Numbers & Operations

Problem 2301

Select the constraint $x_{1} - x_{5} \leq 1$ to ensure that if project 1 is chosen, project 5 must not be chosen.

See Solution

Problem 2302

Determine if the function $y=f(x)$ with given $(x,y)$ pairs is linear or nonlinear. If linear, find the slope.

See Solution

Problem 2303

Find the third term in $(x+y)^{8}$ when $x=0.3$ and $y=0.7$ .

See Solution

Problem 2304

Find $n(B)$ if $n(A \times B)=92$ and $n(A)=23$ .

See Solution

Problem 2305

Complete the expansion of $(y-z)^{3}$ using Pascal's Triangle.
$y^{3}-3y^{2}z+3yz^{2}-z^{3}$

See Solution

Problem 2306

Find the greatest common factor (GCF) of the terms $35c + 14b - 7$ and simplify the expression.

See Solution

Problem 2307

Solve for $x$ in the equation $x+5.15=23.85$ .

See Solution

Problem 2308

Find all possible values of $x$ in the equation $x^2 = 1/36$ .

See Solution

Problem 2309

Find the solutions to the equation $\cos x = -\sqrt{2}/2$ for $0 \leq x < 2\pi$ .

See Solution

Problem 2310

Exponential drug decay: A patient has $400 \mathrm{mg}$ of a drug decreasing by $7 \%$ per hour. Identify the correct equation: $f(x)=400 \cdot 0.93^{x}$

See Solution

Problem 2311

Find the equation of the circle with center at (1,-1) and passing through (-2,3).

See Solution

Problem 2312

Find equations with $x = \pm 3$ as solutions. Select all that apply: $x^2 = 9$ , $x^3 = 27$

See Solution

Problem 2313

Solve for $x$ in the equation $33=32x-31$ .

See Solution

Problem 2314

Find the expression equal to $\frac{7}{8}$ : A) $8-7$ B) $7 \times 8$ C) $\frac{8}{7}$ D) $7 \div 8$

See Solution

Problem 2315

Solve the linear equation $3x - y = -12$ for $y$ .

See Solution

Problem 2316

Solve for $\omega$ in the equation $4\omega=36$ .

See Solution

Problem 2317

Write the $s$ -th term of $(s-t)^2$ using Pascal's Triangle.

See Solution

Problem 2318

At most, how many turning points does the polynomial $P(x)=25 x^{110}-19 x^{37}+43 x^{20}-32 x^{17}$ have?

See Solution

Problem 2319

Find the values of $x$ where $\csc x = -1$ .

See Solution

Problem 2320

Find the value of $x$ that satisfies the equation $12 x = 60$ .

See Solution

Problem 2321

Find all solutions of the equation $\tan x=1$ . The solutions are $x=45^\circ+n\cdot180^\circ$ , where $n$ is any integer.

See Solution

Problem 2322

Find the number of classes and their lower/upper class limits given the minimum, maximum, and class width.
$\text{minimum} = 9, \text{maximum} = 80, \text{number of classes} = 7$
The class width is $11$ . Find the lower class limits and upper class limits.

See Solution

Problem 2323

Plug $-2 x^{2}+10 x-8$ into DESMOS and find the vertex, orientation, axis of symmetry, x-intercepts, y-intercept, domain, and range.

See Solution

Problem 2324

Solve for $k$ in the equation $(k+5)(k-8)=0$ . The solutions are $k=8$ or $k=-5$ .

See Solution

Problem 2325

Find the simplified expression of $g(x) - f(x)$ , where $f(x) = 5x + 3$ and $g(x) = x^2 - x + 1$ . Then, determine the domain of the simplified expression.

See Solution

Problem 2326

Find the size of matrix $B$ if $A$ is a $3 \times 8$ matrix and $A(B B)$ is defined.

See Solution

Problem 2327

Which equation shows a proportional relationship? (B) $y=\frac{2}{3} x$

See Solution

Problem 2328

Solve $x^4 + 5x^2 - 24 = 0$ by factoring. List rational, irrational, and imaginary solutions.

See Solution

Problem 2329

Solve for $y$ in the equation $e^{-8 y}=9$ . Round the answer to the nearest hundredth.

See Solution

Problem 2330

Solve for $x$ in the equation $10^{2x} - 9(10^x) + 18 = 0$ . Round to nearest hundredth. Separate multiple solutions with commas.

See Solution

Problem 2331

Calculate the missing terms in the proportions: $4: 10=x: 50$ and $4.90: 6.30=x: 11.34$ . Round the solutions to two decimal places.

See Solution

Problem 2332

Determine if each number can be written as a fraction, and provide the reason. $9$ , $0.63$ , $0.\overline{3}$ , $0.444\ldots$ , $0.132459\ldots$

See Solution

Problem 2333

Find the equation that represents "25 more than a number is 32".
$x + 25 = 32$

See Solution

Problem 2334

Solve $f(x)=-x^{2}+9=0$ , $f(x)>0$ , $f(x) \geq 9$ , $g(x)=4x+9=0$ , $g(x) \leq 0$ , $f(x)=g(x)$ , $f(x)>g(x)$ . The solution to $f(x)=0$ is $x=3$ .

See Solution

Problem 2335

Solve the linear equation $-5(2n+3)+3(3n+4)=-8$ and choose the correct answer.

See Solution

Problem 2336

Find the intersection and union of the intervals $(-5,1)$ and $(-6,-1)$ , and express the results in interval notation.

See Solution

Problem 2337

Find the value of the expression $-7-14$ .

See Solution

Problem 2338

The function $f(x)=x^2+6x-16$ has real roots. The $x$ -intercepts of $y=x^2+7x+6$ are the factors of $x^2+7x+6$ .

See Solution

Problem 2339

Convert 14 gallons to quarts. $14 \text{ gallons} = \square \text{ quarts}$

See Solution

Problem 2340

Determine the smaller negative integer $x$ given that two negative integers 8 units apart have a product of 308. The equation is $x^{2}-8x-308=0$ .

See Solution

Problem 2341

Solve the differential equation $\frac{d y}{d x} = -\frac{e^{x}}{8}$ .

See Solution

Problem 2342

Find the missing values to make the fractions equivalent: $\frac{2 \cdot \square}{3 \cdot 4}=\frac{\square}{12}$ (Simplify your answer).

See Solution

Problem 2343

Redefine the quadratic equation $4 x^{2}+7 x-4=-2$ to vertex form. What is the first step to factor this quadratic? What is the factored form? What are the solutions?

See Solution

Problem 2344

Find $c-x=11$ , then evaluate: $-(c-x)$ , $x-c$ , and $c+(-x)$ .

See Solution

Problem 2345

Find the value of $v$ if $3v/7=6$ .

See Solution

Problem 2346

Find the other solution to the equation $(6 x+4)^{2}=\square$ given that $x=-\frac{4}{3}$ is one solution.

See Solution

Problem 2347

Isolate the variable in the equation $-\frac{x}{7}=6$ . What operation solves for $x$ ?

See Solution

Problem 2348

Find the modes of the sibling count data: $1, 2, 4, 0, 3$ .

See Solution

Problem 2349

Prove that for any real $x$ , if $x^2 - 6x + 5 > 5$ , then $x \geq 5$ or $x \leq 1$ . Identify the assumed and proven facts in a proof by contrapositive.

See Solution

Problem 2350

Solve the quadratic equation $7x^2 + 15x - 2 = 18$ for exact and approximate solutions.

See Solution

Problem 2351

Convert $1,374,000,000$ to scientific notation.

See Solution

Problem 2352

Solve the equation $4m-5=-1$ and present the solution as an integer or reduced fraction.

See Solution

Problem 2353

Factor the binomial $s^2 + 9$ completely. Select "Prime" if the polynomial cannot be factored.

See Solution

Problem 2354

Divide $61,000,000 \div 912.7$ and express the answer using significant figures.

See Solution

Problem 2355

Find the $\operatorname{LCM}$ and $\operatorname{GCF}$ of given numbers using the list method. Additional materials: eBook.

See Solution

Problem 2356

Find the value of $H$ that satisfies the equation $(2H-3)(3H+1)H=4484$ .

See Solution

Problem 2357

Divide a 3-digit integer ending in 5 by 5 mentally using an appropriate strategy.

See Solution

Problem 2358

Simplify the product $(3x-4)(6x-2)$ using FOIL method. (1 point)

See Solution

Problem 2359

Solve for $a$ when $\frac{a}{9}=6$ .

See Solution

Problem 2360

Simplify the expression $9.26 + \left(\frac{1}{4} \cdot 2\right)$ and find the result.

See Solution

Problem 2361

Rewrite $f(x)$ as $(x-k)q(x)+r$ given $f(x)=2x^3+x^2+x-4$ and $k=-1$ .

See Solution

Problem 2362

Calculate values of $f(x)=2 x^{2}-8 x+6$ for $x=-2, -1, 0, 1, 2$ .

See Solution

Problem 2363

Find the value of $\frac{(9^2 - 65)}{2^2}$ .

See Solution

Problem 2364

Factor -1 from one denominator to simplify binomial expressions. Restrictions apply. a) $\frac{1}{x-2}+\frac{1}{x-2}$ b) $\frac{2x-7}{x-3}+\frac{-(x-9)}{x-3}$

See Solution

Problem 2365

Solve the quadratic equation $(11 v + 5)(6 v - 18) = 0$ to find the values of $v$ .

See Solution

Problem 2366

Simplify the expression $\left(\frac{z}{w}\right)^{2}$ by applying the appropriate property.

See Solution

Problem 2367

Find the value of $c$ that satisfies the Mean Value Theorem for $h(x) = \sqrt{3x-3}$ on the interval $4 \leq x \leq 13$ .

See Solution

Problem 2368

(1 point) A Ferris wheel with 35 m diameter rotates fully every 6 minutes. At $t=0$ , you are at the 3 o'clock position and ascending. Find a formula for $f(t)$ , your height (in m) above ground at $t$ minutes.
$f(t) = 17.5 \sin\left(\frac{\pi t}{3}\right) + 17.5$

See Solution

Problem 2369

Find the value of constant $c$ in the equation $(t+1)^{2} + c = 0$ with solutions at $t = \frac{3}{2}$ and $t = -\frac{7}{2}$ .

See Solution

Problem 2370

Solve for $x$ where $\ln (3x+2)=4$ . The solution is $x=\frac{2}{3}$ .

See Solution

Problem 2371

Find the radius of convergence $R$ of the power series $\sum_{n=1}^{\infty} \frac{(-4)^{n}}{\sqrt{n}}(x+8)^{n}$ . If $R$ is infinite, type "infinity" or "inf". Answer: $R=\frac{1}{4}$ . What is the interval of convergence? Answer (in interval notation): $(-12, -4)$ .

See Solution

Problem 2372

Convert time from 24-hour format to 12-hour format. Given 1825, find the corresponding traditional time.

See Solution

Problem 2373

Sketch the graph of the vertical line $x=3$ .

See Solution

Problem 2374

Select all true statements about the expression $4a + 5b + 9 + 3b$ : $4a$ is a term, $4a$ is a coefficient, $5b$ and $3b$ are like terms, $9$ is a constant.

See Solution

Problem 2375

Find the product of three consecutive integers using the formula $n^3 - n$ . Use the factorization of $2x^3 + 8x^2 + 8x$ to determine the value of $(20)(12)^2$ .

See Solution

Problem 2376

Find the missing addend in the equation $28 + \square = 49$ .

See Solution

Problem 2377

Find the derivative of $g(t)=6t-1$ using the limit definition.

See Solution

Problem 2378

Select the value of $x$ that disproves the statement: for all integers $x$ , $x < x^2$ . Options: $x=-1/2$ , $x=-1$ , $x=1$ , $x=1/2$ .

See Solution

Problem 2379

Find the other roots of $f(x) = x^2 + 158x - 37109$ given that $-79 + 85\sqrt{6}$ is a root.

See Solution

Problem 2380

Find the value of $a$ such that when $x^3 + a x^2 + 4$ is divided by $x + 1$ , the remainder is 6 greater than the remainder when divided by $x - 2$ .

See Solution

Problem 2381

Find the reciprocal of the expression $\frac{1}{g+w}$ .

See Solution

Problem 2382

Solve multi-step linear equations. 1. $7c - 3 + 2c = 15$ 2. $5(x - 7) = 20$ 3. $6h + 5 = 10 + h$ 4. $60 = -4(3y - 6)$ 5. $-5g + 24 = 7g - 24$ 6. $22 = 3u + 10 - 5u$ 7. $-5(3k - 3) + 17 = -43$ 8. $7t - 5 + 4t = 3t - 21$ 9. $5m - 7 = 3(2m + 1)$ 10. $-12 = 4(2q + 7) - 3q$ 11. $-11 - 6b + 3 = 16 + 2b$ 12. $5(8 - 2w) = 4 - 4w$

See Solution

Problem 2383

Evaluate the expression $(2+\sqrt{2})^{2}$ .

See Solution

Problem 2384

Find the value of the expression $\frac{\tan 80^{\circ}+\tan 55^{\circ}}{1-\tan 80^{\circ} \tan 55^{\circ}}$ .

See Solution

Problem 2385

Evaluate the sum of the geometric series $\sum_{n=1}^{5} 6(2)^{n-1}$ and solve for $S$ .

See Solution

Problem 2386

Simplify the expression $\frac{y^{2}-36}{y} \div \frac{y+6}{y-6}$ .

See Solution

Problem 2387

Redefine $m(x) = (3x-1)(3-x) + 4x^2 + 19$ as a trinomial. Solve for $x$ when $m(x) = 0$ .

See Solution

Problem 2388

Solve for the unknown variable $y$ in the equation $6y - 1 = 31 - 6y + 8y$ . Round the solution to two decimal places.

See Solution

Problem 2389

Solve the equation $6x - 5 = 31$ . Select the correct choice: A. The solution set is { $\frac{36}{6}$ }.

See Solution

Problem 2390

Find the inverse cosine of -0.8 and express the result in radians, rounded to the nearest hundredth.

See Solution

Problem 2391

Determine the behavior of the function $f(x) = (2x + 1) \cdot e^{-x}$ for very large and very small values of $x$ .

See Solution

Problem 2392

Evaluate the limit $\lim_{x \to \pi/2} (\sec(x) - \tan(x))$ . Use symbolic notation and fractions.

See Solution

Problem 2393

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

See Solution

Problem 2394

Evaluate the natural logarithm of 0.012 and give the answer to 4 decimal places. $\ln (0.012)$

See Solution

Problem 2395

Distribute $y^{2}(-3 y-7)$ and select the simplified answer.

See Solution

Problem 2396

Write an expression for a number $x$ decreased by $12.5\%$ .

See Solution

Problem 2397

Resuelve la desigualdad $-8.4 \leq w - 0.8$ para encontrar el valor de $w$ .

See Solution

Problem 2398

Analyze the properties of the logarithmic functions $y=\log_2(x+1)$ and $y=\log(x)-3$ , including domain, range, asymptotes, x-intercepts, and transformations.

See Solution

Problem 2399

Solve the quadratic equation $z^{2} - 13z + 12 = 0$ for real values of $z$ .

See Solution

Problem 2400

Use Newton's method to find the solution to $e^{-2x} = -3x + 9$ starting with $x_0 = -5$ . Provide the first two iterates $x_1$ and $x_2$ , and the final solution accurate to 4 decimal places.

See Solution

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Numbers & Operations

Problem 2301

Select the constraint x1−x5≤1x_{1} - x_{5} \leq 1x1​−x5​≤1 to ensure that if project 1 is chosen, project 5 must not be chosen.

Problem 2302

Determine if the function y=f(x)y=f(x)y=f(x) with given (x,y)(x,y)(x,y) pairs is linear or nonlinear. If linear, find the slope.

Problem 2303

Find the third term in (x+y)8(x+y)^{8}(x+y)8 when x=0.3x=0.3x=0.3 and y=0.7y=0.7y=0.7.

Problem 2304

Find n(B)n(B)n(B) if n(A×B)=92n(A \times B)=92n(A×B)=92 and n(A)=23n(A)=23n(A)=23.

Problem 2305

Complete the expansion of (y−z)3(y-z)^{3}(y−z)3 using Pascal's Triangle.y3−3y2z+3yz2−z3y^{3}-3y^{2}z+3yz^{2}-z^{3}y3−3y2z+3yz2−z3

Problem 2306

Find the greatest common factor (GCF) of the terms 35c+14b−735c + 14b - 735c+14b−7 and simplify the expression.

Problem 2307

Solve for xxx in the equation x+5.15=23.85x+5.15=23.85x+5.15=23.85.

Problem 2308

Find all possible values of xxx in the equation x2=1/36x^2 = 1/36x2=1/36.

Problem 2309

Find the solutions to the equation cos⁡x=−2/2\cos x = -\sqrt{2}/2cosx=−2​/2 for 0≤x<2π0 \leq x < 2\pi0≤x<2π.

Problem 2310

Exponential drug decay: A patient has 400mg400 \mathrm{mg}400mg of a drug decreasing by 7%7 \%7% per hour. Identify the correct equation: f(x)=400⋅0.93xf(x)=400 \cdot 0.93^{x}f(x)=400⋅0.93x

Problem 2311

Find the equation of the circle with center at (1,-1) and passing through (-2,3).

Problem 2312

Find equations with x=±3x = \pm 3x=±3 as solutions. Select all that apply: x2=9x^2 = 9x2=9, x3=27x^3 = 27x3=27

Problem 2313

Solve for xxx in the equation 33=32x−3133=32x-3133=32x−31.

Problem 2314

Find the expression equal to 78\frac{7}{8}87​: A) 8−78-78−7 B) 7×87 \times 87×8 C) 87\frac{8}{7}78​ D) 7÷87 \div 87÷8

Problem 2315

Solve the linear equation 3x−y=−123x - y = -123x−y=−12 for yyy.

Problem 2316

Solve for ω\omegaω in the equation 4ω=364\omega=364ω=36.

Problem 2317

Write the sss-th term of (s−t)2(s-t)^2(s−t)2 using Pascal's Triangle.

Problem 2318

At most, how many turning points does the polynomial P(x)=25x110−19x37+43x20−32x17P(x)=25 x^{110}-19 x^{37}+43 x^{20}-32 x^{17}P(x)=25x110−19x37+43x20−32x17 have?

Problem 2319

Find the values of xxx where csc⁡x=−1\csc x = -1cscx=−1.

Problem 2320

Find the value of xxx that satisfies the equation 12x=6012 x = 6012x=60.

Problem 2321

Find all solutions of the equation tan⁡x=1\tan x=1tanx=1. The solutions are x=45∘+n⋅180∘x=45^\circ+n\cdot180^\circx=45∘+n⋅180∘, where nnn is any integer.

Problem 2322

Problem 2323

Plug −2x2+10x−8-2 x^{2}+10 x-8−2x2+10x−8 into DESMOS and find the vertex, orientation, axis of symmetry, x-intercepts, y-intercept, domain, and range.

Problem 2324

Solve for kkk in the equation (k+5)(k−8)=0(k+5)(k-8)=0(k+5)(k−8)=0. The solutions are k=8k=8k=8 or k=−5k=-5k=−5.

Problem 2325

Find the simplified expression of g(x)−f(x)g(x) - f(x)g(x)−f(x), where f(x)=5x+3f(x) = 5x + 3f(x)=5x+3 and g(x)=x2−x+1g(x) = x^2 - x + 1g(x)=x2−x+1. Then, determine the domain of the simplified expression.

Problem 2326

Find the size of matrix BBB if AAA is a 3×83 \times 83×8 matrix and A(BB)A(B B)A(BB) is defined.

Problem 2327

Which equation shows a proportional relationship? (B) y=23xy=\frac{2}{3} xy=32​x

Problem 2328

Solve x4+5x2−24=0x^4 + 5x^2 - 24 = 0x4+5x2−24=0 by factoring. List rational, irrational, and imaginary solutions.

Problem 2329

Solve for yyy in the equation e−8y=9e^{-8 y}=9e−8y=9. Round the answer to the nearest hundredth.

Problem 2330

Solve for xxx in the equation 102x−9(10x)+18=010^{2x} - 9(10^x) + 18 = 0102x−9(10x)+18=0. Round to nearest hundredth. Separate multiple solutions with commas.

Problem 2331

Calculate the missing terms in the proportions: 4:10=x:504: 10=x: 504:10=x:50 and 4.90:6.30=x:11.344.90: 6.30=x: 11.344.90:6.30=x:11.34. Round the solutions to two decimal places.

Problem 2332

Determine if each number can be written as a fraction, and provide the reason. 999, 0.630.630.63, 0.3‾0.\overline{3}0.3, 0.444…0.444\ldots0.444…, 0.132459…0.132459\ldots0.132459…

Problem 2333

Find the equation that represents "25 more than a number is 32".x+25=32x + 25 = 32x+25=32

Problem 2334

Solve f(x)=−x2+9=0f(x)=-x^{2}+9=0f(x)=−x2+9=0, f(x)>0f(x)>0f(x)>0, f(x)≥9f(x) \geq 9f(x)≥9, g(x)=4x+9=0g(x)=4x+9=0g(x)=4x+9=0, g(x)≤0g(x) \leq 0g(x)≤0, f(x)=g(x)f(x)=g(x)f(x)=g(x), f(x)>g(x)f(x)>g(x)f(x)>g(x). The solution to f(x)=0f(x)=0f(x)=0 is x=3x=3x=3.

Problem 2335

Solve the linear equation −5(2n+3)+3(3n+4)=−8-5(2n+3)+3(3n+4)=-8−5(2n+3)+3(3n+4)=−8 and choose the correct answer.

Problem 2336

Find the intersection and union of the intervals (−5,1)(-5,1)(−5,1) and (−6,−1)(-6,-1)(−6,−1), and express the results in interval notation.

Problem 2337

Find the value of the expression −7−14-7-14−7−14.

Problem 2338

The function f(x)=x2+6x−16f(x)=x^2+6x-16f(x)=x2+6x−16 has real roots. The xxx-intercepts of y=x2+7x+6y=x^2+7x+6y=x2+7x+6 are the factors of x2+7x+6x^2+7x+6x2+7x+6.

Problem 2339

Convert 14 gallons to quarts. 14 gallons=□ quarts14 \text{ gallons} = \square \text{ quarts}14 gallons=□ quarts

Problem 2340

Determine the smaller negative integer xxx given that two negative integers 8 units apart have a product of 308. The equation is x2−8x−308=0x^{2}-8x-308=0x2−8x−308=0.

Select the constraint $x_{1} - x_{5} \leq 1$ to ensure that if project 1 is chosen, project 5 must not be chosen.

Determine if the function $y=f(x)$ with given $(x,y)$ pairs is linear or nonlinear. If linear, find the slope.

Find the third term in $(x+y)^{8}$ when $x=0.3$ and $y=0.7$ .

Find $n(B)$ if $n(A \times B)=92$ and $n(A)=23$ .

Complete the expansion of $(y-z)^{3}$ using Pascal's Triangle.
$y^{3}-3y^{2}z+3yz^{2}-z^{3}$

Find the greatest common factor (GCF) of the terms $35c + 14b - 7$ and simplify the expression.

Solve for $x$ in the equation $x+5.15=23.85$ .

Find all possible values of $x$ in the equation $x^2 = 1/36$ .

Find the solutions to the equation $\cos x = -\sqrt{2}/2$ for $0 \leq x < 2\pi$ .

Exponential drug decay: A patient has $400 \mathrm{mg}$ of a drug decreasing by $7 \%$ per hour. Identify the correct equation: $f(x)=400 \cdot 0.93^{x}$

Find equations with $x = \pm 3$ as solutions. Select all that apply: $x^2 = 9$ , $x^3 = 27$

Solve for $x$ in the equation $33=32x-31$ .

Find the expression equal to $\frac{7}{8}$ : A) $8-7$ B) $7 \times 8$ C) $\frac{8}{7}$ D) $7 \div 8$

Solve the linear equation $3x - y = -12$ for $y$ .

Solve for $\omega$ in the equation $4\omega=36$ .

Write the $s$ -th term of $(s-t)^2$ using Pascal's Triangle.

At most, how many turning points does the polynomial $P(x)=25 x^{110}-19 x^{37}+43 x^{20}-32 x^{17}$ have?

Find the values of $x$ where $\csc x = -1$ .

Find the value of $x$ that satisfies the equation $12 x = 60$ .

Find all solutions of the equation $\tan x=1$ . The solutions are $x=45^\circ+n\cdot180^\circ$ , where $n$ is any integer.

Plug $-2 x^{2}+10 x-8$ into DESMOS and find the vertex, orientation, axis of symmetry, x-intercepts, y-intercept, domain, and range.

Solve for $k$ in the equation $(k+5)(k-8)=0$ . The solutions are $k=8$ or $k=-5$ .

Find the simplified expression of $g(x) - f(x)$ , where $f(x) = 5x + 3$ and $g(x) = x^2 - x + 1$ . Then, determine the domain of the simplified expression.

Find the size of matrix $B$ if $A$ is a $3 \times 8$ matrix and $A(B B)$ is defined.

Which equation shows a proportional relationship? (B) $y=\frac{2}{3} x$

Solve $x^4 + 5x^2 - 24 = 0$ by factoring. List rational, irrational, and imaginary solutions.

Solve for $y$ in the equation $e^{-8 y}=9$ . Round the answer to the nearest hundredth.

Solve for $x$ in the equation $10^{2x} - 9(10^x) + 18 = 0$ . Round to nearest hundredth. Separate multiple solutions with commas.

Calculate the missing terms in the proportions: $4: 10=x: 50$ and $4.90: 6.30=x: 11.34$ . Round the solutions to two decimal places.

Determine if each number can be written as a fraction, and provide the reason. $9$ , $0.63$ , $0.\overline{3}$ , $0.444\ldots$ , $0.132459\ldots$

Find the equation that represents "25 more than a number is 32".
$x + 25 = 32$

Solve $f(x)=-x^{2}+9=0$ , $f(x)>0$ , $f(x) \geq 9$ , $g(x)=4x+9=0$ , $g(x) \leq 0$ , $f(x)=g(x)$ , $f(x)>g(x)$ . The solution to $f(x)=0$ is $x=3$ .

Solve the linear equation $-5(2n+3)+3(3n+4)=-8$ and choose the correct answer.

Find the intersection and union of the intervals $(-5,1)$ and $(-6,-1)$ , and express the results in interval notation.

Find the value of the expression $-7-14$ .

The function $f(x)=x^2+6x-16$ has real roots. The $x$ -intercepts of $y=x^2+7x+6$ are the factors of $x^2+7x+6$ .

Convert 14 gallons to quarts. $14 \text{ gallons} = \square \text{ quarts}$

Determine the smaller negative integer $x$ given that two negative integers 8 units apart have a product of 308. The equation is $x^{2}-8x-308=0$ .

Solve the differential equation $\frac{d y}{d x} = -\frac{e^{x}}{8}$ .

Find the missing values to make the fractions equivalent: $\frac{2 \cdot \square}{3 \cdot 4}=\frac{\square}{12}$ (Simplify your answer).

Redefine the quadratic equation $4 x^{2}+7 x-4=-2$ to vertex form. What is the first step to factor this quadratic? What is the factored form? What are the solutions?

Find $c-x=11$ , then evaluate: $-(c-x)$ , $x-c$ , and $c+(-x)$ .

Find the value of $v$ if $3v/7=6$ .

Find the other solution to the equation $(6 x+4)^{2}=\square$ given that $x=-\frac{4}{3}$ is one solution.

Isolate the variable in the equation $-\frac{x}{7}=6$ . What operation solves for $x$ ?

Find the modes of the sibling count data: $1, 2, 4, 0, 3$ .

Prove that for any real $x$ , if $x^2 - 6x + 5 > 5$ , then $x \geq 5$ or $x \leq 1$ . Identify the assumed and proven facts in a proof by contrapositive.

Solve the quadratic equation $7x^2 + 15x - 2 = 18$ for exact and approximate solutions.

Convert $1,374,000,000$ to scientific notation.

Solve the equation $4m-5=-1$ and present the solution as an integer or reduced fraction.

Factor the binomial $s^2 + 9$ completely. Select "Prime" if the polynomial cannot be factored.

Divide $61,000,000 \div 912.7$ and express the answer using significant figures.

Find the $\operatorname{LCM}$ and $\operatorname{GCF}$ of given numbers using the list method. Additional materials: eBook.

Find the value of $H$ that satisfies the equation $(2H-3)(3H+1)H=4484$ .

Simplify the product $(3x-4)(6x-2)$ using FOIL method. (1 point)

Solve for $a$ when $\frac{a}{9}=6$ .

Simplify the expression $9.26 + \left(\frac{1}{4} \cdot 2\right)$ and find the result.

Rewrite $f(x)$ as $(x-k)q(x)+r$ given $f(x)=2x^3+x^2+x-4$ and $k=-1$ .

Calculate values of $f(x)=2 x^{2}-8 x+6$ for $x=-2, -1, 0, 1, 2$ .

Find the value of $\frac{(9^2 - 65)}{2^2}$ .

Factor -1 from one denominator to simplify binomial expressions. Restrictions apply. a) $\frac{1}{x-2}+\frac{1}{x-2}$ b) $\frac{2x-7}{x-3}+\frac{-(x-9)}{x-3}$

Solve the quadratic equation $(11 v + 5)(6 v - 18) = 0$ to find the values of $v$ .

Simplify the expression $\left(\frac{z}{w}\right)^{2}$ by applying the appropriate property.

Find the value of $c$ that satisfies the Mean Value Theorem for $h(x) = \sqrt{3x-3}$ on the interval $4 \leq x \leq 13$ .

Find the value of constant $c$ in the equation $(t+1)^{2} + c = 0$ with solutions at $t = \frac{3}{2}$ and $t = -\frac{7}{2}$ .

Solve for $x$ where $\ln (3x+2)=4$ . The solution is $x=\frac{2}{3}$ .

Sketch the graph of the vertical line $x=3$ .

Select all true statements about the expression $4a + 5b + 9 + 3b$ : $4a$ is a term, $4a$ is a coefficient, $5b$ and $3b$ are like terms, $9$ is a constant.