Algebra

Problem 28201

Find the expected aptitude score for a 17-year-old using the formula: Aptitude = 111.5 - 1.14 * Age. Round to the nearest whole number.

See Solution

Problem 28202

Solve $|3k - 2| - 2|k + 2| = 0$ . Find the solutions for $k$ .

See Solution

Problem 28203

Solve the equation $m + 3 = 7$ for the value of $m$ .

See Solution

Problem 28204

Let s represent "One races fast." Express "One does not race fast" symbolically.

See Solution

Problem 28205

Solve the equation $|4 n-15|=|n|$ . Find the values of $n=$ and $n=$ .

See Solution

Problem 28206

Solve the equation $-4|8-5 n|=13$ for $n$ .

See Solution

Problem 28207

Add or subtract: (a) $\frac{b}{a}+\frac{1}{b}$ and simplify if possible.

See Solution

Problem 28208

Add or subtract the fractions: $\frac{b}{a}+\frac{1}{b}$ and simplify if possible.

See Solution

Problem 28209

Solve $9|A p+2|+8=35$ for the variable $A$ .

See Solution

Problem 28210

Write the symbolic form of "I study and I eat bananas" using $p$ and $q$ .

See Solution

Problem 28211

Symbolically express: The stove is hot and I do not get an A using $p$ and $q$ .

See Solution

Problem 28212

Write the symbolic form of "You're here, but I'm not there" using $p$ and $q$ .

See Solution

Problem 28213

Write the symbolic form of "I eat bananas or it is time to sleep" using $p$ and $q$ .

See Solution

Problem 28214

Write the symbolic form of "I get a promotion if and only if I work hard" using $p$ and $q$ .

See Solution

Problem 28215

Solve the equation $|3 k-2|=2|k+2|$ .

See Solution

Problem 28216

Write the symbolic form of: "It is not Sunday if and only if the campus is not closed." using $p$ and $q$ .

See Solution

Problem 28217

Write the symbolic form of: "I get an A if and only if the job pays well and I do not work hard." Use $p$ , $q$ , and $r$ .

See Solution

Problem 28218

Symbolically express: "The chair is broken and it is time to sleep, or I get an A" using $p$ , $q$ , and $r$ .

See Solution

Problem 28219

Multiply and simplify: $(\sin \theta+5)(\sin \theta+6)$

See Solution

Problem 28220

Write the symbolic form of: Not having a job or not following a budget implies being in debt.

See Solution

Problem 28221

Multiply and simplify: $(4 \cos \theta + 5)(7 \cos \theta - 2)$ .

See Solution

Problem 28222

Multiply and simplify: $(2-\tan \theta)(2+\tan \theta)$ .

See Solution

Problem 28223

Simplify the expression $(\sin \theta - \cos \theta)^{2}$ .

See Solution

Problem 28224

Simplify $\sqrt{x^{2}-16}$ after substituting $x = 4 \sec(\theta)$ , where $0^{\circ}<\theta<90^{\circ}$ .

See Solution

Problem 28225

Simplify $\sqrt{9-x^{2}}$ by substituting $x=3 \sin (\theta)$ , where $0^{\circ}<\theta<90^{\circ}$ .

See Solution

Problem 28226

Sasha's 9-digit passcode starts and ends with 6. Each set of 3 consecutive digits sums to 14. Find the 5th digit.

See Solution

Problem 28227

Find the value of $f(1)$ for the function $f(x)=9.1 x^{2}+0.5 x$ . Provide your answer as a decimal or whole number.

See Solution

Problem 28228

Tushar's age is 7 times his daughter's. In 5 years, he'll be 4 times her age. Find their current ages.

See Solution

Problem 28229

Garima's father is 43, 19 years older than twice her age. Set up and solve the equation: $43 = 2x + 19$ .

See Solution

Problem 28230

Show that $\log _{3} x+\log _{9} x=\frac{3 \lg x}{2 \lg 3}$ and solve $\log _{3} x+\log _{9} x=4$ .

See Solution

Problem 28231

Prove that $\log _{3} x+\log _{9} x=\frac{3 \lg x}{2 \lg 3}$ .

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Problem 28232

Find the mass of a graphite block with the same volume as a $483 \mathrm{~g}$ iron block, given their densities.

See Solution

Problem 28233

Find the values of the following Fibonacci numbers: $F_{22}, F_{46}, F_{20}, F_{12}, F_{18}, F_{6}, F_{28}, F_{19}, F_{25}, F_{10}$ .

See Solution

Problem 28234

Identify equivalent equations for $p-q=-93$ . Which of these are equivalent?
1. $\frac{p-q}{3}=-31$
2. $\frac{p-q}{3}=-32$
3. $\frac{p-q}{-3}=29$
4. $\frac{p-q}{-3}=31$

See Solution

Problem 28235

Identify equivalent equations to $15=t-u$ from the options: $20=t-u+5$ , $17=2+t-u$ , $18=t-u+3$ , $19=t-u+4$ .

See Solution

Problem 28236

Identify all equations equivalent to: $-30=14 y$ . Consider properties of equality. Options: $60=-2 \cdot 14 y$ , $-60=14 y \cdot 2$ , $90=14 y \cdot-3$ , $-90=14 y \cdot 3$ .

See Solution

Problem 28237

Find all equations equivalent to $12=4c$ using properties of equality: $2=4c-10$ , $9=4c-2$ , $10=4c-2$ , $4=4c-8$ .

See Solution

Problem 28238

Find all equations equivalent to: $-62 = r + s$ . Consider the following options.

See Solution

Problem 28239

Select equations equivalent to $15 = r + s$ using properties of equality: $20 = r + s + 5$ , $19 = 4 + r + s$ , $18 = 3 + r + s$ , $17 = r + s + 2$ .

See Solution

Problem 28240

Solve the equation $\log _{2} x - \log _{2} 7 = \log _{2}(x - 1)$ .

See Solution

Problem 28241

Solve the system of equations using an inverse matrix and show the inverse matrix $A^{-1}$ used.
$2x - 3y = -8$ $-4x + y = -2$

See Solution

Problem 28242

Solve the inequality: $\log _{\frac{3}{5}}(2-x)+\log _{\frac{3}{5}}(x+2)>\log _{\frac{3}{5}} 3 x$ .

See Solution

Problem 28243

Solve the inequality: $(\log_{2} x)^{2} - \log_{2} x < 0$ .

See Solution

Problem 28244

Risolvi la disequazione: $472\left(\log _{2} x\right)^{2}-\log _{2} x<0$ .

See Solution

Problem 28245

Solve the inequality: $\log ^{2} x - 7 \log x + 12 < 0$ .

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Problem 28246

Find the growth rate of corn if it is 1 m tall after 4 weeks and 1.8 m tall after 9 weeks. Options: A) 0.16 B) 0.31 C) 0.089 D) 6.25 E) 11.25.

See Solution

Problem 28247

Which expression is NOT equal to $(3 x-12)(x+4)$ ? $3\left(x^{2}-8 x+16\right)$ , $3\left(x^{2}-16\right)$ , $3 x^{2}-48$ , $3 x(x+4)-12(x+4)$

See Solution

Problem 28248

Find the volume of a cylinder with $r=2b$ and $h=5b+3$ using $V=\pi r^{2} h$ in terms of $b$ .

See Solution

Problem 28249

Find the values of $y$ and the gradient at $x=-1$ for the function $y=-4x^3-x^2+3x+1$ .

See Solution

Problem 28250

Solve for $x$ in the equation: $12 x - 30 = -6$ .

See Solution

Problem 28251

Solve for $x$ : $3 x + 1 = 10$

See Solution

Problem 28252

Solve for $t$ in the equation: $8 - 3t = 2$ .

See Solution

Problem 28253

Solve for $y$ in the equation: $15 - 3y = 15$ .

See Solution

Problem 28254

Solve for $a$ in the equation $6 a + 5 = 9$ .

See Solution

Problem 28255

Solve for c in the equation: $8 \cdot 4 - 2 = 3c$ .

See Solution

Problem 28256

Solve for $c$ in the equation: $4 - 2 = 3c$ .

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Problem 28257

Solve the equation: $-8 x + 3 = -29$ .

See Solution

Problem 28258

Show that the curve $y=2 x^{2}-3 x+1$ and the line $y=k x+k^{2}$ intersect for any constant $k$ .

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Problem 28259

Solve the inequality: $6 \leq n + 3 \frac{1}{4}$ .

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Problem 28260

Write the inequality: $6 \leq n + 3 \frac{1}{4}$ . Then solve for $n$ .

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Problem 28261

Solve the equation: $\frac{y-7}{2 y}=\frac{5}{y}$ .

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Problem 28262

Compare earnings per item sold: Lincoln School: $\$ 5$ for 4 boxes; Williams School: $\$ 7$ for 6 rolls.

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Problem 28263

Solve the equation: $\frac{x^{3}-2 x^{2}}{x^{3}}=-2 x^{2}$ .

See Solution

Problem 28264

What fraction of cars in a lot are both gray and electric if $\frac{2}{5}$ are gray and $\frac{1}{3}$ of gray are electric?

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Problem 28265

Solve for $x$ : $-x^{2}+10 x=3 x+6$

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Problem 28266

Evaluate $h + 9g$ for $g=4$ and $h=6$ .

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Problem 28267

Find values for the function $f(x)=6$ : (a) $f(9)$ , (b) $f(-9)$ , (c) $f(3.3)$ , (d) $f(-3.6)$ .

See Solution

Problem 28268

Find the value of $f(p)$ for the function $f(x)=\sqrt{-8-x}$ .

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Problem 28269

Find $f(7)$ , $f(-6)$ , $f(-3.8)$ , and $f(-5.4)$ for the piecewise function: $f(x) = \{-2x + 16 \text{ if } x \leq -4; 3 \text{ if } -4 < x < 3; x + 8 \text{ if } x \geq 3\}$ .

See Solution

Problem 28270

Evaluate $f(x)=x^{2}-4$ for (a) $f(3 p)$ , (b) $f(-3 q)$ , and (c) $f(x+5)$ .

See Solution

Problem 28271

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=9x+1$ and $h \neq 0$ . Simplify your answer.

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Problem 28272

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=x^{2}+4$ where $h \neq 0$ . Simplify your answer.

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Problem 28273

Calculate the state's income tax function $h(x)$ for the following incomes: (a) $h(1260)$ , (b) $h(7160)$ , (c) $h(49070)$ .

See Solution

Problem 28274

Calculate the income tax $h(x)$ for the following incomes: (a) $1260$ , (b) $7160$ , (c) $49070$ . Round to the nearest cent.

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Problem 28275

Find $k$ for which the line $y=-2x+3$ is tangent to the curve $f(x)=k x^{2}$ .

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Problem 28276

Evaluate the expression when $c=6$ and $d=26$ : $d-\frac{30}{0}$ .

See Solution

Problem 28277

Evaluate $d - \frac{30}{c}$ for $c=6$ and $d=26$ .

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Problem 28278

A fish starts at -10.8 m and descends 1.5 m every 2 min. How long to reach -37.8 m? Show your work and explain.

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Problem 28279

A plane flies from city A to city B, 2140 miles apart at 400 mph. Find the function $f(t)$ for distance from B at time $t$ .

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Problem 28280

A pretzel factory has daily costs of \ $2100 and 10 cents per bag. Each bag sells for \$1.70. Find the cost function$ c(x) $.$ $c(x) = 2100 + 0.10x$ $

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Problem 28281

Find the average rate of change of $f(x)$ from $x_{1}=-3$ to $x_{2}=8.5$ for $f(x)=7x-8$ . Round to the nearest hundredth.

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Problem 28282

Solve for $n$ in the equation $\frac{2}{m}+\frac{3}{n}=2$ .

See Solution

Problem 28283

Find $k$ so that the line $y=2x+k$ goes through the minimum point of the curve $y=3x^2+12x+13$ .

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Problem 28284

Find the average rate of change of $f(x)$ from $x_{1}=2$ to $x_{2}=4$ for $f(x)=\sqrt{3x+1}$ , rounded to the nearest hundredth.

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Problem 28285

Find $y$ for $y=\frac{1}{x}$ when $x$ is -4, -3, -2, -1, 0, 1, 2.

See Solution

Problem 28286

Find the values of $y$ for $y=\frac{1}{x}$ when $x = -4, -3, -2, -1, 0, 1, 2, 3, 4$ .

See Solution

Problem 28287

Find values of $x$ for which the volume of a prism is $\geq 500$ cubic units, given width $= x - 5$ and height $= 2x$ .

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Problem 28288

Solve for $m$ in the equation: $251 = m - 8(5m - 7)$ .

See Solution

Problem 28289

Complete the table for $y = \frac{1}{x}$ with $x$ values: -4, -3, -2, -1, 0, 1, 2, 3, 4. Some $y$ values are undefined.

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Problem 28290

Find the length of segment $\overline{F G}$ given $F H=5 x+2$ , $G H=5 x-9$ , and $F G=x+5$ .

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Problem 28291

Find the average rate of change of $f(x)=6x+9$ from $x_1=3.5$ to $x_2=9$ , rounded to the nearest whole number.

See Solution

Problem 28292

Find the average rate of change of $f(x)$ from $x_{1}=-9$ to $x_{2}=-1$ , rounded to the nearest hundred. $f(x)=\sqrt{-8 x+6}$

See Solution

Problem 28293

Factor completely: $r^{2}-r-20$ .

See Solution

Problem 28294

Find the value of $i^{99}$ .

See Solution

Problem 28295

F 4U, déc. 2021 Les fonctions exponentielles Page
6. On a placé une somme d'argent à un taux d'intérêt constant. Les intérêts sont composés annuellement. Au bout de quatre ans, la valeur du placement est de 619,41 $\$$ . Au bout de 10 ans, elle est de 854,07 $\$$ . a. Quelle somme d'argent a été placée au départ ? $619,41 = C$ b. Estime le taux d'intérêt annuel I H

See Solution

Problem 28296

Solve the equation by completing the square.
$x^2 + 16x + 51 = 0$

See Solution

Problem 28297

Return Multiple Choice 20 points used to find the possible values for $p$ ? $\begin{array}{l} p-7>50 \\ p-7<50 \\ p+7 \geq 50 \\ p+7 \leq 50 \end{array}$ Multiple Chaice 20 points

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Problem 28298

1. Solve the system by graphing. $\begin{array}{l} y=\frac{3}{4} x+3 \begin{array}{l} \text { slope } \cdot \frac{3}{4} \\ y \text {-ill }: 3^{3} \end{array} \\ y=3 x-6 \begin{array}{l} \text { slope: } \frac{3}{1} \\ \text { y-int: - } 6 \end{array} \end{array}$
Answer: $\qquad$

See Solution

Problem 28299

5 Matching 20 points Cory has a gym membership that can be represented by the inequality $\frac{z}{12} \leq 7$
Cory has $\qquad$ gym membership that costs x dollars
He pays $\qquad$ each month

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Problem 28300

\begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline 0 & 4.6 \\ \hline 1 & 7.2 \\ \hline 2 & 0 \\ \hline 3 & -17 \\ \hline 4 & -43.8 \\ \hline 5 & -80.4 \\ \hline \end{tabular}
A projectile's motion is modeled by the function given in the table, where $x$ represents time in seconds and $f(x)$ represents height above the ground. At what time is the projectile on the ground? - 80.4 seconds 2 seconds 4.6 seconds It will never hit the ground.

See Solution

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Algebra

Problem 28201

Find the expected aptitude score for a 17-year-old using the formula: Aptitude = 111.5 - 1.14 * Age. Round to the nearest whole number.

Problem 28202

Solve ∣3k−2∣−2∣k+2∣=0|3k - 2| - 2|k + 2| = 0∣3k−2∣−2∣k+2∣=0. Find the solutions for kkk.

Problem 28203

Solve the equation m+3=7m + 3 = 7m+3=7 for the value of mmm.

Problem 28204

Let s represent "One races fast." Express "One does not race fast" symbolically.

Problem 28205

Solve the equation ∣4n−15∣=∣n∣|4 n-15|=|n|∣4n−15∣=∣n∣. Find the values of n=n=n= and n=n=n=.

Problem 28206

Solve the equation −4∣8−5n∣=13-4|8-5 n|=13−4∣8−5n∣=13 for nnn.

Problem 28207

Add or subtract: (a) ba+1b\frac{b}{a}+\frac{1}{b}ab​+b1​ and simplify if possible.

Problem 28208

Add or subtract the fractions: ba+1b\frac{b}{a}+\frac{1}{b}ab​+b1​ and simplify if possible.

Problem 28209

Solve 9∣Ap+2∣+8=359|A p+2|+8=359∣Ap+2∣+8=35 for the variable AAA.

Problem 28210

Write the symbolic form of "I study and I eat bananas" using ppp and qqq.

Problem 28211

Symbolically express: The stove is hot and I do not get an A using ppp and qqq.

Problem 28212

Write the symbolic form of "You're here, but I'm not there" using ppp and qqq.

Problem 28213

Write the symbolic form of "I eat bananas or it is time to sleep" using ppp and qqq.

Problem 28214

Write the symbolic form of "I get a promotion if and only if I work hard" using ppp and qqq.

Problem 28215

Solve the equation ∣3k−2∣=2∣k+2∣|3 k-2|=2|k+2|∣3k−2∣=2∣k+2∣.

Problem 28216

Write the symbolic form of: "It is not Sunday if and only if the campus is not closed." using ppp and qqq.

Problem 28217

Write the symbolic form of: "I get an A if and only if the job pays well and I do not work hard." Use ppp, qqq, and rrr.

Problem 28218

Symbolically express: "The chair is broken and it is time to sleep, or I get an A" using ppp, qqq, and rrr.

Problem 28219

Multiply and simplify: (sin⁡θ+5)(sin⁡θ+6)(\sin \theta+5)(\sin \theta+6)(sinθ+5)(sinθ+6)

Problem 28220

Write the symbolic form of: Not having a job or not following a budget implies being in debt.

Problem 28221

Multiply and simplify: (4cos⁡θ+5)(7cos⁡θ−2)(4 \cos \theta + 5)(7 \cos \theta - 2)(4cosθ+5)(7cosθ−2).

Problem 28222

Multiply and simplify: (2−tan⁡θ)(2+tan⁡θ)(2-\tan \theta)(2+\tan \theta)(2−tanθ)(2+tanθ).

Problem 28223

Simplify the expression (sin⁡θ−cos⁡θ)2(\sin \theta - \cos \theta)^{2}(sinθ−cosθ)2.

Problem 28224

Simplify x2−16\sqrt{x^{2}-16}x2−16​ after substituting x=4sec⁡(θ)x = 4 \sec(\theta)x=4sec(θ), where 0∘<θ<90∘0^{\circ}<\theta<90^{\circ}0∘<θ<90∘.

Problem 28225

Simplify 9−x2\sqrt{9-x^{2}}9−x2​ by substituting x=3sin⁡(θ)x=3 \sin (\theta)x=3sin(θ), where 0∘<θ<90∘0^{\circ}<\theta<90^{\circ}0∘<θ<90∘.

Problem 28226

Sasha's 9-digit passcode starts and ends with 6. Each set of 3 consecutive digits sums to 14. Find the 5th digit.

Problem 28227

Find the value of f(1)f(1)f(1) for the function f(x)=9.1x2+0.5xf(x)=9.1 x^{2}+0.5 xf(x)=9.1x2+0.5x. Provide your answer as a decimal or whole number.

Problem 28228

Tushar's age is 7 times his daughter's. In 5 years, he'll be 4 times her age. Find their current ages.

Problem 28229

Garima's father is 43, 19 years older than twice her age. Set up and solve the equation: 43=2x+1943 = 2x + 1943=2x+19.

Problem 28230

Show that log⁡3x+log⁡9x=3lg⁡x2lg⁡3\log _{3} x+\log _{9} x=\frac{3 \lg x}{2 \lg 3}log3​x+log9​x=2lg33lgx​ and solve log⁡3x+log⁡9x=4\log _{3} x+\log _{9} x=4log3​x+log9​x=4.

Problem 28231

Prove that log⁡3x+log⁡9x=3lg⁡x2lg⁡3\log _{3} x+\log _{9} x=\frac{3 \lg x}{2 \lg 3}log3​x+log9​x=2lg33lgx​.

Problem 28232

Find the mass of a graphite block with the same volume as a 483 g483 \mathrm{~g}483 g iron block, given their densities.

Problem 28233

Find the values of the following Fibonacci numbers: F22,F46,F20,F12,F18,F6,F28,F19,F25,F10F_{22}, F_{46}, F_{20}, F_{12}, F_{18}, F_{6}, F_{28}, F_{19}, F_{25}, F_{10}F22​,F46​,F20​,F12​,F18​,F6​,F28​,F19​,F25​,F10​.

Problem 28234

Identify equivalent equations for p−q=−93p-q=-93p−q=−93. Which of these are equivalent? 1. p−q3=−31\frac{p-q}{3}=-313p−q​=−31 2. p−q3=−32\frac{p-q}{3}=-323p−q​=−32 3. p−q−3=29\frac{p-q}{-3}=29−3p−q​=29 4. p−q−3=31\frac{p-q}{-3}=31−3p−q​=31

Problem 28235

Identify equivalent equations to 15=t−u15=t-u15=t−u from the options: 20=t−u+520=t-u+520=t−u+5, 17=2+t−u17=2+t-u17=2+t−u, 18=t−u+318=t-u+318=t−u+3, 19=t−u+419=t-u+419=t−u+4.

Problem 28236

Identify all equations equivalent to: −30=14y-30=14 y−30=14y. Consider properties of equality. Options: 60=−2⋅14y60=-2 \cdot 14 y60=−2⋅14y, −60=14y⋅2-60=14 y \cdot 2−60=14y⋅2, 90=14y⋅−390=14 y \cdot-390=14y⋅−3, −90=14y⋅3-90=14 y \cdot 3−90=14y⋅3.

Problem 28237

Find all equations equivalent to 12=4c12=4c12=4c using properties of equality: 2=4c−102=4c-102=4c−10, 9=4c−29=4c-29=4c−2, 10=4c−210=4c-210=4c−2, 4=4c−84=4c-84=4c−8.

Problem 28238

Find all equations equivalent to: −62=r+s-62 = r + s−62=r+s. Consider the following options.

Problem 28239

Select equations equivalent to 15=r+s15 = r + s15=r+s using properties of equality: 20=r+s+520 = r + s + 520=r+s+5, 19=4+r+s19 = 4 + r + s19=4+r+s, 18=3+r+s18 = 3 + r + s18=3+r+s, 17=r+s+217 = r + s + 217=r+s+2.

Problem 28240

Solve $|3k - 2| - 2|k + 2| = 0$ . Find the solutions for $k$ .

Solve the equation $m + 3 = 7$ for the value of $m$ .

Solve the equation $|4 n-15|=|n|$ . Find the values of $n=$ and $n=$ .

Solve the equation $-4|8-5 n|=13$ for $n$ .

Add or subtract: (a) $\frac{b}{a}+\frac{1}{b}$ and simplify if possible.

Add or subtract the fractions: $\frac{b}{a}+\frac{1}{b}$ and simplify if possible.

Solve $9|A p+2|+8=35$ for the variable $A$ .

Write the symbolic form of "I study and I eat bananas" using $p$ and $q$ .

Symbolically express: The stove is hot and I do not get an A using $p$ and $q$ .

Write the symbolic form of "You're here, but I'm not there" using $p$ and $q$ .

Write the symbolic form of "I eat bananas or it is time to sleep" using $p$ and $q$ .

Write the symbolic form of "I get a promotion if and only if I work hard" using $p$ and $q$ .

Solve the equation $|3 k-2|=2|k+2|$ .

Write the symbolic form of: "It is not Sunday if and only if the campus is not closed." using $p$ and $q$ .

Write the symbolic form of: "I get an A if and only if the job pays well and I do not work hard." Use $p$ , $q$ , and $r$ .

Symbolically express: "The chair is broken and it is time to sleep, or I get an A" using $p$ , $q$ , and $r$ .

Multiply and simplify: $(\sin \theta+5)(\sin \theta+6)$

Multiply and simplify: $(4 \cos \theta + 5)(7 \cos \theta - 2)$ .

Multiply and simplify: $(2-\tan \theta)(2+\tan \theta)$ .

Simplify the expression $(\sin \theta - \cos \theta)^{2}$ .

Simplify $\sqrt{x^{2}-16}$ after substituting $x = 4 \sec(\theta)$ , where $0^{\circ}<\theta<90^{\circ}$ .

Simplify $\sqrt{9-x^{2}}$ by substituting $x=3 \sin (\theta)$ , where $0^{\circ}<\theta<90^{\circ}$ .

Find the value of $f(1)$ for the function $f(x)=9.1 x^{2}+0.5 x$ . Provide your answer as a decimal or whole number.

Garima's father is 43, 19 years older than twice her age. Set up and solve the equation: $43 = 2x + 19$ .

Show that $\log _{3} x+\log _{9} x=\frac{3 \lg x}{2 \lg 3}$ and solve $\log _{3} x+\log _{9} x=4$ .

Prove that $\log _{3} x+\log _{9} x=\frac{3 \lg x}{2 \lg 3}$ .

Find the mass of a graphite block with the same volume as a $483 \mathrm{~g}$ iron block, given their densities.

Find the values of the following Fibonacci numbers: $F_{22}, F_{46}, F_{20}, F_{12}, F_{18}, F_{6}, F_{28}, F_{19}, F_{25}, F_{10}$ .

Identify equivalent equations for $p-q=-93$ . Which of these are equivalent?
1. $\frac{p-q}{3}=-31$
2. $\frac{p-q}{3}=-32$
3. $\frac{p-q}{-3}=29$
4. $\frac{p-q}{-3}=31$

Identify equivalent equations to $15=t-u$ from the options: $20=t-u+5$ , $17=2+t-u$ , $18=t-u+3$ , $19=t-u+4$ .

Identify all equations equivalent to: $-30=14 y$ . Consider properties of equality. Options: $60=-2 \cdot 14 y$ , $-60=14 y \cdot 2$ , $90=14 y \cdot-3$ , $-90=14 y \cdot 3$ .

Find all equations equivalent to $12=4c$ using properties of equality: $2=4c-10$ , $9=4c-2$ , $10=4c-2$ , $4=4c-8$ .

Find all equations equivalent to: $-62 = r + s$ . Consider the following options.

Select equations equivalent to $15 = r + s$ using properties of equality: $20 = r + s + 5$ , $19 = 4 + r + s$ , $18 = 3 + r + s$ , $17 = r + s + 2$ .

Solve the equation $\log _{2} x - \log _{2} 7 = \log _{2}(x - 1)$ .

Solve the system of equations using an inverse matrix and show the inverse matrix $A^{-1}$ used.
$2x - 3y = -8$ $-4x + y = -2$

Solve the inequality: $\log _{\frac{3}{5}}(2-x)+\log _{\frac{3}{5}}(x+2)>\log _{\frac{3}{5}} 3 x$ .

Solve the inequality: $(\log_{2} x)^{2} - \log_{2} x < 0$ .

Risolvi la disequazione: $472\left(\log _{2} x\right)^{2}-\log _{2} x<0$ .

Solve the inequality: $\log ^{2} x - 7 \log x + 12 < 0$ .

Which expression is NOT equal to $(3 x-12)(x+4)$ ? $3\left(x^{2}-8 x+16\right)$ , $3\left(x^{2}-16\right)$ , $3 x^{2}-48$ , $3 x(x+4)-12(x+4)$

Find the volume of a cylinder with $r=2b$ and $h=5b+3$ using $V=\pi r^{2} h$ in terms of $b$ .

Find the values of $y$ and the gradient at $x=-1$ for the function $y=-4x^3-x^2+3x+1$ .

Solve for $x$ in the equation: $12 x - 30 = -6$ .

Solve for $x$ : $3 x + 1 = 10$

Solve for $t$ in the equation: $8 - 3t = 2$ .

Solve for $y$ in the equation: $15 - 3y = 15$ .

Solve for $a$ in the equation $6 a + 5 = 9$ .

Solve for c in the equation: $8 \cdot 4 - 2 = 3c$ .

Solve for $c$ in the equation: $4 - 2 = 3c$ .

Solve the equation: $-8 x + 3 = -29$ .

Show that the curve $y=2 x^{2}-3 x+1$ and the line $y=k x+k^{2}$ intersect for any constant $k$ .

Solve the inequality: $6 \leq n + 3 \frac{1}{4}$ .

Write the inequality: $6 \leq n + 3 \frac{1}{4}$ . Then solve for $n$ .

Solve the equation: $\frac{y-7}{2 y}=\frac{5}{y}$ .

Compare earnings per item sold: Lincoln School: $\$ 5$ for 4 boxes; Williams School: $\$ 7$ for 6 rolls.

Solve the equation: $\frac{x^{3}-2 x^{2}}{x^{3}}=-2 x^{2}$ .

What fraction of cars in a lot are both gray and electric if $\frac{2}{5}$ are gray and $\frac{1}{3}$ of gray are electric?

Solve for $x$ : $-x^{2}+10 x=3 x+6$

Evaluate $h + 9g$ for $g=4$ and $h=6$ .

Find values for the function $f(x)=6$ : (a) $f(9)$ , (b) $f(-9)$ , (c) $f(3.3)$ , (d) $f(-3.6)$ .

Find the value of $f(p)$ for the function $f(x)=\sqrt{-8-x}$ .

Evaluate $f(x)=x^{2}-4$ for (a) $f(3 p)$ , (b) $f(-3 q)$ , and (c) $f(x+5)$ .

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=9x+1$ and $h \neq 0$ . Simplify your answer.

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=x^{2}+4$ where $h \neq 0$ . Simplify your answer.

Calculate the state's income tax function $h(x)$ for the following incomes: (a) $h(1260)$ , (b) $h(7160)$ , (c) $h(49070)$ .

Calculate the income tax $h(x)$ for the following incomes: (a) $1260$ , (b) $7160$ , (c) $49070$ . Round to the nearest cent.