Algebra

Problem 23301

Identify the form of the polynomial: $x^{2}+10 x-7 x+4+x^{2}-3 x$ . Is it factored, standard, or mixed?

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Problem 23302

Determine if the polynomial $(9 x-4)(x+7)+1$ is in factored, standard, or mixed form.

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Problem 23303

Simplify $\frac{-4^{6} \cdot 4^{3}}{4^{4}}$ .

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Problem 23304

Simplify $\frac{-4^{6} 4^{23}}{4^{4}}$

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Problem 23305

Simplify $\frac{-40_{0} y^{2}}{4}$ .

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Problem 23306

Find the equivalent expression for $(5 x+2)+(4 x-3)$ . Choices: A. $6 x+2$ , B. $7 x+1$ , C. $9 x-1$ , D. $11 x-3$ , E. $20 x-6$ .

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Problem 23307

Simplify the expression $\frac{-4^{6} \cdot 4^{2}}{4^{4}}$ .

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Problem 23308

Solve the equation: $0.25 r - 0.125 + 0.5 r = 0.5 + r$ . Show all steps.

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Problem 23309

Find $g(f(x))$ given $f(x)=\frac{1}{2x+6}$ and $g(x)=\frac{4}{x}-3$ . Simplify fully, no decimals.

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Problem 23310

Solve the equation: $12x - 11x - 18 = 11$ . What is the value of $x$ ?

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Problem 23311

Find the inverse of the function $f(x)=(x-2)^{2}$ .

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Problem 23312

Solve the inequality $-10 \leq \frac{9 x-4}{4}<8$ and express the solution in interval notation.

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Problem 23313

Isolate $y$ in the equation $-\frac{5}{6} y - \frac{1}{5} y = \frac{4}{3} - \frac{1}{5}$ . Express your answer as an integer.

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Problem 23314

A drug uses 3 mL of compound A for every 5 mL of compound B. How much A is needed for 544 mL of the drug?

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Problem 23315

Simplify the expression $\frac{\sqrt{84}}{2 \sqrt{3}}$ to its simplest radical form.

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Problem 23316

A sculptor makes a $\frac{1}{10}$ scale model of a 56-ton landmark. Solve $10 x=56$ to find the model's weight.

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Problem 23317

Find the values of $y$ for the function $y=-2x$ when $x = -4, 0, 2, 4$ .

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Problem 23318

If a bag has 49 purple marbles, how many yellow marbles are there if the ratio is 5 yellow to 7 purple?

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Problem 23319

The city's yes to no vote ratio is 3:4. With 1743 yes votes, find the total number of votes.

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Problem 23320

Rationalize the denominator of $\frac{5}{\sqrt{3}-1}$ .

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Problem 23321

A sculptor is making a $\frac{1}{9}$ scale model of an 89-ton landmark. Find the model's weight by solving $9x=89$ .

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Problem 23322

Given the function $y=-2x$ , fill in the missing $y$ values for $x = -4$ and $x = 0$ .

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Problem 23323

Solve the equation: $\frac{1}{x}+\frac{1}{x+2}=\frac{1}{7}$ . Provide exact answers, using radicals if necessary.

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Problem 23324

Sketch the graphs of $f(x)=-x^{2}+2x+8$ and $g(x)=2x+4$ . Find the coordinates of points $A$ and $B$ where $f$ intersects the x-axis.

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Problem 23325

If Orly uses 2 cups of raisins for every 8 cups of trail mix, how much trail mix can she make with 10 cups of raisins?

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Problem 23326

Which option shows the commutative property of addition: A, B, C, or D?

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Problem 23327

Solve the equation: $5 x^{2}-6 x=8$ . Provide the exact solution set, using radicals if necessary.

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Problem 23328

Which option shows the distributive property: A. $ab=ba$ , B. $a(bc)=(ab)c$ , C. $a(b+c)=ab+ac$ , D. $a \cdot 1=a$ ?

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Problem 23329

Given $y$ varies inversely with $x$ , and $y=3$ when $x=8$ , find the equation and $y$ when $x=15$ .

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Problem 23330

Solve the equation $2 x^{2}-3=-101$ using the square root property. Simplify and express complex numbers with $i$ .

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Problem 23331

Calculate the future value of \$10,000 at 3% interest compounded monthly for 7 years. Round to the nearest cent.

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Problem 23332

Solve the equation $4 x^{2}=192$ . Provide the simplified solution set using radicals and $i$ for complex answers.

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Problem 23333

Given functions $q(x)=\frac{1}{\sqrt{x}}$ and $h(x)=x^{2}-25$ :
a. Domain of $\frac{q(x)}{h(x)}$ : $x>0, x \neq 5$
b. Domain of $q(h(x))$ : $|x|$ [Select] [Select]
c. Domain of $h(q(x))$ : [Select] [Select]
Please clarify parts b and c for completeness.

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Problem 23334

Given $y$ varies inversely with $x$ and $y=-\frac{3}{2}$ when $x=-8$ , find the equation and $y$ when $x=6$ . $y =$

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Problem 23335

Find the slope of the function $y=12-3x$ . Round your answer to one decimal place.

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Problem 23336

Given $y$ varies inversely with $x$ , and $y=8$ when $x=5$ : (a) Find the equation; (b) Determine $y$ when $x=10$ . $y=$

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Problem 23337

Solve the equation $2 x^{2}-3 x-1=0$ using the quadratic formula. Provide the exact solutions.

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Problem 23338

Simplify the expression $\sqrt{90} \cdot \sqrt{40}-\sqrt{8} \cdot \sqrt{18}$ . What is the result? A. 22.9 B. 48 C. 864 D. 3,456

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Problem 23339

Find the future value of \$5,000 at 6\% annual interest compounded quarterly after 5 years. Round to the nearest cent.

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Problem 23340

Prove that the solutions of $z^{2}-2 z+10=0$ are complex (not real).

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Problem 23341

Bill deposits \$4500 at 4\% annual interest. Calculate the account balance after 1 year and after 2 years.

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Problem 23342

Which option shows the associative property of multiplication? A. $ab=ba$ B. $a(bc)=(ab)c$ C. $a \cdot 1=a$ D. $a(b+c)=ab+ac$

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Problem 23343

Solve for $y$ in the equation: $\frac{9}{28} y - \frac{12}{7} y + \frac{3}{7} = \frac{3}{4}$ .

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Problem 23344

Solve for $y$ in the equation: $\frac{9}{28} y - \frac{12}{7} y + \frac{3}{7} = \frac{3}{4}$ .

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Problem 23345

If \$24 was invested at 3\% annual interest from 1626 to 2020, how much is in the account now? Round to the nearest dollar.

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Problem 23346

Expand $(4 x-5)(6 x+5)$ into a trinomial form.

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Problem 23347

Solve for $x$ : $\frac{8}{17}=\frac{5}{7x}$ . Find $x$ in simplest form.

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Problem 23348

Solve for $x$ : $\frac{x+8}{13}=\frac{2}{9}$ . Find $x$ in simplest form.

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Problem 23349

Factor completely: $5 x^{3}-20 x^{2}-60 x$

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Problem 23350

Solve for $y$ in the equation $-\frac{1}{2} y=10$ .

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Problem 23351

Find the slope of a line perpendicular to $y - 2 = 3x$ . Options: A. -3 B. $-\frac{1}{3}$ C. $\frac{1}{3}$ D. 2 E. 3

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Problem 23352

Find the sum of the first four of eight consecutive odd integers if the sum of the last four is 232.

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Problem 23353

Find the $y$ -intercept of $y=\frac{1}{4} x-\frac{2}{3}$ . A. $-\frac{2}{3}$ B. $\frac{2}{3}$ C. $-\frac{1}{4}$ D. $\frac{1}{4}$

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Problem 23354

Find the $y$ -intercept of the line $2x + y = -3$ . A. -2 B. 2 C. 3 D. -3

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Problem 23355

Find the slope of the line given by the equation $y=-x+2$ .

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Problem 23356

Find the product of the complex numbers $2+7i$ and $3-2i$ . What is the result?

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Problem 23357

Which expression equals $\log \frac{B^{A}}{D^{C}}$ ? F. $A C \log (B-D)$ G. $A \log B-C \log D$ H. $B \log A+D \log C$ J. $B \log A-D \log C$ K. $A \log B \div C \log D$

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Problem 23358

Solve the inequality $153 w + 2 < -12 - (3 w - 2)$ . What is the correct range for $w$ ?

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Problem 23359

Find the explicit formula for the arithmetic sequence starting with $a_{1}=54$ and the first six terms: $54, 73, 92, 111, 130, 149$ .

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Problem 23360

If $|r|=-s$ , what must be true? A. $r=s$ B. $r \neq s$ C. $s=0$ D. $s \leq 0$ E. $r>0$

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Problem 23361

Calculate the investment value using $A=5000(1+0.08)^{15}$ . What is $A$ after 15 years? Options: A. \$2,000 B. \$5,400 C. \$10,882 D. \$15,861 E. \$21,499

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Problem 23362

Rowan's average must stay above 90 after five tests. What is the minimum score he needs on the fifth test?

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Problem 23363

Sketch the graph of $f(x)=(x-4)^{2}-9$ . Find the axis of symmetry, domain, and range. Axis: $x=4$ . Domain: $(-\infty, \infty)$ .

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Problem 23364

Find the mode of the numbers $x, 2x, 2x+6, 3x-1, 4x-8$ if their average is 9.

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Problem 23365

Evaluate $f(x)=4 x^{2}-5$ at $x=5$ and $x=-3$ . Find $f(5)$ and $f(-3)$ .

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Problem 23366

Solve $(x+4)^{2}-4=0$ for real $x$ . Provide simplified solutions, separated by commas if multiple. $x=$

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Problem 23367

Sketch the graph of $f(x)=2(x+3)^{2}-3$ using its vertex and intercepts. Find the axis of symmetry, domain, and range.

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Problem 23368

Evaluate $f(x) = x - 2$ for $x = 0$ and graph the ordered pair $(x, f(x))$ .

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Problem 23369

A store bought 24 keyboards and 15 chargers for \$120, sold keyboards for \$35 and chargers for \$15. Find profit expression.
Part A: Choose the profit expression. $(24)(35)+(15)(15)-120$
Part B: Explain your choice.
Part C: Calculate the chosen expression's value, showing all steps.

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Problem 23370

Find the price $p$ to maximize revenue given the function $R(p)=-7p^2+21,000p$ , and calculate the max revenue.

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Problem 23371

Evaluate $f(x)=(x-5)^{2}$ for $x=3, 4$ and graph the points $(x, f(x))$ .

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Problem 23372

Find the dimensions of a rectangle where length is $11 \mathrm{yd}$ more than twice the width and area is $63 \mathrm{yd}^{2}$ .

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Problem 23373

Solve the equation $x^{2}-12 x+61=0$ using the quadratic formula. Provide the exact solution with radicals and $i$ .

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Problem 23374

Find the zeros of the function $f(x)=x^{2}-147$ using the square root method. What are the $x$ -intercepts?

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Problem 23375

The function $G(x)=-0.01 x^{2}+x+62$ models the wage gap in Country $A$ . Find $G(30)$ and interpret it as a point on the graph.

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Problem 23376

Find the zeros of the function $f(x)=3x^{2}+10x+6$ using the quadratic formula. Are the zeros and $x$ -intercepts the same?

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Problem 23377

Determine if the function $f(x)=-2 x^{2}+16 x-1$ has a max or min value and find that value.

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Problem 23378

Find the zeros of the function $g(x)=5 x^{2}+14 x+8$ using the quadratic formula. What are the x-intercepts?

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Problem 23379

Find $g(x)=|x-x^{2}|$ for $g(4)$ , $g(-7)$ , and $g(-3)$ .

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Problem 23380

Sketch the graph of the function $f(x)=(x-2)^{2}+6$ . Find the axis of symmetry, domain, and range in interval notation.

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Problem 23381

Determine the x-values where $g(x)=\left|x-x^{2}\right|$ reaches its maximum and minimum for all real numbers x.

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Problem 23382

Sketch the graph of $f(x)=2(x-3)^{2}-3$ . Find the axis of symmetry, domain, and range in interval notation.

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Problem 23383

Find the slope of the line through points $(-1,3)$ and $(2,4)$ , and state if it rises, falls, is horizontal, or vertical.

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Problem 23384

For the function $f(x)=x^{2}+4x+4$ , find the vertex, axis of symmetry, $y$ -intercept, and determine if it opens up or down.

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Problem 23385

Find $g(9)$ and $g(-1)$ for the function $g(x)=-x^{2}+10x-3$ .

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Problem 23386

Find $h(x)=|1-7 x|$ and calculate: a. $h(1)$ , b. $h(-7)$ , c. $h(9)$ .

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Problem 23387

Graph the line with slope -4 and $y$ -intercept 5 given by the equation $y=-4x+5$ .

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Problem 23388

A ball is thrown from a building with height $S(t)=112+96t-16t^2$ .
(a) When does it hit the ground? (b) When does it pass the building's top again?

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Problem 23389

Simplify the expression: $\frac{3(8-6)+2}{2^{2}-2}$ . Choose A or B if it's undefined.

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Problem 23390

Find $f(x)=\frac{9}{5} x+32$ . Calculate $f(60)$ , $f(0)$ , and $f(25)$ .

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Problem 23391

Find the real zeros of $f(x)=x^{2}+6x+4$ using the quadratic formula. What are the x-intercepts?

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Problem 23392

Calculate the slope of the line through points (22,40) and (62,17). Round your answer to one decimal place.

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Problem 23393

Find the zeros of the function $P(x)=2x^{2}-50$ . Are they the same as the $x$ -intercepts?

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Problem 23394

Find the linear function $M(x)=mx+b$ for men's average yearly earnings using points (0,21) and (30,66). Round to two decimals.

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Problem 23395

For the function $f(x)=x^{2}+4x+4$ , find the vertex, axis of symmetry, and intercepts. Does it open up or down?

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Problem 23396

Analyze a graph with x-values -4, -2, 0, 2, 4 and y-values -96, -64, -32, 0, 32, 64, 96.
1. a) Identify the function type (linear, quadratic, etc.) and justify. b) Explain why it's a function.
2. a) Determine the domain, range, and intercepts. b) Describe end behavior as $x \rightarrow \infty$ and $x \rightarrow -\infty$ .
3. a) Does the graph extend upward in quadrants 1 and 2? b) Is there line or point symmetry? Explain. c) Compare with similar graphs.
4. a) Does one end extend down in quadrant 3 and the other up in quadrant 1? b) Is there line or point symmetry? Explain. c) Compare with similar graphs.

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Problem 23397

The cost $C(x)=0.20x+45$ gives truck rental costs. Find costs for $x=80$ miles, solve for $C=60$ , max miles for $C \leq 150$ , domain, slope, and intercept.

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Problem 23398

Simplify the expression: $\frac{6+|9-2|+8^{2}}{5-2}$ and enter your answer as a number.

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Problem 23399

For the function $f(x)=x^{2}+6x+9$ , find the vertex, axis of symmetry, $y$ -intercept, and $x$ -intercepts.

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Problem 23400

Identify the arithmetic sequence with the formula: $a_{n}=10 n+12$ .

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1 ...231 232 233 234 235 236 237 ...313

Algebra

Problem 23301

Identify the form of the polynomial: x2+10x−7x+4+x2−3xx^{2}+10 x-7 x+4+x^{2}-3 xx2+10x−7x+4+x2−3x. Is it factored, standard, or mixed?

Problem 23302

Determine if the polynomial (9x−4)(x+7)+1(9 x-4)(x+7)+1(9x−4)(x+7)+1 is in factored, standard, or mixed form.

Problem 23303

Simplify −46⋅4344\frac{-4^{6} \cdot 4^{3}}{4^{4}}44−46⋅43​.

Problem 23304

Simplify −4642344\frac{-4^{6} 4^{23}}{4^{4}}44−46423​

Problem 23305

Simplify −400y24\frac{-40_{0} y^{2}}{4}4−400​y2​.

Problem 23306

Find the equivalent expression for (5x+2)+(4x−3)(5 x+2)+(4 x-3)(5x+2)+(4x−3). Choices: A. 6x+26 x+26x+2, B. 7x+17 x+17x+1, C. 9x−19 x-19x−1, D. 11x−311 x-311x−3, E. 20x−620 x-620x−6.

Problem 23307

Simplify the expression −46⋅4244\frac{-4^{6} \cdot 4^{2}}{4^{4}}44−46⋅42​.

Problem 23308

Solve the equation: 0.25r−0.125+0.5r=0.5+r0.25 r - 0.125 + 0.5 r = 0.5 + r0.25r−0.125+0.5r=0.5+r. Show all steps.

Problem 23309

Find g(f(x))g(f(x))g(f(x)) given f(x)=12x+6f(x)=\frac{1}{2x+6}f(x)=2x+61​ and g(x)=4x−3g(x)=\frac{4}{x}-3g(x)=x4​−3. Simplify fully, no decimals.

Problem 23310

Solve the equation: 12x−11x−18=1112x - 11x - 18 = 1112x−11x−18=11. What is the value of xxx?

Problem 23311

Find the inverse of the function f(x)=(x−2)2f(x)=(x-2)^{2}f(x)=(x−2)2.

Problem 23312

Solve the inequality −10≤9x−44<8-10 \leq \frac{9 x-4}{4}<8−10≤49x−4​<8 and express the solution in interval notation.

Problem 23313

Isolate yyy in the equation −56y−15y=43−15-\frac{5}{6} y - \frac{1}{5} y = \frac{4}{3} - \frac{1}{5}−65​y−51​y=34​−51​. Express your answer as an integer.

Problem 23314

A drug uses 3 mL of compound A for every 5 mL of compound B. How much A is needed for 544 mL of the drug?

Problem 23315

Simplify the expression 8423\frac{\sqrt{84}}{2 \sqrt{3}}23​84​​ to its simplest radical form.

Problem 23316

A sculptor makes a 110\frac{1}{10}101​ scale model of a 56-ton landmark. Solve 10x=5610 x=5610x=56 to find the model's weight.

Problem 23317

Find the values of yyy for the function y=−2xy=-2xy=−2x when x=−4,0,2,4x = -4, 0, 2, 4x=−4,0,2,4.

Problem 23318

If a bag has 49 purple marbles, how many yellow marbles are there if the ratio is 5 yellow to 7 purple?

Problem 23319

The city's yes to no vote ratio is 3:4. With 1743 yes votes, find the total number of votes.

Problem 23320

Rationalize the denominator of 53−1\frac{5}{\sqrt{3}-1}3​−15​.

Problem 23321

A sculptor is making a 19\frac{1}{9}91​ scale model of an 89-ton landmark. Find the model's weight by solving 9x=899x=899x=89.

Problem 23322

Given the function y=−2xy=-2xy=−2x, fill in the missing yyy values for x=−4x = -4x=−4 and x=0x = 0x=0.

Problem 23323

Solve the equation: 1x+1x+2=17\frac{1}{x}+\frac{1}{x+2}=\frac{1}{7}x1​+x+21​=71​. Provide exact answers, using radicals if necessary.

Problem 23324

Sketch the graphs of f(x)=−x2+2x+8f(x)=-x^{2}+2x+8f(x)=−x2+2x+8 and g(x)=2x+4g(x)=2x+4g(x)=2x+4. Find the coordinates of points AAA and BBB where fff intersects the x-axis.

Problem 23325

If Orly uses 2 cups of raisins for every 8 cups of trail mix, how much trail mix can she make with 10 cups of raisins?

Problem 23326

Which option shows the commutative property of addition: A, B, C, or D?

Problem 23327

Solve the equation: 5x2−6x=85 x^{2}-6 x=85x2−6x=8. Provide the exact solution set, using radicals if necessary.

Problem 23328

Which option shows the distributive property: A. ab=baab=baab=ba, B. a(bc)=(ab)ca(bc)=(ab)ca(bc)=(ab)c, C. a(b+c)=ab+aca(b+c)=ab+aca(b+c)=ab+ac, D. a⋅1=aa \cdot 1=aa⋅1=a?

Problem 23329

Given yyy varies inversely with xxx, and y=3y=3y=3 when x=8x=8x=8, find the equation and yyy when x=15x=15x=15.

Problem 23330

Solve the equation 2x2−3=−1012 x^{2}-3=-1012x2−3=−101 using the square root property. Simplify and express complex numbers with iii.

Problem 23331

Calculate the future value of \$10,000 at 3% interest compounded monthly for 7 years. Round to the nearest cent.

Problem 23332

Solve the equation 4x2=1924 x^{2}=1924x2=192. Provide the simplified solution set using radicals and iii for complex answers.

Problem 23333

Problem 23334

Given yyy varies inversely with xxx and y=−32y=-\frac{3}{2}y=−23​ when x=−8x=-8x=−8, find the equation and yyy when x=6x=6x=6. y= y = y=

Problem 23335

Find the slope of the function y=12−3xy=12-3xy=12−3x. Round your answer to one decimal place.

Problem 23336

Given yyy varies inversely with xxx, and y=8y=8y=8 when x=5x=5x=5: (a) Find the equation; (b) Determine yyy when x=10x=10x=10. y= y= y=

Problem 23337

Solve the equation 2x2−3x−1=02 x^{2}-3 x-1=02x2−3x−1=0 using the quadratic formula. Provide the exact solutions.

Problem 23338

Simplify the expression 90⋅40−8⋅18\sqrt{90} \cdot \sqrt{40}-\sqrt{8} \cdot \sqrt{18}90​⋅40​−8​⋅18​. What is the result? A. 22.9 B. 48 C. 864 D. 3,456

Problem 23339

Find the future value of \$5,000 at 6\% annual interest compounded quarterly after 5 years. Round to the nearest cent.

Problem 23340

Prove that the solutions of z2−2z+10=0z^{2}-2 z+10=0z2−2z+10=0 are complex (not real).

Identify the form of the polynomial: $x^{2}+10 x-7 x+4+x^{2}-3 x$ . Is it factored, standard, or mixed?

Determine if the polynomial $(9 x-4)(x+7)+1$ is in factored, standard, or mixed form.

Simplify $\frac{-4^{6} \cdot 4^{3}}{4^{4}}$ .

Simplify $\frac{-4^{6} 4^{23}}{4^{4}}$

Simplify $\frac{-40_{0} y^{2}}{4}$ .

Find the equivalent expression for $(5 x+2)+(4 x-3)$ . Choices: A. $6 x+2$ , B. $7 x+1$ , C. $9 x-1$ , D. $11 x-3$ , E. $20 x-6$ .

Simplify the expression $\frac{-4^{6} \cdot 4^{2}}{4^{4}}$ .

Solve the equation: $0.25 r - 0.125 + 0.5 r = 0.5 + r$ . Show all steps.

Find $g(f(x))$ given $f(x)=\frac{1}{2x+6}$ and $g(x)=\frac{4}{x}-3$ . Simplify fully, no decimals.

Solve the equation: $12x - 11x - 18 = 11$ . What is the value of $x$ ?

Find the inverse of the function $f(x)=(x-2)^{2}$ .

Solve the inequality $-10 \leq \frac{9 x-4}{4}<8$ and express the solution in interval notation.

Isolate $y$ in the equation $-\frac{5}{6} y - \frac{1}{5} y = \frac{4}{3} - \frac{1}{5}$ . Express your answer as an integer.

Simplify the expression $\frac{\sqrt{84}}{2 \sqrt{3}}$ to its simplest radical form.

A sculptor makes a $\frac{1}{10}$ scale model of a 56-ton landmark. Solve $10 x=56$ to find the model's weight.

Find the values of $y$ for the function $y=-2x$ when $x = -4, 0, 2, 4$ .

Rationalize the denominator of $\frac{5}{\sqrt{3}-1}$ .

A sculptor is making a $\frac{1}{9}$ scale model of an 89-ton landmark. Find the model's weight by solving $9x=89$ .

Given the function $y=-2x$ , fill in the missing $y$ values for $x = -4$ and $x = 0$ .

Solve the equation: $\frac{1}{x}+\frac{1}{x+2}=\frac{1}{7}$ . Provide exact answers, using radicals if necessary.

Sketch the graphs of $f(x)=-x^{2}+2x+8$ and $g(x)=2x+4$ . Find the coordinates of points $A$ and $B$ where $f$ intersects the x-axis.

Solve the equation: $5 x^{2}-6 x=8$ . Provide the exact solution set, using radicals if necessary.

Which option shows the distributive property: A. $ab=ba$ , B. $a(bc)=(ab)c$ , C. $a(b+c)=ab+ac$ , D. $a \cdot 1=a$ ?

Given $y$ varies inversely with $x$ , and $y=3$ when $x=8$ , find the equation and $y$ when $x=15$ .

Solve the equation $2 x^{2}-3=-101$ using the square root property. Simplify and express complex numbers with $i$ .

Solve the equation $4 x^{2}=192$ . Provide the simplified solution set using radicals and $i$ for complex answers.

Given $y$ varies inversely with $x$ and $y=-\frac{3}{2}$ when $x=-8$ , find the equation and $y$ when $x=6$ . $y =$

Find the slope of the function $y=12-3x$ . Round your answer to one decimal place.

Given $y$ varies inversely with $x$ , and $y=8$ when $x=5$ : (a) Find the equation; (b) Determine $y$ when $x=10$ . $y=$

Solve the equation $2 x^{2}-3 x-1=0$ using the quadratic formula. Provide the exact solutions.

Simplify the expression $\sqrt{90} \cdot \sqrt{40}-\sqrt{8} \cdot \sqrt{18}$ . What is the result? A. 22.9 B. 48 C. 864 D. 3,456

Prove that the solutions of $z^{2}-2 z+10=0$ are complex (not real).

Which option shows the associative property of multiplication? A. $ab=ba$ B. $a(bc)=(ab)c$ C. $a \cdot 1=a$ D. $a(b+c)=ab+ac$

Solve for $y$ in the equation: $\frac{9}{28} y - \frac{12}{7} y + \frac{3}{7} = \frac{3}{4}$ .

Solve for $y$ in the equation: $\frac{9}{28} y - \frac{12}{7} y + \frac{3}{7} = \frac{3}{4}$ .

Expand $(4 x-5)(6 x+5)$ into a trinomial form.

Solve for $x$ : $\frac{8}{17}=\frac{5}{7x}$ . Find $x$ in simplest form.

Solve for $x$ : $\frac{x+8}{13}=\frac{2}{9}$ . Find $x$ in simplest form.

Factor completely: $5 x^{3}-20 x^{2}-60 x$

Solve for $y$ in the equation $-\frac{1}{2} y=10$ .

Find the slope of a line perpendicular to $y - 2 = 3x$ . Options: A. -3 B. $-\frac{1}{3}$ C. $\frac{1}{3}$ D. 2 E. 3

Find the $y$ -intercept of $y=\frac{1}{4} x-\frac{2}{3}$ . A. $-\frac{2}{3}$ B. $\frac{2}{3}$ C. $-\frac{1}{4}$ D. $\frac{1}{4}$

Find the $y$ -intercept of the line $2x + y = -3$ . A. -2 B. 2 C. 3 D. -3

Find the slope of the line given by the equation $y=-x+2$ .

Find the product of the complex numbers $2+7i$ and $3-2i$ . What is the result?

Solve the inequality $153 w + 2 < -12 - (3 w - 2)$ . What is the correct range for $w$ ?

Find the explicit formula for the arithmetic sequence starting with $a_{1}=54$ and the first six terms: $54, 73, 92, 111, 130, 149$ .

If $|r|=-s$ , what must be true? A. $r=s$ B. $r \neq s$ C. $s=0$ D. $s \leq 0$ E. $r>0$

Calculate the investment value using $A=5000(1+0.08)^{15}$ . What is $A$ after 15 years? Options: A. \$2,000 B. \$5,400 C. \$10,882 D. \$15,861 E. \$21,499

Sketch the graph of $f(x)=(x-4)^{2}-9$ . Find the axis of symmetry, domain, and range. Axis: $x=4$ . Domain: $(-\infty, \infty)$ .

Find the mode of the numbers $x, 2x, 2x+6, 3x-1, 4x-8$ if their average is 9.

Evaluate $f(x)=4 x^{2}-5$ at $x=5$ and $x=-3$ . Find $f(5)$ and $f(-3)$ .

Solve $(x+4)^{2}-4=0$ for real $x$ . Provide simplified solutions, separated by commas if multiple. $x=$

Sketch the graph of $f(x)=2(x+3)^{2}-3$ using its vertex and intercepts. Find the axis of symmetry, domain, and range.

Evaluate $f(x) = x - 2$ for $x = 0$ and graph the ordered pair $(x, f(x))$ .

Find the price $p$ to maximize revenue given the function $R(p)=-7p^2+21,000p$ , and calculate the max revenue.

Evaluate $f(x)=(x-5)^{2}$ for $x=3, 4$ and graph the points $(x, f(x))$ .

Find the dimensions of a rectangle where length is $11 \mathrm{yd}$ more than twice the width and area is $63 \mathrm{yd}^{2}$ .

Solve the equation $x^{2}-12 x+61=0$ using the quadratic formula. Provide the exact solution with radicals and $i$ .

Find the zeros of the function $f(x)=x^{2}-147$ using the square root method. What are the $x$ -intercepts?