposite and $h$ is the hypotenuse.

Solve for the value of $v$ given the equation $11.1 \cdot 0.2=v$ .

Find the number of terms and constants in the expression $4 x^{2} - 2 x^{2} + 9 x - 2$ .

Find $\cos A$ , $\tan A$ , and $\sin A$ for a right triangle with side lengths 8, 15, and 17.

Find the number $x$ such that $6x + 8 = 68$ .

Solve for $v$ in the equation $6 = -\frac{8}{v}$ .

Find the value of $m$ given the equations $-1.23m = -0.492$ and $m = 0.738, 0.60516, 0.4$ .

Solve the equation $8-6y=7-7y$ using the addition property of equality. The solution set is $\{1/13\}$ .

Find the product of the binomial expression $(3h+2)(3h-2)$ .

Find the expression that correctly describes a swimmer diving 300 feet, swimming up 150 feet, and then swimming down 50 feet. The correct expression is $-300 + 150 + (-50)$ .

Solve $5|{-8 x - 9}| = 20$ and write the fractional solutions separated by a comma.

Find the equation with the correct sign on the product: $(-8)(-8)=-64$ or $(-18)4=-72$ or $45(-4)=180$ or $13 \cdot 3=-39$ ?

Find the derivative of $y = \cos^{-1}(\sin(x))$ .

Jill's mom bought a generator that holds 6.6 gallons of gas and consumes 0.75 gallons/hour. Write a linear function $h(x) = mx + b$ to model the remaining gas after $x$ hours.

Find the center of the hyperbola given by the equation $\frac{y^{2}}{25}-\frac{x^{2}}{36}=1$ .

Solve the equation $10=z+6$ .

Find the limit of $\frac{\tan(2x)}{x\cos(x)}$ as $x$ approaches 0.

Find the values of $a$ , $b$ , and $c$ that make the equation $(2x-1)(3x+4) = ax^2 + bx + c$ true.

Find the ordered pair $(x, y)$ such that $f(x) = y$ and $f(5) = 4$ .

Solve for $b$ where $|b| + 4 = 87$ . Write the solution as an integer or simplified fraction.

Solve for x when 8(x+1) = 7(x+8). The number is $\frac{8}{3}$ .

Calculate the percent grade and angle of elevation for a highway with a vertical rise of $140$ feet over $2000$ feet of horizontal distance.

Simplify the rational expression $\frac{56 x^{2}+29 x+3}{48 x^{2}+58 x+15}$ and specify any variable restrictions.

Solve the equation in one step by dividing both sides by 1.1: $\frac{t}{1.1}=8.8$

Solve for $x$ in the equation $5 \ln x = -15$ . Select the correct choice: A. $x = e^{-3}$ , or B. The solution is not a real number.

Choose the formula that describes the inverse relationship between $T$ and $r$ . Options: A. $r=kT$ , B. $T=krz$ , C. $T=\frac{k}{r}$ , D. $T=kr$ .

Solve for $t$ in the equation $t + 3.21 = 5.1$ . Show your work.

Solve the equation $\frac{7}{5 x+3}-\frac{1}{x-6}=0$ for the variable $x$ .

Solve for $t$ where $|t| + 1 = 17$ . Write the solution as an integer or simplified fraction.

Find the angle whose cosine is $-\sqrt{2}/2$ .

Find the value of $k$ if the solutions to $\frac{1}{3}x^2 - 5 = 16$ are $\pm 3\sqrt{k}$ .

Solve for the value of $a$ given the equation $b = a - 15$ .

Lili a mangé quelle fraction du pâté entier si elle a mangé la moitié de $\frac{3}{8}$ du pâté?

Find the characteristic of the graph $y = -3(2)^x$ that is displayed as a constant or coefficient in the equation.

Solve for the unknown in the equation $8=8 \sqrt{-15-2n}$ .

Two cyclists travel towards each other from towns 152 miles apart. One is $8 \frac{\mathrm{mi}}{\mathrm{h}}$ faster. They meet in 4 hours. Find their rates: $\square \frac{\mathrm{mi}}{\mathrm{h}}$ , $\square \frac{\mathrm{mi}}{\mathrm{h}}$ .

Find the missing value in the equation $9 / 11 = ? / 22$ .

Find the most common birth weight among 8 babies with weights $4, 5, 5, 3, 5, 4, 5, 4$ kg.

Plot $2.25$ and $4.75$ on the number line.

Solve for the variable $y$ in the formula $W=X+Xyz$ .

Find the length of the kite string if the kite's height is $12 \mathrm{m}$ and the string makes a $30^{\circ}$ angle with the ground.

Find the integrating factor for the first-order linear ODE $y' = -y + \cos x$ .

Find the critical points of the polynomial function $f(x) = x^4 + 4x^3 - 9$ .

Find the area between the cubic curves $y=x^{3}-13x^{2}+30x$ and $y=-x^{3}+13x^{2}-30x$ .

Identify the real number property shown in the equation $8+(-8)=0$ .

Mateo ate 3/8 of a pizza with 510 calories. Which equation can be used to find the total calories in the pizza? $\frac{3}{8} x=510$

The function $f(x)$ satisfies $f(-2) = 4$ . What property of the function must be true?

Find the negative square root of $\frac{4}{81}$ . Express the answer as a proper fraction, improper fraction, or whole number.

Sketch the graph of $f(x)=-e^{x-3}$ using transformations of $y=e^x$ . Find the domain, range, $y$ -intercept, and horizontal asymptote.