Algebra

Problem 24301

Determine the y-intercept and slope of the equation $3x + 12y = 9$ .

See Solution

Problem 24302

Solve the inequality $\frac{2 x+5}{4} \geq \frac{x+3}{3}+1$ and express the solution in interval notation.

See Solution

Problem 24303

Is $88\%$ greater than $\frac{17}{20}$ ?

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Problem 24304

Find expressions equivalent to $(-4 d-1)+(-7 d-6)$ .

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Problem 24305

Choose the expressions equivalent to $7(3 n+5)+4$ : $(3 n+5) 7+4$ , $21 n+39$ , $5(3 n+7)+4$ , $7(5 n+3)+4$ .

See Solution

Problem 24306

Find the ordered pair for $y=x^{3}+9$ when $x=-3$ and describe its graph.

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Problem 24307

In a city vote with a yes to no ratio of 7 to 4 and 8514 total votes, how many no votes were there?

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Problem 24308

Find expressions equivalent to $-8(-5 r-2)-5 r$ . Options: $35 r-2$ , $35 r+16$ , $-2(-8 r-5)-5 r$ , $16 r+35$ .

See Solution

Problem 24309

Find expressions equivalent to $8(-2 k+3)$ : - $-2(3 k+8)$ - $24 k-16$ - $-16 k+24$ - $-2(8 k+3)$

See Solution

Problem 24310

To make 532 liters of Petrolyn oil, how many liters of synthetic oil are needed if the ratio is 4 liters natural to 3 liters synthetic?

See Solution

Problem 24311

Choose the equivalent expressions for $2(6 f+8)+3$ :
1. $6(8 f+2)+3$
2. $2(8 f+6)+3$
3. $12 f+19$
4. $19 f+12$

See Solution

Problem 24312

Find expressions equivalent to $(-4 d-3)-(9 d+4)$ . Options: $-13 d-7$ , $-7 d-13$ , $-4-3+-13 d$ , $(-3 d-4)-(4 d+9)$ .

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Problem 24313

Solve the inequality and provide the solution set as an interval and a graph: $m-2(m-8)+3 \leq 3 m-1$ .

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Problem 24314

Choose the equivalent expressions for $(-7 b-3)-(2 b+3)$ .

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Problem 24315

Solve and graph the compound inequality: $-2<\frac{3 x-6}{6}<4$ .

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Problem 24316

Use the table to find the equation for $\mathrm{Y}_{2}$ :
X: -3, -2, -1, 0, 1, 2, 3; Y₂: 0, -1, -2, -3, -4, -5, -6.
Options: A. $y_{2}=-3-x$ B. $y_{2}=2-3x$ C. $y_{2}=x-3$ D. $y_{2}=x+2$ .

See Solution

Problem 24317

Express the inequality $-9 \leq x < 2$ using interval notation.

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Problem 24318

Find expressions equivalent to $9(-2 g+4)+5 g$ . Options: $36 g-13$ , $-13 g+4$ , $(-2 g+4) 9+5 g$ , $3 g+36$ .

See Solution

Problem 24319

Express the interval $[3, \infty)$ as an inequality and sketch it on a number line.

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Problem 24320

Choose the equivalent expressions for $3(3 v+1)+4$ . Options include:
1. $(3 v+1) 3+4$
2. $3(2 v+v+1)+4$
3. $1(3 v+3)+4$
4. $3(1+3 v)+4$

See Solution

Problem 24321

Find intervals where cost $C=50x+400$ equals revenue $R=70x$ for break-even points.

See Solution

Problem 24322

Find the intersection points of $Y_{1}$ and $Y_{2}$ from the table: (-3, 6), (-2, 1), (-1, -2), (0, -3), (1, -2), (2, 1), (3, 6).

See Solution

Problem 24323

Find expressions equivalent to $(-2 z-1)+(-5 z-3)$ .

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Problem 24324

Choose the equivalent expressions for $(-2z - 1) + (-5z - 3)$ .

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Problem 24325

Choose the equivalent expressions for $(-2 z-1)+(-5 z-(-2 z-1))$ .

See Solution

Problem 24326

Solve the equation and simplify: $3(x+3)+x = 2x+15$ . Find $x$ .

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Problem 24327

Find the intervals where production of $x$ units of wire breaks even, given $C=55x+450$ and $R=80x$ .

See Solution

Problem 24328

Solve the equation step-by-step and simplify:
$3(x+3)+x = 2x+15$
Find $x$ .

See Solution

Problem 24329

Solve the equation: $\frac{1}{2} x+\frac{3}{7}=\frac{2}{3}+\frac{8}{21} x$

See Solution

Problem 24330

Find the intersection points of the graphs of $Y_{1}$ and $Y_{2}$ using the given table values. List as ordered pairs.

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Problem 24331

Solve the inequality and graph the solution: $|x - \frac{7}{2}| < 7$

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Problem 24332

Leonard has 25 coins (quarters and nickels) worth \$1.65. Find the number of each type of coin.

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Problem 24333

Simplify $-9^{2}$ using exponent properties and provide only positive exponents in your answer.

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Problem 24334

If 18 adults volunteer, how many students can attend the trip based on a 2:9 adult to student ratio? Use diagrams and tables.

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Problem 24335

A company awarded \$3000 in bonuses of \$250 or \$750. If at least one of each was given, how many \$250 bonuses could there be?

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Problem 24336

A company awarded bonuses totaling \$3000 in \$250 or \$750 amounts. If both types were given, how many \$250 bonuses could there be?

See Solution

Problem 24337

A psychologist models recall after $t$ months with $f(t)=90-22 \ln (t+1)$ . What is the recall after 2 months?

See Solution

Problem 24338

At 8:00 a.m., bacteria count is recorded. Create a function $f(t)$ for the growth pattern given: $f(0)=8$ , $f(1)=32$ , $f(2)=128$ , $f(3)=512$ .

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Problem 24339

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

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Problem 24340

Find the pH of apple juice with a hydrogen ion concentration of [H⁺]=0.00042. Round to the nearest hundredth.

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Problem 24341

Antimony has isotopes ${ }^{121} \mathrm{Sb}$ (120.9038 u) and ${ }^{123} \mathrm{Sb}$ (122.9042 u). Find their percent abundances.

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Problem 24342

Find the frequency of note $F$ , 4 half steps below $A_{3}$ (220 Hz), using $F(x)=F_{0}(1.059463)^{x}$ . Round to nearest whole number.

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Problem 24343

Simplify $\left(\frac{x}{y}\right)^{5}$ using exponent rules, expanding numbers and keeping only positive exponents.

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Problem 24344

Bacteria quadruple each minute. If there are 1 at 9:00 a.m., how many are there at 9:13 a.m.? Calculate using $N = 1 \cdot 4^{t}$ .

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Problem 24345

Simplify the expression $-4(3mn^{-1})^{-2}$ using exponent rules, showing only positive exponents.

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Problem 24346

The price of milk rises by $1\%$ yearly. If it costs \$3.5 in 2016, what will it cost in 2018?

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Problem 24347

Find the population on January 1, 2028, using the model $f(x)=18,791(1.023)^{x}$ where $x=16$ .

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Problem 24348

What is the earthquake magnitude for intensity $I = 3 \times 10^{7}$ using $R=\log \left(\frac{I}{1}\right)$ ? Round to the nearest hundredth.

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Problem 24349

Write the equation for "The $y$ -value is three increased by the square of the $x$ -value" and choose the correct option.

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Problem 24350

El equipo Argonautas ganó 3/4 en casa y 2/3 fuera, con 40 victorias más que derrotas. ¿Cuál es su récord final?

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Problem 24351

A child is 20 inches at birth. Use $f(x)=20+47 \log (x+2)$ to find age for $70\%$ adult height. Round to nearest year.

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Problem 24352

Classify each expression as a rational function, equation, or inequality:
1. $\frac{5 x+2}{3}+\frac{x}{4}=15$
2. $2 x+3<123$
3. $\frac{a^{2}+6 a+5}{a+1}=2 a+4$
4. $f(x)=\frac{x^{2}-25}{x}$
5. $6 x+4 \geq 8$

See Solution

Problem 24353

Simplify $(y^{2})^{-3}$ using exponent properties and show only positive exponents.

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Problem 24354

Simplify $4(m n^{-2})$ using exponent rules and show only positive exponents.

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Problem 24355

A child is 20 inches at birth. Use $f(x)=20+47 \log (x+2)$ to find height percentage at age 3. Round to nearest percent.

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Problem 24356

Convert "The $y$ -value is three increased by the square of the $x$ -value" into an equation and graph it.

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Problem 24357

If the credit card balance grows exponentially as $f(x)=700(1+0.13)^{x}$ , what is the balance after 40.5 months?

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Problem 24358

Simplify $(6 x^{4})^{2}$ using exponent rules and write only positive exponents.

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Problem 24359

A child is 20 inches long at birth. Find the percent of adult height at age 7 using $f(x)=20+47 \log (x+2)$ .

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Problem 24360

A company's net income of \ $400,000 grows by 13% yearly. When will it reach \$3,600,000? Use$ f(x)=400,000(1+0.13)^{x}$.

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Problem 24361

Simplify $\left(\frac{-4 x^{2}}{y^{2}}\right)^{2}$ using exponent properties and show only positive exponents.

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Problem 24362

Find the initial total sales of a spy novel modeled by $f(x)=18,245(1.021)^{x}$ when $x=0$ .

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Problem 24363

Simplify the expression: $-2(6xy^2)^0$ and use only positive exponents in your answer.

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Problem 24364

Simplify the expression $-2\left(3 m^{-2} n^{2}\right)^{-1}$ using exponent rules and show only positive exponents.

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Problem 24365

Solve $4^{\lg 2}=\left(\frac{1}{9 x}\right)^{\lg 4}$ without a calculator.

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Problem 24366

Find the equation of a line parallel to $12 x - 18 y = -36$ that passes through the point $P(-3, -6)$ .

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Problem 24367

Find the intensity, $I$ , of an earthquake with a magnitude of 6.7 using $R=\log \left(\frac{I}{1}\right)$ . Round to the nearest whole number.

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Problem 24368

Find the equation of the line parallel to $12 x-18 y=-36$ that goes through the point $P(-3,-6)$ .

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Problem 24369

Find the percentage of information retained after 3 months using the function $f(t)=89-22 \ln (t+1)$ for $1 \leq t \leq 12$ .

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Problem 24370

A population of 25,200 is decreasing by $5\%$ annually. What will it be in 10 years? Round to the nearest whole number.

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Problem 24371

A baby is 20 inches at birth. Find the percentage of adult height at age 6 using $f(x)=20+47 \log (x+2)$ .

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Problem 24372

A baby is 20 inches long at birth. Use the function $f(x)=20+47 \log (x+2)$ to find when she reaches $90\%$ of her adult height.

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Problem 24373

Find the total sales of a strategy game on January 1, 2030, using $f(x)=10,333(1.046)^{x}$ with $x=17$ .

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Problem 24374

A population of 24,800 decreases by $4\%$ yearly. What will it be in 9 years? Round to the nearest whole number.

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Problem 24375

Calculate the GPA from grades A, C, B, A, D with credit hours 4, 4, 3, 3, 2. Is the GPA ≥ 3.00 for the dean's list?

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Problem 24376

Find the frequency of note A# (1 half step above A3 at 220 Hz) using the formula $F(x)=F_{0}(1.059463)^{x}$ . Round to the nearest whole number.

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Problem 24377

Calculate the final score for a student with midterm 70, project 93, homework 87, final exam 74 using weights: midterm $5\%$ , project $20\%$ , homework $50\%$ , final $25\%$ . What letter grade did he earn?

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Problem 24378

What is the balance after 61.5 months if it grows exponentially as $f(x)=800(1+0.122)^{x}$ ? Round to the nearest cent.

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Problem 24379

Find the intensity $I$ of an earthquake with a magnitude of 4.5 using $R=\log \left(\frac{I}{1}\right)$ . Round to the nearest whole number.

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Problem 24380

Milk's price rises by $2\%$ yearly. If it was $\$3.75$ in 2014, what will it cost in 2019?

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Problem 24381

A baby is 20 inches long at birth. Find the percentage of adult height at age 13 using $f(x)=20+47 \log (x+2)$ .

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Problem 24382

If your credit card balance grows exponentially as $f(x)=700(1+0.13)^{x}$ , what is the balance after 46.9 months? Round to the nearest cent.

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Problem 24383

Calculate the ordinary annuity value for \$500, quarterly deposits, 8\%, over 6 years. Round to the nearest cent.

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Problem 24384

What was the initial population of a Texas town modeled by $f(x)=10,906(1.032)^{x}$ on January 1, 2013?

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Problem 24385

Determine if the polynomial $3 x(x^{2}+5 x-24)(2 x+1)$ is in factored, standard, or mixed form.

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Problem 24386

A company's income of \ $200,000 in 2020 grows by 10% yearly. When will it reach \$800,000? Use$ f(x)=200,000(1+0.1)^{x}$.

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Problem 24387

Determine if the polynomial $x + 9 \cdot (x^{2} \cdot 5x + 4)$ is in factored, standard, or mixed form.

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Problem 24388

Solve the equations: $2^{x+1}-3^{y+1}=4$ and $2^{2(x+1)}-3^{2(y+1)}=64$ to three significant figures.

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Problem 24389

Calculate the monthly payment $\mathrm{R}$ for a sinking fund to reach \$5,000 at a 7% annual interest rate over 1 year.

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Problem 24390

Determine the form of the polynomial: $(x+2) 7 x(x+1) 3 x^{4}(x-8)$ (factored, standard, or mixed).

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Problem 24391

Matt saves \$65 monthly at 5.5% annual interest. How much will he have in 30 months? Round to the nearest cent.

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Problem 24392

Find the intercepts of the line given by $y-3=5(x-2)$ . $y$ -intercept: $(\quad, \quad)$ , $x$ -intercept: $(, \quad)$ .

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Problem 24393

Julio saves \$1,350/year from age 21-35; Max saves \$2,700/year from age 41-65. How much do they have at age 65?

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Problem 24394

Find the intercepts of the line given by $y=-9x-14$ . $x$ -intercept: $(\quad, \quad)$ , $y$ -intercept:

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Problem 24395

Doug, Dick y Dean son trillizos con un promedio de clase de $74\%$ . Al irse, el promedio sube a $75\%$ . Sus puntajes están en la proporción $6:5:3$ . ¿Cuáles son sus puntajes?

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Problem 24396

Check if the following expressions are equivalent by rewriting them: 1) $7 n(3 n+1)$ 2) $x^{2}-25$ 3) $(4 w+2)^{2}$

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Problem 24397

Simplify: $4|6-7|-27 \div 3 =$

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Problem 24398

Find the inverse function $f^{-1}$ of $f(x)=\left(x^{4}+4\right)^{-1}$ for $x \in (-\infty, 0]$ .

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Problem 24399

Factor the expression: $14ab - 2a + 21b - 3$ into the form $(?a + [])(?b - [])$ .

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Problem 24400

An item bought for \ $2,475 depreciates to \$15 in 15 years. Find the linear depreciation function$ V(t) $in slope-intercept form.$ $V(t)=$ $

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Algebra

Problem 24301

Determine the y-intercept and slope of the equation 3x+12y=93x + 12y = 93x+12y=9.

Problem 24302

Solve the inequality 2x+54≥x+33+1\frac{2 x+5}{4} \geq \frac{x+3}{3}+142x+5​≥3x+3​+1 and express the solution in interval notation.

Problem 24303

Is 88%88\%88% greater than 1720\frac{17}{20}2017​?

Problem 24304

Find expressions equivalent to (−4d−1)+(−7d−6)(-4 d-1)+(-7 d-6)(−4d−1)+(−7d−6).

Problem 24305

Choose the expressions equivalent to 7(3n+5)+47(3 n+5)+47(3n+5)+4: (3n+5)7+4(3 n+5) 7+4(3n+5)7+4, 21n+3921 n+3921n+39, 5(3n+7)+45(3 n+7)+45(3n+7)+4, 7(5n+3)+47(5 n+3)+47(5n+3)+4.

Problem 24306

Find the ordered pair for y=x3+9y=x^{3}+9y=x3+9 when x=−3x=-3x=−3 and describe its graph.

Problem 24307

In a city vote with a yes to no ratio of 7 to 4 and 8514 total votes, how many no votes were there?

Problem 24308

Find expressions equivalent to −8(−5r−2)−5r-8(-5 r-2)-5 r−8(−5r−2)−5r. Options: 35r−235 r-235r−2, 35r+1635 r+1635r+16, −2(−8r−5)−5r-2(-8 r-5)-5 r−2(−8r−5)−5r, 16r+3516 r+3516r+35.

Problem 24309

Find expressions equivalent to 8(−2k+3)8(-2 k+3)8(−2k+3): - −2(3k+8)-2(3 k+8)−2(3k+8) - 24k−1624 k-1624k−16 - −16k+24-16 k+24−16k+24 - −2(8k+3)-2(8 k+3)−2(8k+3)

Problem 24310

To make 532 liters of Petrolyn oil, how many liters of synthetic oil are needed if the ratio is 4 liters natural to 3 liters synthetic?

Problem 24311

Choose the equivalent expressions for 2(6f+8)+32(6 f+8)+32(6f+8)+3: 1. 6(8f+2)+36(8 f+2)+36(8f+2)+3 2. 2(8f+6)+32(8 f+6)+32(8f+6)+3 3. 12f+1912 f+1912f+19 4. 19f+1219 f+1219f+12

Problem 24312

Find expressions equivalent to (−4d−3)−(9d+4)(-4 d-3)-(9 d+4)(−4d−3)−(9d+4). Options: −13d−7-13 d-7−13d−7, −7d−13-7 d-13−7d−13, −4−3+−13d-4-3+-13 d−4−3+−13d, (−3d−4)−(4d+9)(-3 d-4)-(4 d+9)(−3d−4)−(4d+9).

Problem 24313

Solve the inequality and provide the solution set as an interval and a graph: m−2(m−8)+3≤3m−1m-2(m-8)+3 \leq 3 m-1m−2(m−8)+3≤3m−1.

Problem 24314

Choose the equivalent expressions for (−7b−3)−(2b+3)(-7 b-3)-(2 b+3)(−7b−3)−(2b+3).

Problem 24315

Solve and graph the compound inequality: −2<3x−66<4-2<\frac{3 x-6}{6}<4−2<63x−6​<4.

Problem 24316

Use the table to find the equation for Y2\mathrm{Y}_{2}Y2​:X: -3, -2, -1, 0, 1, 2, 3; Y₂: 0, -1, -2, -3, -4, -5, -6.Options: A. y2=−3−xy_{2}=-3-xy2​=−3−x B. y2=2−3xy_{2}=2-3xy2​=2−3x C. y2=x−3y_{2}=x-3y2​=x−3 D. y2=x+2y_{2}=x+2y2​=x+2.

Problem 24317

Express the inequality −9≤x<2-9 \leq x < 2−9≤x<2 using interval notation.

Problem 24318

Find expressions equivalent to 9(−2g+4)+5g9(-2 g+4)+5 g9(−2g+4)+5g. Options: 36g−1336 g-1336g−13, −13g+4-13 g+4−13g+4, (−2g+4)9+5g(-2 g+4) 9+5 g(−2g+4)9+5g, 3g+363 g+363g+36.

Problem 24319

Express the interval [3,∞)[3, \infty)[3,∞) as an inequality and sketch it on a number line.

Problem 24320

Choose the equivalent expressions for 3(3v+1)+43(3 v+1)+43(3v+1)+4. Options include: 1. (3v+1)3+4(3 v+1) 3+4(3v+1)3+42. 3(2v+v+1)+43(2 v+v+1)+43(2v+v+1)+43. 1(3v+3)+41(3 v+3)+41(3v+3)+44. 3(1+3v)+43(1+3 v)+43(1+3v)+4

Problem 24321

Find intervals where cost C=50x+400C=50x+400C=50x+400 equals revenue R=70xR=70xR=70x for break-even points.

Problem 24322

Find the intersection points of Y1Y_{1}Y1​ and Y2Y_{2}Y2​ from the table: (-3, 6), (-2, 1), (-1, -2), (0, -3), (1, -2), (2, 1), (3, 6).

Problem 24323

Find expressions equivalent to (−2z−1)+(−5z−3)(-2 z-1)+(-5 z-3)(−2z−1)+(−5z−3).

Problem 24324

Choose the equivalent expressions for (−2z−1)+(−5z−3)(-2z - 1) + (-5z - 3)(−2z−1)+(−5z−3).

Problem 24325

Choose the equivalent expressions for (−2z−1)+(−5z−(−2z−1))(-2 z-1)+(-5 z-(-2 z-1))(−2z−1)+(−5z−(−2z−1)).

Problem 24326

Solve the equation and simplify: 3(x+3)+x=2x+153(x+3)+x = 2x+153(x+3)+x=2x+15. Find xxx.

Problem 24327

Find the intervals where production of xxx units of wire breaks even, given C=55x+450C=55x+450C=55x+450 and R=80xR=80xR=80x.

Problem 24328

Solve the equation step-by-step and simplify: 3(x+3)+x=2x+15 3(x+3)+x = 2x+15 3(x+3)+x=2x+15 Find xxx.

Problem 24329

Solve the equation: 12x+37=23+821x\frac{1}{2} x+\frac{3}{7}=\frac{2}{3}+\frac{8}{21} x21​x+73​=32​+218​x

Problem 24330

Find the intersection points of the graphs of Y1Y_{1}Y1​ and Y2Y_{2}Y2​ using the given table values. List as ordered pairs.

Problem 24331

Solve the inequality and graph the solution: ∣x−72∣<7|x - \frac{7}{2}| < 7∣x−27​∣<7

Problem 24332

Leonard has 25 coins (quarters and nickels) worth \$1.65. Find the number of each type of coin.

Problem 24333

Simplify −92-9^{2}−92 using exponent properties and provide only positive exponents in your answer.

Problem 24334

If 18 adults volunteer, how many students can attend the trip based on a 2:9 adult to student ratio? Use diagrams and tables.

Problem 24335

A company awarded \$3000 in bonuses of \$250 or \$750. If at least one of each was given, how many \$250 bonuses could there be?

Problem 24336

A company awarded bonuses totaling \$3000 in \$250 or \$750 amounts. If both types were given, how many \$250 bonuses could there be?

Problem 24337

A psychologist models recall after ttt months with f(t)=90−22ln⁡(t+1)f(t)=90-22 \ln (t+1)f(t)=90−22ln(t+1). What is the recall after 2 months?

Problem 24338

At 8:00 a.m., bacteria count is recorded. Create a function f(t)f(t)f(t) for the growth pattern given: f(0)=8f(0)=8f(0)=8, f(1)=32f(1)=32f(1)=32, f(2)=128f(2)=128f(2)=128, f(3)=512f(3)=512f(3)=512.

Problem 24339

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

Problem 24340

Determine the y-intercept and slope of the equation $3x + 12y = 9$ .

Solve the inequality $\frac{2 x+5}{4} \geq \frac{x+3}{3}+1$ and express the solution in interval notation.

Is $88\%$ greater than $\frac{17}{20}$ ?

Find expressions equivalent to $(-4 d-1)+(-7 d-6)$ .

Choose the expressions equivalent to $7(3 n+5)+4$ : $(3 n+5) 7+4$ , $21 n+39$ , $5(3 n+7)+4$ , $7(5 n+3)+4$ .

Find the ordered pair for $y=x^{3}+9$ when $x=-3$ and describe its graph.

Find expressions equivalent to $-8(-5 r-2)-5 r$ . Options: $35 r-2$ , $35 r+16$ , $-2(-8 r-5)-5 r$ , $16 r+35$ .

Find expressions equivalent to $8(-2 k+3)$ : - $-2(3 k+8)$ - $24 k-16$ - $-16 k+24$ - $-2(8 k+3)$

Choose the equivalent expressions for $2(6 f+8)+3$ :
1. $6(8 f+2)+3$
2. $2(8 f+6)+3$
3. $12 f+19$
4. $19 f+12$

Find expressions equivalent to $(-4 d-3)-(9 d+4)$ . Options: $-13 d-7$ , $-7 d-13$ , $-4-3+-13 d$ , $(-3 d-4)-(4 d+9)$ .

Solve the inequality and provide the solution set as an interval and a graph: $m-2(m-8)+3 \leq 3 m-1$ .

Choose the equivalent expressions for $(-7 b-3)-(2 b+3)$ .

Solve and graph the compound inequality: $-2<\frac{3 x-6}{6}<4$ .

Use the table to find the equation for $\mathrm{Y}_{2}$ :
X: -3, -2, -1, 0, 1, 2, 3; Y₂: 0, -1, -2, -3, -4, -5, -6.
Options: A. $y_{2}=-3-x$ B. $y_{2}=2-3x$ C. $y_{2}=x-3$ D. $y_{2}=x+2$ .

Express the inequality $-9 \leq x < 2$ using interval notation.

Find expressions equivalent to $9(-2 g+4)+5 g$ . Options: $36 g-13$ , $-13 g+4$ , $(-2 g+4) 9+5 g$ , $3 g+36$ .

Express the interval $[3, \infty)$ as an inequality and sketch it on a number line.

Choose the equivalent expressions for $3(3 v+1)+4$ . Options include:
1. $(3 v+1) 3+4$
2. $3(2 v+v+1)+4$
3. $1(3 v+3)+4$
4. $3(1+3 v)+4$

Find intervals where cost $C=50x+400$ equals revenue $R=70x$ for break-even points.

Find the intersection points of $Y_{1}$ and $Y_{2}$ from the table: (-3, 6), (-2, 1), (-1, -2), (0, -3), (1, -2), (2, 1), (3, 6).

Find expressions equivalent to $(-2 z-1)+(-5 z-3)$ .

Choose the equivalent expressions for $(-2z - 1) + (-5z - 3)$ .

Choose the equivalent expressions for $(-2 z-1)+(-5 z-(-2 z-1))$ .

Solve the equation and simplify: $3(x+3)+x = 2x+15$ . Find $x$ .

Find the intervals where production of $x$ units of wire breaks even, given $C=55x+450$ and $R=80x$ .

Solve the equation step-by-step and simplify:
$3(x+3)+x = 2x+15$
Find $x$ .

Solve the equation: $\frac{1}{2} x+\frac{3}{7}=\frac{2}{3}+\frac{8}{21} x$

Find the intersection points of the graphs of $Y_{1}$ and $Y_{2}$ using the given table values. List as ordered pairs.

Solve the inequality and graph the solution: $|x - \frac{7}{2}| < 7$

Simplify $-9^{2}$ using exponent properties and provide only positive exponents in your answer.

A psychologist models recall after $t$ months with $f(t)=90-22 \ln (t+1)$ . What is the recall after 2 months?

At 8:00 a.m., bacteria count is recorded. Create a function $f(t)$ for the growth pattern given: $f(0)=8$ , $f(1)=32$ , $f(2)=128$ , $f(3)=512$ .

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

Antimony has isotopes ${ }^{121} \mathrm{Sb}$ (120.9038 u) and ${ }^{123} \mathrm{Sb}$ (122.9042 u). Find their percent abundances.

Find the frequency of note $F$ , 4 half steps below $A_{3}$ (220 Hz), using $F(x)=F_{0}(1.059463)^{x}$ . Round to nearest whole number.

Simplify $\left(\frac{x}{y}\right)^{5}$ using exponent rules, expanding numbers and keeping only positive exponents.

Bacteria quadruple each minute. If there are 1 at 9:00 a.m., how many are there at 9:13 a.m.? Calculate using $N = 1 \cdot 4^{t}$ .

Simplify the expression $-4(3mn^{-1})^{-2}$ using exponent rules, showing only positive exponents.

The price of milk rises by $1\%$ yearly. If it costs \$3.5 in 2016, what will it cost in 2018?

Find the population on January 1, 2028, using the model $f(x)=18,791(1.023)^{x}$ where $x=16$ .

What is the earthquake magnitude for intensity $I = 3 \times 10^{7}$ using $R=\log \left(\frac{I}{1}\right)$ ? Round to the nearest hundredth.

Write the equation for "The $y$ -value is three increased by the square of the $x$ -value" and choose the correct option.

A child is 20 inches at birth. Use $f(x)=20+47 \log (x+2)$ to find age for $70\%$ adult height. Round to nearest year.

Simplify $(y^{2})^{-3}$ using exponent properties and show only positive exponents.

Simplify $4(m n^{-2})$ using exponent rules and show only positive exponents.

A child is 20 inches at birth. Use $f(x)=20+47 \log (x+2)$ to find height percentage at age 3. Round to nearest percent.

Convert "The $y$ -value is three increased by the square of the $x$ -value" into an equation and graph it.

If the credit card balance grows exponentially as $f(x)=700(1+0.13)^{x}$ , what is the balance after 40.5 months?

Simplify $(6 x^{4})^{2}$ using exponent rules and write only positive exponents.

A child is 20 inches long at birth. Find the percent of adult height at age 7 using $f(x)=20+47 \log (x+2)$ .

A company's net income of \ $400,000 grows by 13% yearly. When will it reach \$3,600,000? Use$ f(x)=400,000(1+0.13)^{x}$.

Simplify $\left(\frac{-4 x^{2}}{y^{2}}\right)^{2}$ using exponent properties and show only positive exponents.

Find the initial total sales of a spy novel modeled by $f(x)=18,245(1.021)^{x}$ when $x=0$ .

Simplify the expression: $-2(6xy^2)^0$ and use only positive exponents in your answer.

Simplify the expression $-2\left(3 m^{-2} n^{2}\right)^{-1}$ using exponent rules and show only positive exponents.

Solve $4^{\lg 2}=\left(\frac{1}{9 x}\right)^{\lg 4}$ without a calculator.

Find the equation of a line parallel to $12 x - 18 y = -36$ that passes through the point $P(-3, -6)$ .

Find the intensity, $I$ , of an earthquake with a magnitude of 6.7 using $R=\log \left(\frac{I}{1}\right)$ . Round to the nearest whole number.

Find the equation of the line parallel to $12 x-18 y=-36$ that goes through the point $P(-3,-6)$ .

Find the percentage of information retained after 3 months using the function $f(t)=89-22 \ln (t+1)$ for $1 \leq t \leq 12$ .

A population of 25,200 is decreasing by $5\%$ annually. What will it be in 10 years? Round to the nearest whole number.

A baby is 20 inches at birth. Find the percentage of adult height at age 6 using $f(x)=20+47 \log (x+2)$ .

A baby is 20 inches long at birth. Use the function $f(x)=20+47 \log (x+2)$ to find when she reaches $90\%$ of her adult height.

Find the total sales of a strategy game on January 1, 2030, using $f(x)=10,333(1.046)^{x}$ with $x=17$ .

A population of 24,800 decreases by $4\%$ yearly. What will it be in 9 years? Round to the nearest whole number.