Browse Math problems in the Studdy Learning Bank!

Problem 8401

Solve the linear equations: $-5a = -0.2$ , $b + 14.5 = 10$ , and $2 = -\frac{1}{5}c$ .

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Problem 8402

Demuestra que si $a$ es impar, entonces $a^2 + 3a + 5$ es impar.

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Problem 8403

Find the solution(s) to the quadratic equation $y^2 - 2y - 8 = 7$ .

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Problem 8404

Andre wants to make an open-top box by cutting out corners of a 22 in x 28 in poster board and folding up the sides. Find the volume $V(x)$ of the box, where $x$ is the side length of the square cutout. Determine the volume when $x=6$ and the reasonable domain for $V$ .

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Problem 8405

Show that if $x=\frac{\sqrt{5}+1}{2}$ , then $1+\frac{1}{x}=x$ .

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Problem 8406

Solve for $x$ where $5(4-x)-2x \geq 3-(x-1)$ and $x \leq \frac{8}{3}$ .

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Problem 8407

Find the value of $x$ that satisfies the equation $14x - 12 = 8 - 21x$ . Options: F) $\frac{7}{4}$ , G) $\frac{4}{7}$ , H) 0, J) $\frac{8}{21}$ .

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Problem 8408

Find the derivative of the function $g(u) = \frac{u+1}{2u-1}$ using the definition of derivative. State the domain of $g(u)$ and its derivative in interval notation.

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Problem 8409

Solve the linear equation $-10 = -10 + 7m$ for the unknown variable $m$ .

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Problem 8410

Evaluate and simplify $c^{2} = 3^{2} + 10^{2} - 2(3)(10) \cos(34^{\circ})$ , then find $c$ .

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Problem 8411

Find the derivative of $3x(2x+1)^3$ .

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Problem 8412

Solve for the value of $x$ in the equation $-4(2x-11)=12$ . (1 point)

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Problem 8413

Find the value of $x$ when $f(x) = -x - 1 = 6$ .

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Problem 8414

Find the options that equal $60\%$ of $94$ .

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Problem 8415

Factor quadratic expressions and find the value to complete the square. a) $x^2 - 10x + 25$ b) $x^2 + 6x + 9$ c) $x^2 + 5x + 25/4$ d) $x^2 - 3/2 x + 9/16$ What value is required to complete the square?

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Problem 8416

Find the number of times the quadratic function $y = 15x^{2} + 36x + 21$ intersects the $x$ -axis.

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Problem 8417

Find the value of $j$ if the product of 7 and $j$ is 91.

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Problem 8418

Find the area of a triangle with base $14 \mathrm{~cm}$ and height $5.5 \mathrm{~cm}$ .

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Problem 8419

Find the number of megabytes of data that 5 flash drives can hold, given that 7 flash drives can hold 1792 megabytes.
Solution: Let $x$ be the number of megabytes of data that 5 flash drives can hold. Then, we can set up the proportion: $\frac{7}{1792} = \frac{5}{x}$ Solving for $x$ , we get $x = \frac{5 \times 1792}{7} = 1280$ megabytes.

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Problem 8420

Find the factorization of the quadratic function $f(x)=2x^2+14x+24$ .

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Problem 8421

Shau-uen solved $18.5w + 6.5w - 2.8w = 149.1$ . In which step did she make her first error? $w = -2.13$

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Problem 8422

Determine which of the following statements is true given an invertible $3 \times 3$ matrix $A$ such that $\frac{1}{2}$ is an eigenvalue of $A^{-1}$ with eigenvector $v$ .

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Problem 8423

Find the present value of $\$ 100,000$ due in 6 years at a continuous 7% interest rate. The present value is $\$ \square$ .

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Problem 8424

Find the adjoint of a matrix $A$ given its inverse $A^{-1}=\left[\begin{array}{cc}0 & \frac{1}{2} \\ 1 & \frac{-1}{2}\end{array}\right]$ .

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Problem 8425

Solve the quadratic equation $\sqrt{x^2 - 5x} + 4 = 10$ .

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Problem 8426

Simplify the expression $\frac{3 c}{7}+\frac{18 c}{7}$ .

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Problem 8427

Find all complex numbers $z$ that satisfy the equation $z^2 = z$ .

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Problem 8428

Solve the quadratic equation $5 p(2 p-3)(p+7)=0$ and find the values of $p$ .

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Problem 8429

Solve the initial value problem: $\frac{d y}{d x}=8 x e^{-6 y}, \quad y(0)=0$ .

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Problem 8430

Solve for $y$ in the linear equation $3x + 4y = 5$ .

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Problem 8431

Identify the exact ordinary differential equation (ODE) from the given options.
$(x+y) dx + (y+x) dy = 0$ $(xy+y) dx + (xy+x) dy = 0$ $(y+2) dx + (2x+1) dy = 0$

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Problem 8432

Find the equation of the line with $\nabla = -3$ that passes through the point $(3, 1)$ .

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Problem 8433

Find the derivative of y with respect to x evaluated at x=1 for the following functions: (21) $y=\frac{2 x-1}{x+3}$ , (22) $y=\frac{5 x-2}{x^{2}+3}$ , (23) $y=\left(\frac{3 x+2}{x}\right)\left(x^{-5}+1\right)$ , (24) $y=\left(2 x^{7}-x^{2}\right)\left(\frac{x-1}{x+1}\right)$ .

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Problem 8434

Find the value of $g\left(\frac{1}{2}\right)$ where $g(x)=-x^{2}+6 x-3$ . (Type an integer or a fraction.)

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Problem 8435

Simplify the expression $(x-3)(x+9)$ .

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Problem 8436

Solve for $b$ in the equation $D b^{2} - 4 g = m$ , where all variables are positive.

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Problem 8437

Calculate the value of the expression $4(g-h)+10$ when $g=12$ and $h=7$ .

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Problem 8438

If a polynomial divides a binomial with zero remainder, the binomial is a factor of the polynomial.

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Problem 8439

Are $3x + 2$ and $2 + 3x$ equivalent algebraic expressions? Yes or no?

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Problem 8440

Find the range of values for $\sin^{-1} x$ , the inverse sine function.

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Problem 8441

Find the value of $y$ when $x=5$ in the rational function $y=\frac{35}{x}$ . The correct answer is $y=7$ .

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Problem 8442

Convert $4$ quarter hours to hours.

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Problem 8443

(1 point) If you drive 17.5 laps around a circular track and go $27 \mathrm{mi}$ , what is the track's radius? Round to 2 decimal places.

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Problem 8444

Solve for $b$ in the equation $-3=\frac{6}{5}b$ .

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Problem 8445

Solve for $x$ using cross multiplication. Show all work on both sides of the equation: $\frac{x}{5} = \frac{8.5}{2.5}$ , $2.5x = 42.5$ , $x = 17$ .

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Problem 8446

Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel. Find the system of equations representing this situation.
(A) $\left\{\begin{array}{l}k=d+3 \\ k-2=4(d-2)\end{array}\right.$ (B) $\left\{\begin{array}{l}d=k+3 \\ d-2=4(k-2)\end{array}\right.$

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Problem 8447

Multiply the expression $(\sqrt{7}+x)^{2}$ assuming all variables represent positive real numbers.

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Problem 8448

Find the sum of $9x - 9y$ and $-9x + 9$ .

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Problem 8449

Solve the linear equation $5x + 6 + 7x = 0$ for the unknown variable $x$ .

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Problem 8450

Solve the equation $7x - (5x - 1) = 2$ and express the answer as an integer or simplified fraction.

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Problem 8451

Solve the equation $3(2u-1)+4u+3=4(u+5)+2u$ . Express the solution $u$ as an integer or simplified fraction.

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Problem 8452

Find a number where 4 times the number minus 18 is -6. Write an equation and solve for the number.
$4n - 18 = -6$

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Problem 8453

Find the product of $(y+1)(2y+3)$ and simplify the result.

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Problem 8454

Evaluate the expression: $(3.4+4.4) \times(4.8 \div 0.4)$

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Problem 8455

Solve for the interval where $5x + 5 < 2x - 4$ graphically using the intersection method.

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Problem 8456

Find the solution set for the inequality $x - 21.8 < 19.7$ . The solution set is $2.1 < x < 41.5$ .

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Problem 8457

Multiply the expression $\frac{1}{2}(4 y+4 x-8 z)$ and simplify the result.

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Problem 8458

Solve the riddle: "I am the start of everything, the end of everywhere. I'm the start of eternity, the end of time and space. What am I?"

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Problem 8459

Solve the quadratic equation $x=\frac{-(-3) \pm \sqrt{(-3)^{2}-4(-2)(5)}}{2(-2)}$ for $x$ .

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Problem 8460

What is the binary representation of the decimal number 12? a. 1100 b. 1110 c. 1010 d. 1101

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Problem 8461

Find the number Riley thought of, given that when tripled and subtracted by 5, the result is 7.

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Problem 8462

Evaluate the expression $\frac{a^{2}-b^{2}}{a-b}$ when $a=9$ and $b=5$ .

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Problem 8463

Rewrite the polynomial $y + \frac{1}{3} - x$ in the form $a x + b y + c$ , then find $a, b, c$ .

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Problem 8464

Solve the absolute value equation $|z+10|=|z-6|$ . Select the correct choice: A. The solution is $z = -8, 4$ or B. There is no solution.

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Problem 8465

Solve for $x$ where $|x|>10$ . Select the correct solution: A. $x<-10$ or $x>10$ (Simplified) B. $-\infty<x<-10$ or $10<x<\infty$ (Simplified)

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Problem 8466

Find the product of two binomials. Simplify completely. a) $(6x + \sqrt{11})(6x - \sqrt{11})$ b) $(\sqrt{2}x - 7)(\sqrt{2}x + 7)$

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Problem 8467

The point is moving along $x^{3}y^{2}=72$ . When at $(2,3)$ , the $x$ -coordinate changes at -5 units/min. Find the rate of change of the $y$ -coordinate.
$\frac{dy}{dt}=$ (Type an integer or a fraction. Simplify your answer.)

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Problem 8468

Formular la afirmación como una desigualdad. $x - 2 \leq -17$

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Problem 8469

Solve the quadratic equation $\tan^{2} x - 6 \tan x + 5 = 0$ for $x$ .

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Problem 8470

Simplify the expression $x^2 \cdot x^3$ .

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Problem 8471

Find the value of $x$ that satisfies the inequality $\frac{4}{7} < x < 62\%$ .

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Problem 8472

Solve for $x$ using the multiplication principle: $5x=50$ .

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Problem 8473

Convert fractions to decimals rounded to nearest hundredth. Examples: $1/3 \approx 0.33$ , $1/6 \approx$ , $4/9 \approx$ , $5/7 \approx$ .

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Problem 8474

Divide the mixed number $3 \frac{1}{3}$ by the fraction $\frac{2}{3}$ .

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Problem 8475

Solve for the variable $v$ in the equation $\frac{5}{v} = -6$ .

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Problem 8476

Divide 8.35 by 0.62 and round the result to the nearest hundredth.

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Problem 8477

Formular la afirmación como una desigualdad. $x - 3 < 23$

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Problem 8478

Find the value of $y$ when $y = 5 \cdot \frac{1}{2}$ .

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Problem 8479

Which set of $(x, y)$ pairs represents a linear function? $\mathbf{A}=\{(-6,0),(-3,3),(0,6),(3,9)\}$

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Problem 8480

Determinar la pendiente y el punto de intersección con el eje y de la línea recta $y=7-\frac{1}{4}x$ .

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Problem 8481

What is the value of $x$ that satisfies $7 \cdot \ln x=2.4$ ? (Round to two decimal places.) A. $x=18.48$ B. $x=99.48$ C. $x=1.98$ D. $x=1.41$

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Problem 8482

Find the exponent that makes the equation $\left(\frac{1}{5}\right)^{?}=25$ true.

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Problem 8483

Solve for $x$ in the equation $4x + 8 = 28$ by first performing which operation?

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Problem 8484

Simplify the expression $\left(y^{6}\right)^{-2}$ without using negative exponents.

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Problem 8485

Find the value of $C(-2)$ where $C(t) = t^2 - 2t - 4$ .

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Problem 8486

Solve for $x$ in the equation $x-5=t$ .

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Problem 8487

Find the value of $z$ given the equations $ST = -z + 91$ , $RU = z$ , and $QV = z + 23$ .

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Problem 8488

Determine which of the given points $(2,0)$ , $(0,4)$ , $(3,1)$ , or $(-1,6)$ do not satisfy the equation $2x + y = 4$ .

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Problem 8489

Evaluate the expression $9+5(3+9)$ and enter the result as an integer or decimal number.

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Problem 8490

Simplify $(w^{1/2})^{2/5}$ and write the answer in exponential form.

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Problem 8491

Calculate $g(4)$ and $g'(4)$ where $g(x)$ is the inverse of $f(x)=\sqrt{x^2+6x}$ for $x \geq 0$ .

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Problem 8492

Solve for the value of $r$ given the equation $5=r-8$ .

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Problem 8493

Generate a scatter plot with regression equation $y=32.73x+15.14$ and $r=0.044$ . What proportion of variation in $y$ can be explained by the regression? Round to 3 decimals. What is the symbol for this calculation? What is this term called?

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Problem 8494

Depreciate a $2,100 computer over 7 years using straight-line method. Find the book value function, domain, graph, value after 3 years, and when value is$ 600.

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Problem 8495

Find the product of $f(x) = 1/x$ and $g(x) = 4x + 7$ .

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Problem 8496

Solve for $w$ in the proportion $(w+4)/7 = 5/4$ . Simplify the result.

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Problem 8497

Simplify $3(x^2 - 2) - 4x(5 - x)$ and express in standard form.

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Problem 8498

Find the indefinite integral of $\frac{6}{x}+\frac{10}{9\sqrt{x}}$ on the positive real numbers. Translate the password using $\sin(2x)$ and $\sqrt{a}$ .

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Problem 8499

Evaluate $\sin(-3\pi/8)$ using half-angle formula. Find measure of angle $\alpha$ where $\alpha/2=-3\pi/8$ . Determine quadrant of half-angle $\alpha/2$ .

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Problem 8500

Solve the cubic equation $\sqrt[3]{7x-7} = \sqrt[3]{8x+7}$ for the unknown variable $x$ .

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Math

Problem 8401

Solve the linear equations: −5a=−0.2-5a = -0.2−5a=−0.2, b+14.5=10b + 14.5 = 10b+14.5=10, and 2=−15c2 = -\frac{1}{5}c2=−51​c.

Problem 8402

Demuestra que si aaa es impar, entonces a2+3a+5a^2 + 3a + 5a2+3a+5 es impar.

Problem 8403

Find the solution(s) to the quadratic equation y2−2y−8=7y^2 - 2y - 8 = 7y2−2y−8=7.

Problem 8404

Andre wants to make an open-top box by cutting out corners of a 22 in x 28 in poster board and folding up the sides. Find the volume V(x)V(x)V(x) of the box, where xxx is the side length of the square cutout. Determine the volume when x=6x=6x=6 and the reasonable domain for VVV.

Problem 8405

Show that if x=5+12x=\frac{\sqrt{5}+1}{2}x=25​+1​, then 1+1x=x1+\frac{1}{x}=x1+x1​=x.

Problem 8406

Solve for xxx where 5(4−x)−2x≥3−(x−1)5(4-x)-2x \geq 3-(x-1)5(4−x)−2x≥3−(x−1) and x≤83x \leq \frac{8}{3}x≤38​.

Problem 8407

Find the value of xxx that satisfies the equation 14x−12=8−21x14x - 12 = 8 - 21x14x−12=8−21x. Options: F) 74\frac{7}{4}47​, G) 47\frac{4}{7}74​, H) 0, J) 821\frac{8}{21}218​.

Problem 8408

Find the derivative of the function g(u)=u+12u−1g(u) = \frac{u+1}{2u-1}g(u)=2u−1u+1​ using the definition of derivative. State the domain of g(u)g(u)g(u) and its derivative in interval notation.

Problem 8409

Solve the linear equation −10=−10+7m-10 = -10 + 7m−10=−10+7m for the unknown variable mmm.

Problem 8410

Evaluate and simplify c2=32+102−2(3)(10)cos⁡(34∘)c^{2} = 3^{2} + 10^{2} - 2(3)(10) \cos(34^{\circ})c2=32+102−2(3)(10)cos(34∘), then find ccc.

Problem 8411

Find the derivative of 3x(2x+1)33x(2x+1)^33x(2x+1)3.

Problem 8412

Solve for the value of xxx in the equation −4(2x−11)=12-4(2x-11)=12−4(2x−11)=12. (1 point)

Problem 8413

Find the value of xxx when f(x)=−x−1=6f(x) = -x - 1 = 6f(x)=−x−1=6.

Problem 8414

Find the options that equal 60%60\%60% of 949494.

Problem 8415

Factor quadratic expressions and find the value to complete the square. a) x2−10x+25x^2 - 10x + 25x2−10x+25 b) x2+6x+9x^2 + 6x + 9x2+6x+9 c) x2+5x+25/4x^2 + 5x + 25/4x2+5x+25/4 d) x2−3/2x+9/16x^2 - 3/2 x + 9/16x2−3/2x+9/16 What value is required to complete the square?

Problem 8416

Find the number of times the quadratic function y=15x2+36x+21y = 15x^{2} + 36x + 21y=15x2+36x+21 intersects the xxx-axis.

Problem 8417

Find the value of jjj if the product of 7 and jjj is 91.

Problem 8418

Find the area of a triangle with base 14 cm14 \mathrm{~cm}14 cm and height 5.5 cm5.5 \mathrm{~cm}5.5 cm.

Problem 8419

Problem 8420

Find the factorization of the quadratic function f(x)=2x2+14x+24f(x)=2x^2+14x+24f(x)=2x2+14x+24.

Problem 8421

Shau-uen solved 18.5w+6.5w−2.8w=149.118.5w + 6.5w - 2.8w = 149.118.5w+6.5w−2.8w=149.1. In which step did she make her first error? w=−2.13w = -2.13w=−2.13

Problem 8422

Determine which of the following statements is true given an invertible 3×33 \times 33×3 matrix AAA such that 12\frac{1}{2}21​ is an eigenvalue of A−1A^{-1}A−1 with eigenvector vvv.

Problem 8423

Find the present value of $100,000\$ 100,000$100,000 due in 6 years at a continuous 7% interest rate. The present value is $□\$ \square$□.

Problem 8424

Find the adjoint of a matrix AAA given its inverse A−1=[0121−12]A^{-1}=\left[\begin{array}{cc}0 & \frac{1}{2} \\ 1 & \frac{-1}{2}\end{array}\right]A−1=[01​21​2−1​​].

Problem 8425

Solve the quadratic equation x2−5x+4=10\sqrt{x^2 - 5x} + 4 = 10x2−5x​+4=10.

Problem 8426

Simplify the expression 3c7+18c7\frac{3 c}{7}+\frac{18 c}{7}73c​+718c​.

Problem 8427

Find all complex numbers zzz that satisfy the equation z2=zz^2 = zz2=z.

Problem 8428

Solve the quadratic equation 5p(2p−3)(p+7)=05 p(2 p-3)(p+7)=05p(2p−3)(p+7)=0 and find the values of ppp.

Problem 8429

Solve the initial value problem: dydx=8xe−6y,y(0)=0\frac{d y}{d x}=8 x e^{-6 y}, \quad y(0)=0dxdy​=8xe−6y,y(0)=0.

Problem 8430

Solve for yyy in the linear equation 3x+4y=53x + 4y = 53x+4y=5.

Problem 8431

Identify the exact ordinary differential equation (ODE) from the given options.(x+y)dx+(y+x)dy=0(x+y) dx + (y+x) dy = 0(x+y)dx+(y+x)dy=0 (xy+y)dx+(xy+x)dy=0(xy+y) dx + (xy+x) dy = 0(xy+y)dx+(xy+x)dy=0 (y+2)dx+(2x+1)dy=0(y+2) dx + (2x+1) dy = 0(y+2)dx+(2x+1)dy=0

Problem 8432

Find the equation of the line with ∇=−3\nabla = -3∇=−3 that passes through the point (3,1)(3, 1)(3,1).

Problem 8433

Problem 8434

Find the value of g(12)g\left(\frac{1}{2}\right)g(21​) where g(x)=−x2+6x−3g(x)=-x^{2}+6 x-3g(x)=−x2+6x−3. (Type an integer or a fraction.)

Problem 8435

Simplify the expression (x−3)(x+9)(x-3)(x+9)(x−3)(x+9).

Problem 8436

Solve for bbb in the equation Db2−4g=mD b^{2} - 4 g = mDb2−4g=m, where all variables are positive.

Problem 8437

Calculate the value of the expression 4(g−h)+104(g-h)+104(g−h)+10 when g=12g=12g=12 and h=7h=7h=7.

Problem 8438

If a polynomial divides a binomial with zero remainder, the binomial is a factor of the polynomial.

Problem 8439

Are 3x+23x + 23x+2 and 2+3x2 + 3x2+3x equivalent algebraic expressions? Yes or no?

Problem 8440

Find the range of values for sin⁡−1x\sin^{-1} xsin−1x, the inverse sine function.

Problem 8441

Solve the linear equations: $-5a = -0.2$ , $b + 14.5 = 10$ , and $2 = -\frac{1}{5}c$ .

Demuestra que si $a$ es impar, entonces $a^2 + 3a + 5$ es impar.

Find the solution(s) to the quadratic equation $y^2 - 2y - 8 = 7$ .

Andre wants to make an open-top box by cutting out corners of a 22 in x 28 in poster board and folding up the sides. Find the volume $V(x)$ of the box, where $x$ is the side length of the square cutout. Determine the volume when $x=6$ and the reasonable domain for $V$ .

Show that if $x=\frac{\sqrt{5}+1}{2}$ , then $1+\frac{1}{x}=x$ .

Solve for $x$ where $5(4-x)-2x \geq 3-(x-1)$ and $x \leq \frac{8}{3}$ .

Find the value of $x$ that satisfies the equation $14x - 12 = 8 - 21x$ . Options: F) $\frac{7}{4}$ , G) $\frac{4}{7}$ , H) 0, J) $\frac{8}{21}$ .

Find the derivative of the function $g(u) = \frac{u+1}{2u-1}$ using the definition of derivative. State the domain of $g(u)$ and its derivative in interval notation.

Solve the linear equation $-10 = -10 + 7m$ for the unknown variable $m$ .

Evaluate and simplify $c^{2} = 3^{2} + 10^{2} - 2(3)(10) \cos(34^{\circ})$ , then find $c$ .

Find the derivative of $3x(2x+1)^3$ .

Solve for the value of $x$ in the equation $-4(2x-11)=12$ . (1 point)

Find the value of $x$ when $f(x) = -x - 1 = 6$ .

Find the options that equal $60\%$ of $94$ .

Factor quadratic expressions and find the value to complete the square. a) $x^2 - 10x + 25$ b) $x^2 + 6x + 9$ c) $x^2 + 5x + 25/4$ d) $x^2 - 3/2 x + 9/16$ What value is required to complete the square?

Find the number of times the quadratic function $y = 15x^{2} + 36x + 21$ intersects the $x$ -axis.

Find the value of $j$ if the product of 7 and $j$ is 91.

Find the area of a triangle with base $14 \mathrm{~cm}$ and height $5.5 \mathrm{~cm}$ .

Find the factorization of the quadratic function $f(x)=2x^2+14x+24$ .

Shau-uen solved $18.5w + 6.5w - 2.8w = 149.1$ . In which step did she make her first error? $w = -2.13$

Determine which of the following statements is true given an invertible $3 \times 3$ matrix $A$ such that $\frac{1}{2}$ is an eigenvalue of $A^{-1}$ with eigenvector $v$ .

Find the present value of $\$ 100,000$ due in 6 years at a continuous 7% interest rate. The present value is $\$ \square$ .

Find the adjoint of a matrix $A$ given its inverse $A^{-1}=\left[\begin{array}{cc}0 & \frac{1}{2} \\ 1 & \frac{-1}{2}\end{array}\right]$ .

Solve the quadratic equation $\sqrt{x^2 - 5x} + 4 = 10$ .

Simplify the expression $\frac{3 c}{7}+\frac{18 c}{7}$ .

Find all complex numbers $z$ that satisfy the equation $z^2 = z$ .

Solve the quadratic equation $5 p(2 p-3)(p+7)=0$ and find the values of $p$ .

Solve the initial value problem: $\frac{d y}{d x}=8 x e^{-6 y}, \quad y(0)=0$ .

Solve for $y$ in the linear equation $3x + 4y = 5$ .

Identify the exact ordinary differential equation (ODE) from the given options.
$(x+y) dx + (y+x) dy = 0$ $(xy+y) dx + (xy+x) dy = 0$ $(y+2) dx + (2x+1) dy = 0$

Find the equation of the line with $\nabla = -3$ that passes through the point $(3, 1)$ .

Find the value of $g\left(\frac{1}{2}\right)$ where $g(x)=-x^{2}+6 x-3$ . (Type an integer or a fraction.)

Simplify the expression $(x-3)(x+9)$ .

Solve for $b$ in the equation $D b^{2} - 4 g = m$ , where all variables are positive.

Calculate the value of the expression $4(g-h)+10$ when $g=12$ and $h=7$ .

Are $3x + 2$ and $2 + 3x$ equivalent algebraic expressions? Yes or no?

Find the range of values for $\sin^{-1} x$ , the inverse sine function.

Find the value of $y$ when $x=5$ in the rational function $y=\frac{35}{x}$ . The correct answer is $y=7$ .

Convert $4$ quarter hours to hours.

(1 point) If you drive 17.5 laps around a circular track and go $27 \mathrm{mi}$ , what is the track's radius? Round to 2 decimal places.

Solve for $b$ in the equation $-3=\frac{6}{5}b$ .

Solve for $x$ using cross multiplication. Show all work on both sides of the equation: $\frac{x}{5} = \frac{8.5}{2.5}$ , $2.5x = 42.5$ , $x = 17$ .

Multiply the expression $(\sqrt{7}+x)^{2}$ assuming all variables represent positive real numbers.

Find the sum of $9x - 9y$ and $-9x + 9$ .

Solve the linear equation $5x + 6 + 7x = 0$ for the unknown variable $x$ .

Solve the equation $7x - (5x - 1) = 2$ and express the answer as an integer or simplified fraction.

Solve the equation $3(2u-1)+4u+3=4(u+5)+2u$ . Express the solution $u$ as an integer or simplified fraction.

Find a number where 4 times the number minus 18 is -6. Write an equation and solve for the number.
$4n - 18 = -6$

Find the product of $(y+1)(2y+3)$ and simplify the result.

Evaluate the expression: $(3.4+4.4) \times(4.8 \div 0.4)$

Solve for the interval where $5x + 5 < 2x - 4$ graphically using the intersection method.

Find the solution set for the inequality $x - 21.8 < 19.7$ . The solution set is $2.1 < x < 41.5$ .

Multiply the expression $\frac{1}{2}(4 y+4 x-8 z)$ and simplify the result.

Solve the quadratic equation $x=\frac{-(-3) \pm \sqrt{(-3)^{2}-4(-2)(5)}}{2(-2)}$ for $x$ .

Evaluate the expression $\frac{a^{2}-b^{2}}{a-b}$ when $a=9$ and $b=5$ .

Rewrite the polynomial $y + \frac{1}{3} - x$ in the form $a x + b y + c$ , then find $a, b, c$ .

Solve the absolute value equation $|z+10|=|z-6|$ . Select the correct choice: A. The solution is $z = -8, 4$ or B. There is no solution.

Solve for $x$ where $|x|>10$ . Select the correct solution: A. $x<-10$ or $x>10$ (Simplified) B. $-\infty<x<-10$ or $10<x<\infty$ (Simplified)

Find the product of two binomials. Simplify completely. a) $(6x + \sqrt{11})(6x - \sqrt{11})$ b) $(\sqrt{2}x - 7)(\sqrt{2}x + 7)$

The point is moving along $x^{3}y^{2}=72$ . When at $(2,3)$ , the $x$ -coordinate changes at -5 units/min. Find the rate of change of the $y$ -coordinate.
$\frac{dy}{dt}=$ (Type an integer or a fraction. Simplify your answer.)

Formular la afirmación como una desigualdad. $x - 2 \leq -17$

Solve the quadratic equation $\tan^{2} x - 6 \tan x + 5 = 0$ for $x$ .

Simplify the expression $x^2 \cdot x^3$ .

Find the value of $x$ that satisfies the inequality $\frac{4}{7} < x < 62\%$ .

Solve for $x$ using the multiplication principle: $5x=50$ .

Convert fractions to decimals rounded to nearest hundredth. Examples: $1/3 \approx 0.33$ , $1/6 \approx$ , $4/9 \approx$ , $5/7 \approx$ .

Divide the mixed number $3 \frac{1}{3}$ by the fraction $\frac{2}{3}$ .