Algebra

Problem 23201

Solve for $x$ : $2 + 7x = 9x$ .

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Problem 23202

Simplify $5(2x - 3) - 8x$

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Problem 23203

A clock business has fixed costs of \ $7000. Find the average cost per clock for$ x=100, 1000, 10,000 $:$ \frac{0.4x + 7000}{x}$.

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Problem 23204

A clock manufacturer has fixed costs of \ $7000. Average cost per clock is$ \frac{0.4x + 7000}{x} $. Find average costs for$ x=100, 1000, 10,000$. Can they profit if selling at \$1.50 each while producing 2000 clocks?

See Solution

Problem 23205

Find the average cost per clock for manufacturing $x$ clocks, given $C(x) = \frac{0.4x + 7000}{x}$ , at $x = 100, 1000, 10000$ .

See Solution

Problem 23206

Simplify $3(4 x^{2}+2 x)+2(5 x^{2}+x)$ .

See Solution

Problem 23207

Calculate calories needed for females aged 4-8 using $F=-81 x^{2}+655 x+616$ . Is this estimate vs. $F=1113$ over/under? By how much?

See Solution

Problem 23208

Halla "m.n" si el sistema es corrónatible indeterminado: $5x + 3y = 1$ y $mx - ny = 4$ .

See Solution

Problem 23209

Sal sells two types of socks: type $a$ for R45 and type $b$ for R30. He sold 16 pairs for R585. Find pairs of sock $b$ .

See Solution

Problem 23210

Find the rational zeros of $f(x)=x^3-31x-30$ . If none, enter DNE. Test: $x=1,-1,2,-2,3,-3,5,-5,6,-6,10,-10,15,-15,30,-30$ .

See Solution

Problem 23211

Solve the system of equations: 5x = -71 - 13y and -18x = 19 + 13y. Provide (x,y) as the answer.

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Problem 23212

Solve the system: 6x = -32 - 10y and 11x = 8 - 10y. Provide (x, y) in parentheses.

See Solution

Problem 23213

Find the size limits for Fish $A$ as $[28, 32]$ and for Fish $B$ as $[11, \infty)$ in interval and set-builder notation.

See Solution

Problem 23214

Solve for $y$ in the equation: $13=-2(y-4)+3y$ .

See Solution

Problem 23215

Solve the equation: $5(3-x)+2(3-x)=14$ .

See Solution

Problem 23216

Find the number $n$ such that $2n + 13 = 75$ . What is $n$ ?

See Solution

Problem 23217

Determine if the following tables represent functions:
1. $x$ : 9.2, 9.4, 9.6, 9.8, 10; $y$ : 6, 8, 10, 12, 14
2. $x$ : 3.3, 3.5, 3.7, 3.5, 3.9; $y$ : 1.2, 1.4, 1.6, 1.8, 2

See Solution

Problem 23218

Solve the equation: $3(4g + 6) = 2(6g + 9)$ .

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Problem 23219

Solve the equation: $5(1+2 m)=\frac{1}{2}(8+20 m)$ .

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Problem 23220

Complete the table for $x + 2y = 3$ and graph the resulting equation.

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Problem 23221

Identify and fix the mistake in solving the equation: $-\frac{m}{3}=-4$ leading to $m=-12$ .

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Problem 23222

Jim drove 290 miles in 5 hours. How far will he drive in 11 hours at the same rate? Calculate: $d = \frac{290}{5} \times 11$ .

See Solution

Problem 23223

Marta solves $S=2 \pi r h+2 \pi r^{2}$ for $h$ . What is the correct expression for $h$ ?

See Solution

Problem 23224

Show that $f(x) = 2x - 7$ and $g(x) = \frac{x+7}{2}$ are inverses by verifying $f(g(x)) = x$ and $g(f(x)) = x$ .

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Problem 23225

Find the inverse equation of the relation $y=3x+2$ .

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Problem 23226

Find $y$ in the equation $\frac{9}{12}=\frac{y}{8}$ . Simplify your answer.

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Problem 23227

Is the equation $3 x-7=0$ equivalent to $3 x=-7$ true or false? If false, correct it.

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Problem 23228

Expand and simplify the expression: $(3x + 7)(x + 5)$ into a trinomial.

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Problem 23229

Solve the equation $8x = -16$ and verify your solution by substituting it back into the equation.

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Problem 23230

Solve the equation $8 x = -16$ and check your solution. What is the solution set? (Type an integer or simplified fraction.)

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Problem 23231

Solve the equation $3x - 12 = -63$ and verify your solution by substituting it back into the equation.

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Problem 23232

Solve the proportion $\frac{7}{13}=\frac{8}{v}$ for $v$ and round to the nearest tenth. What is $v$ ?

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Problem 23233

Solve the equation $2(8x - 1) = 25$ and verify your solution by substituting it back into the original equation.

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Problem 23234

You practiced 300 minutes in 6 days. What inequality for $m$ shows the minutes needed on day 7 to average 45 min/day?

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Problem 23235

Solve for $y$ in the equation $\frac{5}{2}=\frac{3}{y-3}$ . Simplify your answer.

See Solution

Problem 23236

Solve the equation: $5x + 7 = 3x + 41$

See Solution

Problem 23237

Solve for $u$ in the equation $4(v-4)-6=-4(-3 v+3)-4 u$ .

See Solution

Problem 23238

Solve the equation: 24(y+2) = 3(7y+8)

See Solution

Problem 23239

Solve the equation: $4(u-4)-6=-4(-3 u+3)-4 u$

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Problem 23240

Rewrite the polynomial $x^{2}+9+\frac{x}{6}$ in standard form.

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Problem 23241

Solve for $x$ in the equation: $\frac{8 x}{5}-5=11$ .

See Solution

Problem 23242

Solve for $x$ : $\frac{24}{x+4}=\frac{8}{x}$

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Problem 23243

Solve the equation: $\frac{5 r+15}{20}=\frac{3 r-36}{3}$

See Solution

Problem 23244

Find the height of a hot-air balloon at $t = 7$ minutes using the equation $y = 870 - 14.8t$ .

See Solution

Problem 23245

Solve the equation $4 t = 48$ .

See Solution

Problem 23246

Find the healthy weight $W$ for a height $H=6$ (5'6") using $\frac{W}{2}-3H=53$ . How many pounds below the upper range?

See Solution

Problem 23247

Identify the student's first mistake in solving the equation $|d+600|=400$ . Steps are: $d+600=400$ or $d+600=-400$ .

See Solution

Problem 23248

Find the healthy weight for a person 5'6'' tall using $\frac{\mathrm{W}}{2}-3 \mathrm{H}=53$ . How many pounds below the max?

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Problem 23249

5 decreased by the sum of 8 and $n$ . Is $\frac{3 a + 4 b}{2} = -7$ true for $a=6$ and $b=-1$ ? Show your work.

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Problem 23250

Write the expression for: The product of 7.4 and 9 decreased by 13 is $7.4 \times 9 - 13$ .

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Problem 23251

Find the blood volume for an 80-pound person, given that 200 pounds corresponds to 6 quarts. Use the proportion $\frac{6}{200} = \frac{x}{80}$ .

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Problem 23252

A quarterback throws an average of 65 yards ± 10 yards. Write equations for max and min yards thrown. $|y+10|=65$ $|y-10|=65$ $|y+65|=10$ $|y-65|=10$

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Problem 23253

Simplify $7 \cdot 6 \cdot 2 h d$ . Options: $48 d h$ , $84 dh$ , $42 + 2 h + d$ .

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Problem 23254

Determine if a score of 77 is within 4 strokes of par 72. Use $|p - 72| \leq 4$ to analyze the score.

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Problem 23255

Identify the changes from $f(x)=|x+3|$ to $g(x)=|x-4|+2$ .

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Problem 23256

Find the dollar amount of merchandise needed for equal costs under Plan A ( $\$ 110 + 0.8x$ ) and Plan B ( $\$ 20 + 0.9x$ ).

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Problem 23257

a. 5 - 8n b. 8 - 5n c. 5 - (8 + n) d. 8n - 5

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Problem 23258

A car averages 28 miles per gallon, varying by 6 to 10 mpg.
Part A: Pick a value from 6 to 10 for mpg. Write an equation for the mileage range.
Part B: Solve the equation and explain the result. Show all work.

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Problem 23259

Evaluate $3 x^{2}-7 x+9$ for $x=4$ .

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Problem 23260

Graph the linear function for Tim's truck fuel: $y = 200 - 10x$ , where $x$ is time in hours and $y$ is fuel in gallons.

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Problem 23261

Calculate the time to double an investment given by $y = y_{0} e^{0.055 t}$ . Round your answer to the nearest tenth.

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Problem 23262

Factor the expression: $(x^{2}-x+4)(x-5)$ .

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Problem 23263

Calculate the $\mathrm{pH}$ for $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=5.79 \times 10^{-4} \mathrm{M}$ .

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Problem 23264

Simplify the expressions: $7.5+n+9.63$ , $n+17.13$ , $17.13 n$ , and $7.5 n+9.63$ .

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Problem 23265

Solve the inequality: $x \leq 3$ .

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Problem 23266

Solve the compound inequality: $i \cdot x \leq 3$ .

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Problem 23267

Simplify the expression $7.95 - 3.86 + n$ .

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Problem 23268

Find the half-life of Nobelium-259 given the decay function $y=y_{0} e^{-0.0119 t}$ . Round to the nearest tenth.

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Problem 23269

Which expression does not equal $3 \cdot S \cdot R$ ? Options: 3RS, 3SR, $3+S+R$ .

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Problem 23270

Plot the solution set for $x \leq 10$ on the number line below.

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Problem 23271

Calculate the pH for a solution with $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] = 1.0 \times 10^{-11} M$ .

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Problem 23272

Graph the numbers greater than 5 on a number line: $\{x \mid x>5\}$

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Problem 23273

Find the concentration of $\mathrm{H}_{3} \mathrm{O}^{+}$ in a solution with $\mathrm{pH} = 3.6$ using $\mathrm{pH}=-\log_{10}\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ .

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Problem 23274

Identify the true characteristics of the function $f(x)=-|x+2|-3$ . Options include domain, range, and behavior as $x$ approaches infinity.

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Problem 23275

Jocelyn's expression for hours to complete $p$ problems is $\frac{5+4p}{60}$ . How long for 22 problems?

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Problem 23276

Which set of pairs does NOT represent a function? (A) $(0,1),(2,2),(4,8),(2,7),(5,8),(7,9)$ (B) $(-4,2),(-3,2),(-2,2),(-1,2),(0,2),(1,2)$ (C) $(-3,6),(2,7),(0,5),(1,5),(4,9),(5,4)$ (D) $(0,1),(2,2),(4,8),(-2,7),(5,8)$

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Problem 23277

Solve the inequality $-5x < 25$ . What is the solution set in inequality notation?

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Problem 23278

Sasha sells T-shirts and earns a set amount plus commission. What is the reasonable domain? (A) all whole numbers (B) $1 \leq x \leq 5$ (C) all real numbers (D) $68 \leq x \leq 80$

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Problem 23279

Find the hourly growth rate of a bacteria population that grows from 2200 to 2522 in 5 hours using continuous growth model.

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Problem 23280

Solve the inequality $5x - 6 > 4x + 2$ and graph the solution on a number line. What is the solution set? $\{x \mid \square \text{ (Type an inequality.) }$

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Problem 23281

Find the concentration of $\mathrm{H}_{3} \mathrm{O}^{+}$ in moles per liter for a solution with a $\mathrm{pH}$ of $9.000$ .

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Problem 23282

Find the equation for the acceptable weight range of bags filled with 14 ounces of chocolate, given a tolerance of 0.3 ounces.

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Problem 23283

What score do you need on the final exam to achieve an average of at least 90 with grades of 86 and 91?

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Problem 23284

Evaluate the function $f(x)=2x+5$ for $x=5, 0, 4, -2, 3$ and identify the true statements.

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Problem 23285

You have grades of 86 and 91. What do you need on the final to average at least 90? Also, what final grades risk dropping below a B (80)?

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Problem 23286

Does the table show a function? Check if each input in the domain has a unique output in the range. Domain: $2 \to 3$ , $4 \to 5$ , $6 \to 5$ , $8 \to 5$ .

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Problem 23287

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

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Problem 23288

A car costs \$75 weekly and \$0.05 per mile. How many miles can you drive with a budget of \$320?

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Problem 23289

Solve the inequality: $3 \leq 2x + 3 \leq 13$ .

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Problem 23290

Describe the translation of a tile from $(x, y)$ to fill a row with no spaces. What is the notation for no movement?

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Problem 23291

A player made 15 foul shots, which is $75\%$ of their attempts. How many total foul shots did they attempt?

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Problem 23292

Solve for $x$ in the equation: $4 x + 9 = 6 x - 27$ .

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Problem 23293

Solve for $x$ in the equation $\frac{1}{7} \cdot x=1$ .

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Problem 23294

Calculate the slope of the line between points $(-5, 3)$ and $(-2, -3)$ using $m = \frac{{y_{2} - y_{1}}}{{x_{2} - x_{1}}}$ .

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Problem 23295

Is the inequality $-2(2 x+9)>-4 x+9$ true always, sometimes, or never? (1 point)

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Problem 23296

Solve for 'x' in the equation $\frac{2x+24}{-76+7x} = 0$ .

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Problem 23297

Calculate $6^{2} \div 3 a - 2 b + 4$ for $a=3$ and $b=4$ .

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Problem 23298

If Earth spins faster, find the period $T$ for centripetal acceleration $a = 9.8 \, \mathrm{m/s}^{2}$ using $a = \frac{4\pi^{2}r}{T^{2}}$ . Use $r = 6.38 \times 10^{6}$ m. Output $T$ in minutes.

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Problem 23299

Which inequality represents that twelve times the sum of three and $c$ is greater than $27$ ?

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Problem 23300

Find the sum of $\sqrt{50}$ and $\sqrt{18}$ . What is it? A. $2 \sqrt{17}$ B. $8 \sqrt{2}$ C. $15 \sqrt{2}$ D. 34

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Algebra

Problem 23201

Solve for xxx: 2+7x=9x2 + 7x = 9x2+7x=9x.

Problem 23202

Simplify 5(2x−3)−8x5(2x - 3) - 8x5(2x−3)−8x

Problem 23203

A clock business has fixed costs of \7000.Findtheaveragecostperclockfor7000. Find the average cost per clock for 7000.Findtheaveragecostperclockforx=100, 1000, 10,000:: :\frac{0.4x + 7000}{x}$.

Problem 23204

Problem 23205

Find the average cost per clock for manufacturing xxx clocks, given C(x)=0.4x+7000xC(x) = \frac{0.4x + 7000}{x}C(x)=x0.4x+7000​, at x=100,1000,10000x = 100, 1000, 10000x=100,1000,10000.

Problem 23206

Simplify 3(4x2+2x)+2(5x2+x)3(4 x^{2}+2 x)+2(5 x^{2}+x)3(4x2+2x)+2(5x2+x).

Problem 23207

Calculate calories needed for females aged 4-8 using F=−81x2+655x+616F=-81 x^{2}+655 x+616F=−81x2+655x+616. Is this estimate vs. F=1113F=1113F=1113 over/under? By how much?

Problem 23208

Halla "m.n" si el sistema es corrónatible indeterminado: 5x+3y=15x + 3y = 15x+3y=1 y mx−ny=4mx - ny = 4mx−ny=4.

Problem 23209

Sal sells two types of socks: type aaa for R45 and type bbb for R30. He sold 16 pairs for R585. Find pairs of sock bbb.

Problem 23210

Find the rational zeros of f(x)=x3−31x−30f(x)=x^3-31x-30f(x)=x3−31x−30. If none, enter DNE. Test: x=1,−1,2,−2,3,−3,5,−5,6,−6,10,−10,15,−15,30,−30x=1,-1,2,-2,3,-3,5,-5,6,-6,10,-10,15,-15,30,-30x=1,−1,2,−2,3,−3,5,−5,6,−6,10,−10,15,−15,30,−30.

Problem 23211

Solve the system of equations: 5x = -71 - 13y and -18x = 19 + 13y. Provide (x,y) as the answer.

Problem 23212

Solve the system: 6x = -32 - 10y and 11x = 8 - 10y. Provide (x, y) in parentheses.

Problem 23213

Find the size limits for Fish AAA as [28,32][28, 32][28,32] and for Fish BBB as [11,∞)[11, \infty)[11,∞) in interval and set-builder notation.

Problem 23214

Solve for yyy in the equation: 13=−2(y−4)+3y13=-2(y-4)+3y13=−2(y−4)+3y.

Problem 23215

Solve the equation: 5(3−x)+2(3−x)=145(3-x)+2(3-x)=145(3−x)+2(3−x)=14.

Problem 23216

Find the number nnn such that 2n+13=752n + 13 = 752n+13=75. What is nnn?

Problem 23217

Determine if the following tables represent functions:1. xxx: 9.2, 9.4, 9.6, 9.8, 10; yyy: 6, 8, 10, 12, 142. xxx: 3.3, 3.5, 3.7, 3.5, 3.9; yyy: 1.2, 1.4, 1.6, 1.8, 2

Problem 23218

Solve the equation: 3(4g+6)=2(6g+9)3(4g + 6) = 2(6g + 9)3(4g+6)=2(6g+9).

Problem 23219

Solve the equation: 5(1+2m)=12(8+20m)5(1+2 m)=\frac{1}{2}(8+20 m)5(1+2m)=21​(8+20m).

Problem 23220

Complete the table for x+2y=3x + 2y = 3x+2y=3 and graph the resulting equation.

Problem 23221

Identify and fix the mistake in solving the equation: −m3=−4-\frac{m}{3}=-4−3m​=−4 leading to m=−12m=-12m=−12.

Problem 23222

Jim drove 290 miles in 5 hours. How far will he drive in 11 hours at the same rate? Calculate: d=2905×11d = \frac{290}{5} \times 11d=5290​×11.

Problem 23223

Marta solves S=2πrh+2πr2S=2 \pi r h+2 \pi r^{2}S=2πrh+2πr2 for hhh. What is the correct expression for hhh?

Problem 23224

Show that f(x)=2x−7f(x) = 2x - 7f(x)=2x−7 and g(x)=x+72g(x) = \frac{x+7}{2}g(x)=2x+7​ are inverses by verifying f(g(x))=xf(g(x)) = xf(g(x))=x and g(f(x))=xg(f(x)) = xg(f(x))=x.

Problem 23225

Find the inverse equation of the relation y=3x+2y=3x+2y=3x+2.

Problem 23226

Find yyy in the equation 912=y8\frac{9}{12}=\frac{y}{8}129​=8y​. Simplify your answer.

Problem 23227

Is the equation 3x−7=03 x-7=03x−7=0 equivalent to 3x=−73 x=-73x=−7 true or false? If false, correct it.

Problem 23228

Expand and simplify the expression: (3x+7)(x+5)(3x + 7)(x + 5)(3x+7)(x+5) into a trinomial.

Problem 23229

Solve the equation 8x=−168x = -168x=−16 and verify your solution by substituting it back into the equation.

Problem 23230

Solve the equation 8x=−168 x = -168x=−16 and check your solution. What is the solution set? (Type an integer or simplified fraction.)

Problem 23231

Solve the equation 3x−12=−633x - 12 = -633x−12=−63 and verify your solution by substituting it back into the equation.

Problem 23232

Solve the proportion 713=8v\frac{7}{13}=\frac{8}{v}137​=v8​ for vvv and round to the nearest tenth. What is vvv?

Problem 23233

Solve the equation 2(8x−1)=252(8x - 1) = 252(8x−1)=25 and verify your solution by substituting it back into the original equation.

Problem 23234

You practiced 300 minutes in 6 days. What inequality for mmm shows the minutes needed on day 7 to average 45 min/day?

Problem 23235

Solve for yyy in the equation 52=3y−3\frac{5}{2}=\frac{3}{y-3}25​=y−33​. Simplify your answer.

Problem 23236

Solve the equation: 5x+7=3x+415x + 7 = 3x + 415x+7=3x+41

Problem 23237

Solve for uuu in the equation 4(v−4)−6=−4(−3v+3)−4u4(v-4)-6=-4(-3 v+3)-4 u4(v−4)−6=−4(−3v+3)−4u.

Problem 23238

Solve the equation: 24(y+2) = 3(7y+8)

Problem 23239

Solve the equation: 4(u−4)−6=−4(−3u+3)−4u4(u-4)-6=-4(-3 u+3)-4 u4(u−4)−6=−4(−3u+3)−4u

Problem 23240

Rewrite the polynomial x2+9+x6x^{2}+9+\frac{x}{6}x2+9+6x​ in standard form.

Solve for $x$ : $2 + 7x = 9x$ .

Simplify $5(2x - 3) - 8x$

A clock business has fixed costs of \ $7000. Find the average cost per clock for$ x=100, 1000, 10,000 $:$ \frac{0.4x + 7000}{x}$.

Find the average cost per clock for manufacturing $x$ clocks, given $C(x) = \frac{0.4x + 7000}{x}$ , at $x = 100, 1000, 10000$ .

Simplify $3(4 x^{2}+2 x)+2(5 x^{2}+x)$ .

Calculate calories needed for females aged 4-8 using $F=-81 x^{2}+655 x+616$ . Is this estimate vs. $F=1113$ over/under? By how much?

Halla "m.n" si el sistema es corrónatible indeterminado: $5x + 3y = 1$ y $mx - ny = 4$ .

Sal sells two types of socks: type $a$ for R45 and type $b$ for R30. He sold 16 pairs for R585. Find pairs of sock $b$ .

Find the rational zeros of $f(x)=x^3-31x-30$ . If none, enter DNE. Test: $x=1,-1,2,-2,3,-3,5,-5,6,-6,10,-10,15,-15,30,-30$ .

Find the size limits for Fish $A$ as $[28, 32]$ and for Fish $B$ as $[11, \infty)$ in interval and set-builder notation.

Solve for $y$ in the equation: $13=-2(y-4)+3y$ .

Solve the equation: $5(3-x)+2(3-x)=14$ .

Find the number $n$ such that $2n + 13 = 75$ . What is $n$ ?

Determine if the following tables represent functions:
1. $x$ : 9.2, 9.4, 9.6, 9.8, 10; $y$ : 6, 8, 10, 12, 14
2. $x$ : 3.3, 3.5, 3.7, 3.5, 3.9; $y$ : 1.2, 1.4, 1.6, 1.8, 2

Solve the equation: $3(4g + 6) = 2(6g + 9)$ .

Solve the equation: $5(1+2 m)=\frac{1}{2}(8+20 m)$ .

Complete the table for $x + 2y = 3$ and graph the resulting equation.

Identify and fix the mistake in solving the equation: $-\frac{m}{3}=-4$ leading to $m=-12$ .

Jim drove 290 miles in 5 hours. How far will he drive in 11 hours at the same rate? Calculate: $d = \frac{290}{5} \times 11$ .

Marta solves $S=2 \pi r h+2 \pi r^{2}$ for $h$ . What is the correct expression for $h$ ?

Show that $f(x) = 2x - 7$ and $g(x) = \frac{x+7}{2}$ are inverses by verifying $f(g(x)) = x$ and $g(f(x)) = x$ .

Find the inverse equation of the relation $y=3x+2$ .

Find $y$ in the equation $\frac{9}{12}=\frac{y}{8}$ . Simplify your answer.

Is the equation $3 x-7=0$ equivalent to $3 x=-7$ true or false? If false, correct it.

Expand and simplify the expression: $(3x + 7)(x + 5)$ into a trinomial.

Solve the equation $8x = -16$ and verify your solution by substituting it back into the equation.

Solve the equation $8 x = -16$ and check your solution. What is the solution set? (Type an integer or simplified fraction.)

Solve the equation $3x - 12 = -63$ and verify your solution by substituting it back into the equation.

Solve the proportion $\frac{7}{13}=\frac{8}{v}$ for $v$ and round to the nearest tenth. What is $v$ ?

Solve the equation $2(8x - 1) = 25$ and verify your solution by substituting it back into the original equation.

You practiced 300 minutes in 6 days. What inequality for $m$ shows the minutes needed on day 7 to average 45 min/day?

Solve for $y$ in the equation $\frac{5}{2}=\frac{3}{y-3}$ . Simplify your answer.

Solve the equation: $5x + 7 = 3x + 41$

Solve for $u$ in the equation $4(v-4)-6=-4(-3 v+3)-4 u$ .

Solve the equation: $4(u-4)-6=-4(-3 u+3)-4 u$

Rewrite the polynomial $x^{2}+9+\frac{x}{6}$ in standard form.

Solve for $x$ in the equation: $\frac{8 x}{5}-5=11$ .

Solve for $x$ : $\frac{24}{x+4}=\frac{8}{x}$

Solve the equation: $\frac{5 r+15}{20}=\frac{3 r-36}{3}$

Find the height of a hot-air balloon at $t = 7$ minutes using the equation $y = 870 - 14.8t$ .

Solve the equation $4 t = 48$ .

Find the healthy weight $W$ for a height $H=6$ (5'6") using $\frac{W}{2}-3H=53$ . How many pounds below the upper range?

Identify the student's first mistake in solving the equation $|d+600|=400$ . Steps are: $d+600=400$ or $d+600=-400$ .

Find the healthy weight for a person 5'6'' tall using $\frac{\mathrm{W}}{2}-3 \mathrm{H}=53$ . How many pounds below the max?

5 decreased by the sum of 8 and $n$ . Is $\frac{3 a + 4 b}{2} = -7$ true for $a=6$ and $b=-1$ ? Show your work.

Write the expression for: The product of 7.4 and 9 decreased by 13 is $7.4 \times 9 - 13$ .

Find the blood volume for an 80-pound person, given that 200 pounds corresponds to 6 quarts. Use the proportion $\frac{6}{200} = \frac{x}{80}$ .

A quarterback throws an average of 65 yards ± 10 yards. Write equations for max and min yards thrown. $|y+10|=65$ $|y-10|=65$ $|y+65|=10$ $|y-65|=10$

Simplify $7 \cdot 6 \cdot 2 h d$ . Options: $48 d h$ , $84 dh$ , $42 + 2 h + d$ .

Determine if a score of 77 is within 4 strokes of par 72. Use $|p - 72| \leq 4$ to analyze the score.

Identify the changes from $f(x)=|x+3|$ to $g(x)=|x-4|+2$ .

Find the dollar amount of merchandise needed for equal costs under Plan A ( $\$ 110 + 0.8x$ ) and Plan B ( $\$ 20 + 0.9x$ ).

A car averages 28 miles per gallon, varying by 6 to 10 mpg.
Part A: Pick a value from 6 to 10 for mpg. Write an equation for the mileage range.
Part B: Solve the equation and explain the result. Show all work.

Evaluate $3 x^{2}-7 x+9$ for $x=4$ .

Graph the linear function for Tim's truck fuel: $y = 200 - 10x$ , where $x$ is time in hours and $y$ is fuel in gallons.

Calculate the time to double an investment given by $y = y_{0} e^{0.055 t}$ . Round your answer to the nearest tenth.

Factor the expression: $(x^{2}-x+4)(x-5)$ .

Calculate the $\mathrm{pH}$ for $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=5.79 \times 10^{-4} \mathrm{M}$ .

Simplify the expressions: $7.5+n+9.63$ , $n+17.13$ , $17.13 n$ , and $7.5 n+9.63$ .

Solve the inequality: $x \leq 3$ .

Solve the compound inequality: $i \cdot x \leq 3$ .

Simplify the expression $7.95 - 3.86 + n$ .

Find the half-life of Nobelium-259 given the decay function $y=y_{0} e^{-0.0119 t}$ . Round to the nearest tenth.

Which expression does not equal $3 \cdot S \cdot R$ ? Options: 3RS, 3SR, $3+S+R$ .

Plot the solution set for $x \leq 10$ on the number line below.

Calculate the pH for a solution with $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] = 1.0 \times 10^{-11} M$ .

Graph the numbers greater than 5 on a number line: $\{x \mid x>5\}$

Find the concentration of $\mathrm{H}_{3} \mathrm{O}^{+}$ in a solution with $\mathrm{pH} = 3.6$ using $\mathrm{pH}=-\log_{10}\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]$ .

Identify the true characteristics of the function $f(x)=-|x+2|-3$ . Options include domain, range, and behavior as $x$ approaches infinity.