Numbers & Operations

Problem 2201

Solve the equation $4(4x-3)=2(3x+3)$ for the given variable. Express the solution in reduced fractional form.

See Solution

Problem 2202

Find the range of the quadratic function $f(x)=-6(x-7)^{2}+5$ .

See Solution

Problem 2203

Find the smallest nonnegative angle $\theta_C$ coterminal with $\theta = -\pi/20$ .

See Solution

Problem 2204

Find the two integers whose sum is $10$ and the sum of their squares is minimized.

See Solution

Problem 2205

Solve the linear equation $3(3-4x) = 3(5x+1)$ and verify the solution.

See Solution

Problem 2206

Determine the amplitude, period, and phase shift of $y=\cos(x-\pi/4)$ . The amplitude is $1$ , the period is $2\pi$ , and the phase shift is $-\pi/4$ .

See Solution

Problem 2207

Solve the equation $\frac{7}{x} + \frac{1}{4} = \frac{5}{x} + \frac{1}{3}$ and check the solution.

See Solution

Problem 2208

Estimate the proportion of oil tankers that had spills given a sample of 712 tankers, where 570 did not have spills. Enter the result as a fraction or decimal rounded to 3 decimal places.

See Solution

Problem 2209

Find the indefinite integral of $5x^3$ .

See Solution

Problem 2210

Simplify the expression $-2(-8 x+10)+9 x$ .

See Solution

Problem 2211

Solve linear equation $3(2x-1)-3=0$ for $x$

See Solution

Problem 2212

Solve for $x$ where $\frac{x}{4}-2=-10$ .

See Solution

Problem 2213

Find the value of $x$ in the equation $\frac{6a}{7b} = \frac{x}{-14b}$ .

See Solution

Problem 2214

Solve for $\theta$ given the equation $5+4\cos\theta=6$ .

See Solution

Problem 2215

A snowball's radius decreases at $0.1$ cm/min. Find the rate of volume decrease when radius is $11$ cm. (Round answer to 3 decimal places)
$\frac{d V}{d t} = -4 \pi r^2 \frac{d r}{d t} = -4 \pi (11)^2 (0.1) = -\boxed{12.116} \frac{\mathrm{cm}^3}{\min}$

See Solution

Problem 2216

Find the value of $d$ given the relationship $d=2.5 r$ and $r=64$ .

See Solution

Problem 2217

Show that $y=\sin(t)$ solves the ODE $(\frac{dy}{dt})^2=1-y^2$ . Justify your answer in terms of $t$ .

See Solution

Problem 2218

Determine the length of Teresa's workout plans A and B given the number of clients and total training hours on Friday and Saturday. Plan A: $\square$ hour(s) Plan B: $\square$ hour(s)

See Solution

Problem 2219

Evaluate the definite integral of $0.25e^{-0.25x}$ .

See Solution

Problem 2220

a. Janessa paid $\$ 390.96$ for a 2-year magazine subscription. After receiving 25 magazines in the second year, she cancelled. How many magazines will she receive a refund for? Round up to a whole number.
b. Calculate the pro-rated refund Janessa should receive from the magazine company. Round up to the nearest cent.

See Solution

Problem 2221

Find the largest integer value of $t$ that satisfies the inequality $\frac{t}{4} + 2 < 11$ .

See Solution

Problem 2222

1. Find $n$ for arithmetic series: a) $t_1=8, t_n=68, S_n=608$ b) $t_1=-6, t_n=21, S_n=75$
2. Find $t_{10}$ and $S_{10}$ for series: a) $5+10+15+\cdots$ b) $10+7+4+\cdots$ c) $(-10)+(-14)+(-18)+\cdots$ d) $2.5+3+3.5+\cdots$
3. a) Sum of multiples of 4 between 1 and 999 b) Sum of multiples of 6 between 1 and 999

See Solution

Problem 2223

Solve the equation $6(t+12)=114$ by applying the Distributive Property. Determine the first and last operations needed.

See Solution

Problem 2224

Find the square of 8. Find the cube of 7.

See Solution

Problem 2225

Find the value of $9^3$ .

See Solution

Problem 2226

Find the total temperature change when the temperature increases by $2^{\circ} \mathrm{C}$ each hour for $9 \mathrm{~h}$ .

See Solution

Problem 2227

Find the value of the sine function evaluated at $\frac{2 \pi}{3}$ .

See Solution

Problem 2228

Find the change in the function $f(x) = 7 - 6x$ from $x = 5$ to $x = 7$ .

See Solution

Problem 2229

Solve the inequality $x^2 - 169 < 0$

See Solution

Problem 2230

Flights from Dallas to Chicago are on time 80% of the time. 20 flights are randomly selected. Find the probability of exactly 12 on-time flights, fewer than 12 on-time flights, at least 12 on-time flights, and between 10 and 12 on-time flights. Interpret the probabilities.

See Solution

Problem 2231

Jared's bicycle rides: given distances and times, find the missing time for 40 miles, assuming constant speed.
\begin{tabular}{|c|c|} \hline Miles (x) & Minutes (y) \\ \hline 6 & 45 \\ \hline 17 & 127.5 \\ \hline 40 & \\ \hline \end{tabular}

See Solution

Problem 2232

Find the number where the result of dividing the number by 3 is 4.

See Solution

Problem 2233

Find the solutions of the system of linear inequalities $8x + 5y > 40$ and $-6x + 2y \geq -18$ .

See Solution

Problem 2234

Solve for the variable $v$ in the equation $1.4 = -6v + 20.6$ .

See Solution

Problem 2235

Solve the equation $24+0.44x=19+1.69x$ and select the correct answer from the options provided.

See Solution

Problem 2236

Translate Chau's height decreased by 16 is 60 into an equation using variable $c$ to represent Chau's height.

See Solution

Problem 2237

Simplify expressions like $a^3$ , $6yx$ , $4x^2$ , $15x^2y$ , and $-4y^2z^2$ .

See Solution

Problem 2238

Determine the tire lifespan warranty that will replace no more than $10\%$ of tires, given a normal distribution with $\mu=47,700$ miles and $\sigma=2,000$ miles.

See Solution

Problem 2239

Identify whether $7-8(x+3)$ is an expression or an equation.

See Solution

Problem 2240

Expand $(6-x)^{2}$ using special product of binomials and choose correct answer: (A) $36+12x-x^{2}$ (B) $36-12x+x^{2}$ (C) $6-36x-x^{2}$ (D) $6-12x+x^{2}$

See Solution

Problem 2241

Reduce the ratio $0.13: 0.052$ to its smallest terms.

See Solution

Problem 2242

Find the value of $x$ that satisfies the equation $\frac{2 x}{x-2}-1=\frac{4}{x-2}$ .

See Solution

Problem 2243

Calculate the daily energy consumption of a light bulb that uses $7650$ watt-hours in $4$ days and $6$ hours.

See Solution

Problem 2244

Find the distance between the point $(-2,7)$ and the line $6x + 4y + 1 = 0$ .

See Solution

Problem 2245

Find the value of $y=a b^{x}$ given $a=1600, b=.25, x=12$ , rounded to 7 decimal places.

See Solution

Problem 2246

Find all complex solutions to the cubic equation $f(x) = x^3 - 8x^2 + 21x - 20$ .

See Solution

Problem 2247

Solve the equation $-4 x = 16 x^{2}$ for $x$ .

See Solution

Problem 2248

Evaluate $y=x^5$ when $x=4$ . Round the result to five decimal places.

See Solution

Problem 2249

Find the value of $a^{2} + 3b/c - 2d$ when $a=3, b=8, c=2$ , and $d=5$ .

See Solution

Problem 2250

Determine the nature of the roots based on the discriminant value of $64$ .

See Solution

Problem 2251

Which transformation turns a figure around a point? $\{1\text{. reflection}, 2\text{. translation}, 3\text{. rotation}, 4\text{. none of the above}\}$

See Solution

Problem 2252

Find the value of $(-870 \div 5) \cdot(-6)$ .

See Solution

Problem 2253

Calculate the area of a circle with radius 7.

See Solution

Problem 2254

Multiplicar y simplificar: $(z-10)(z+10)$

See Solution

Problem 2255

Evaluate $\frac{\sqrt{x-3}}{9}$ when $x=12$ . Options: A) $\frac{1}{3}$ B) 1 C) 3 D) 81.

See Solution

Problem 2256

A. Probability that none of the 32 people are Independent: $\left(1 - 0.12\right)^{32}$
B. Probability that fewer than 6 are Independent: $\sum_{i=0}^{5} \binom{32}{i} \left(0.12\right)^{i} \left(1 - 0.12\right)^{32-i}$
C. Probability that more than 3 people are Independent: $1 - \sum_{i=0}^{3} \binom{32}{i} \left(0.12\right)^{i} \left(1 - 0.12\right)^{32-i}$

See Solution

Problem 2257

Find the equation of the line passing through the point $(4,5)$ and parallel to the $x$ -axis.

See Solution

Problem 2258

Solve for the value of $v$ that satisfies the equation $5.2-(2 \div v)=5.1$ .

See Solution

Problem 2259

Resolver para $g$ donde $9g=W$ .

See Solution

Problem 2260

Write a quadratic function $h$ with zeros at -4 and -5.

See Solution

Problem 2261

Prove that the function $f(x)=x^{7}+8 x-2$ has at most one real root using Rolle's Theorem. Show it has exactly one using the Intermediate Value Theorem.

See Solution

Problem 2262

A plane flies 2316 mi with the wind and 2004 mi against the wind. Find the wind speed $\square \mathrm{mph}$ given the plane's cruising speed is $540 \mathrm{mph}$ .

See Solution

Problem 2263

Classic Movie DVDs are on sale from June 19-25. 60 titles available. 2 for $\$ 15.00$ , 3 for $\$ 20.00$ , or 5 for $\$ 30.00$ with coupon. After June 25, $\$ 8.50$ each. Cost of 5 DVDs on June 26 is $\$ 32.50$ .

See Solution

Problem 2264

Solve the equation $\frac{8}{x}+\frac{7}{6 x}=\frac{-5}{6}$ for $x$ .

See Solution

Problem 2265

Find a vector $\vec{b}$ with opposite direction of $\vec{a}$ and $|\vec{b}|=3$ , where $\vec{a}$ is a nonzero vector.

See Solution

Problem 2266

Solve for $x$ in the equation $\frac{x+3}{4}=\frac{5}{2}$ . Simplify the solution.

See Solution

Problem 2267

Find the exact value of $\cot \frac{-11 \pi}{6}$ .

See Solution

Problem 2268

Find the integer closest to $x$ such that $2^{x} = 100$ .

See Solution

Problem 2269

Find complex solutions of $9 x^3 - 17 x^2 + 43 x + 5 = 0$ using possible rational roots: $\pm 1, \pm 1/3, \pm 1/9, \pm 5, \pm 5/3, \pm 5/9$ .

See Solution

Problem 2270

Solve the absolute value equation: $|2x+1| = 9$

See Solution

Problem 2271

Solve for $x$ in the equation $\frac{3}{8} x=48$ . Simplify the solution.

See Solution

Problem 2272

Solve the equation $10-c=-3$ and express the solution as an integer or simplified fraction.

See Solution

Problem 2273

Solve the linear equation $12p - 0.7 = 5p + 3.2$ for the variable $p$ .

See Solution

Problem 2274

Find the average velocity of an object moving along a vertical line with position $L(t)=-3t^2+t+8$ (m) at time $t$ (s) for the given intervals: [3s, 9s], [2s, 7s], [5s, 8s].

See Solution

Problem 2275

Find the domain of the function $f(x) = \frac{9}{x^2 - 5x}$ . Express the answer in interval notation.

See Solution

Problem 2276

Write a story to match the equation $x + 2.5 = 10$ .

See Solution

Problem 2277

Graph the parabola $y=\frac{1}{2}(x-4)^{2}$ representing a bird's height over time as it lands. Find 3 points on the graph.

See Solution

Problem 2278

Find the derivative of $f(x)=\sqrt{5 x-10}$ using the limit definition.

See Solution

Problem 2279

Solve $F g = 5$ for the variable $F$ , accounting for capitalization.

See Solution

Problem 2280

Find the time (in h) to administer $3 \mathrm{L}$ IV at $40 \mathrm{drops} / \mathrm{min}$ with $10 \mathrm{drops} / \mathrm{mL}$ drop factor.

See Solution

Problem 2281

Find the quotient of 36.75 divided by 5.25.

See Solution

Problem 2282

Solve $a=2b-5c$ for $b$ . Options: (A) $\frac{a-5c}{2}=b$ (B) $\frac{a+5c}{2}=b$ (C) $\frac{a-2b}{5}=c$ (D) $\frac{a+2b}{5}=c$

See Solution

Problem 2283

Choose the expression equivalent to $\frac{\tan \left(\frac{3 \pi}{5}\right)-\tan \left(\frac{13 \pi}{30}\right)}{1+\tan \left(\frac{3 \pi}{5}\right) \tan \left(\frac{13 \pi}{30}\right)}$ : $\sin \left(\frac{3 \pi}{5}+\frac{13 \pi}{30}\right) \tan \left(\frac{3 \pi}{5}-\frac{13 \pi}{30}\right) \tan \left(\frac{3 \pi}{5}+\frac{13 \pi}{30}\right) \cos \left(\frac{3 \pi}{5}-\frac{13 \pi}{30}\right)$

See Solution

Problem 2284

Find the radius $r$ given the formula for the area $A$ of a circle: $A = \pi r^2$ .

See Solution

Problem 2285

Find the simple interest rate $r$ for a loan with principal $P=\$2300$ , future value $A=\$2775$ , and duration $t=3$ months.

See Solution

Problem 2286

Karen is saving $\$ 60$ per week. After $W$ weeks, the total amount in the savings account is $S = 350 + 60W$ . The total amount after 18 weeks is $\$ 1,430$ .

See Solution

Problem 2287

TechWiz sells MP3 ( $35 profit) and DVD ($ 18 profit) players. Last week, they sold 137 total. Find the total profit. Total profit = $35x +$ 18(137 - x), where $x$ is the number of MP3 players sold.

See Solution

Problem 2288

Find the value of $d$ that satisfies the equation $d + 9 = 23$ .

See Solution

Problem 2289

Find the capital position (CP) when the selling price (SP) is $Rs. 0.924$ and the gain is 10%.

See Solution

Problem 2290

Convert the given units to find the product of two quantities.

See Solution

Problem 2291

Find the simplified form of $(3^2 y^4)^{-2}$ . A. $-81 y^{8}$ B. $-\frac{y^{8}}{12}$ C. $9 y^{2}$ D. $y^{2}$ E. $\frac{1}{81 y^{8}}$

See Solution

Problem 2292

Simplify the expression $\frac{8}{x^{2}-8 x}-\frac{x}{8 x-64}$ .

See Solution

Problem 2293

Find the amount of wrapping paper needed to cover a $5$ in. by $7$ in. cylindrical gift box, including the top, bottom, and sides. Use $\pi = 3.14$ . Round to the nearest tenth of a square inch.

See Solution

Problem 2294

Find the value of the linear function $P(x)=-7x+9$ . Determine the value of $P(-2)$ .

See Solution

Problem 2295

Find the length of the adjacent side of a rectangular garden with total area $8 x^{2} - 12 x + 4$ sq. ft. and one side measuring $2 x - 2$ ft.

See Solution

Problem 2296

Radioactive fallout from a 1981 nuclear lab explosion is described by $f(x) = 1000(0.5)^{\frac{x}{30}}$ , where $f(x)$ is the remaining amount (kg) $x$ years later. Determine $f(40)$ and if the area will be safe by 2021.

See Solution

Problem 2297

Find the period of the function $y = \tan(4x) + 1$ .

See Solution

Problem 2298

Multiply two decimal numbers: $0.7 \times 0.7$

See Solution

Problem 2299

Simplify the rational expression $\frac{v+\frac{64}{v^{2}}}{1+\frac{4}{v}}$ .

See Solution

Problem 2300

Find the missing value in the scale: $1: \square = 17: 51$ . Options: A) 3, B) 0.4, C) 0.08, D) 0.02.

See Solution

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Numbers & Operations

Problem 2201

Solve the equation 4(4x−3)=2(3x+3)4(4x-3)=2(3x+3)4(4x−3)=2(3x+3) for the given variable. Express the solution in reduced fractional form.

Problem 2202

Find the range of the quadratic function f(x)=−6(x−7)2+5f(x)=-6(x-7)^{2}+5f(x)=−6(x−7)2+5.

Problem 2203

Find the smallest nonnegative angle θC\theta_CθC​ coterminal with θ=−π/20\theta = -\pi/20θ=−π/20.

Problem 2204

Find the two integers whose sum is 101010 and the sum of their squares is minimized.

Problem 2205

Solve the linear equation 3(3−4x)=3(5x+1)3(3-4x) = 3(5x+1)3(3−4x)=3(5x+1) and verify the solution.

Problem 2206

Determine the amplitude, period, and phase shift of y=cos⁡(x−π/4)y=\cos(x-\pi/4)y=cos(x−π/4). The amplitude is 111, the period is 2π2\pi2π, and the phase shift is −π/4-\pi/4−π/4.

Problem 2207

Solve the equation 7x+14=5x+13\frac{7}{x} + \frac{1}{4} = \frac{5}{x} + \frac{1}{3}x7​+41​=x5​+31​ and check the solution.

Problem 2208

Estimate the proportion of oil tankers that had spills given a sample of 712 tankers, where 570 did not have spills. Enter the result as a fraction or decimal rounded to 3 decimal places.

Problem 2209

Find the indefinite integral of 5x35x^35x3.

Problem 2210

Simplify the expression −2(−8x+10)+9x-2(-8 x+10)+9 x−2(−8x+10)+9x.

Problem 2211

Solve linear equation 3(2x−1)−3=03(2x-1)-3=03(2x−1)−3=0 for xxx

Problem 2212

Solve for xxx where x4−2=−10\frac{x}{4}-2=-104x​−2=−10.

Problem 2213

Find the value of xxx in the equation 6a7b=x−14b\frac{6a}{7b} = \frac{x}{-14b}7b6a​=−14bx​.

Problem 2214

Solve for θ\thetaθ given the equation 5+4cos⁡θ=65+4\cos\theta=65+4cosθ=6.

Problem 2215

Problem 2216

Find the value of ddd given the relationship d=2.5rd=2.5 rd=2.5r and r=64r=64r=64.

Problem 2217

Show that y=sin⁡(t)y=\sin(t)y=sin(t) solves the ODE (dydt)2=1−y2(\frac{dy}{dt})^2=1-y^2(dtdy​)2=1−y2. Justify your answer in terms of ttt.

Problem 2218

Determine the length of Teresa's workout plans A and B given the number of clients and total training hours on Friday and Saturday. Plan A: □\square□ hour(s) Plan B: □\square□ hour(s)

Problem 2219

Evaluate the definite integral of 0.25e−0.25x0.25e^{-0.25x}0.25e−0.25x.

Problem 2220

Problem 2221

Find the largest integer value of ttt that satisfies the inequality t4+2<11\frac{t}{4} + 2 < 114t​+2<11.

Problem 2222

Problem 2223

Solve the equation 6(t+12)=1146(t+12)=1146(t+12)=114 by applying the Distributive Property. Determine the first and last operations needed.

Problem 2224

Find the square of 8. Find the cube of 7.

Problem 2225

Find the value of 939^393.

Problem 2226

Find the total temperature change when the temperature increases by 2∘C2^{\circ} \mathrm{C}2∘C each hour for 9 h9 \mathrm{~h}9 h.

Problem 2227

Find the value of the sine function evaluated at 2π3\frac{2 \pi}{3}32π​.

Problem 2228

Find the change in the function f(x)=7−6xf(x) = 7 - 6xf(x)=7−6x from x=5x = 5x=5 to x=7x = 7x=7.

Problem 2229

Solve the inequality x2−169<0x^2 - 169 < 0x2−169<0

Problem 2230

Flights from Dallas to Chicago are on time 80% of the time. 20 flights are randomly selected. Find the probability of exactly 12 on-time flights, fewer than 12 on-time flights, at least 12 on-time flights, and between 10 and 12 on-time flights. Interpret the probabilities.

Problem 2231

Jared's bicycle rides: given distances and times, find the missing time for 40 miles, assuming constant speed.\begin{tabular}{|c|c|} \hline Miles (x) & Minutes (y) \\ \hline 6 & 45 \\ \hline 17 & 127.5 \\ \hline 40 & \\ \hline \end{tabular}

Problem 2232

Find the number where the result of dividing the number by 3 is 4.

Problem 2233

Find the solutions of the system of linear inequalities 8x+5y>408x + 5y > 408x+5y>40 and −6x+2y≥−18-6x + 2y \geq -18−6x+2y≥−18.

Problem 2234

Solve for the variable vvv in the equation 1.4=−6v+20.61.4 = -6v + 20.61.4=−6v+20.6.

Problem 2235

Solve the equation 24+0.44x=19+1.69x24+0.44x=19+1.69x24+0.44x=19+1.69x and select the correct answer from the options provided.

Problem 2236

Translate Chau's height decreased by 16 is 60 into an equation using variable ccc to represent Chau's height.

Problem 2237

Simplify expressions like a3a^3a3, 6yx6yx6yx, 4x24x^24x2, 15x2y15x^2y15x2y, and −4y2z2-4y^2z^2−4y2z2.

Problem 2238

Determine the tire lifespan warranty that will replace no more than 10%10\%10% of tires, given a normal distribution with μ=47,700\mu=47,700μ=47,700 miles and σ=2,000\sigma=2,000σ=2,000 miles.

Problem 2239

Identify whether 7−8(x+3)7-8(x+3)7−8(x+3) is an expression or an equation.

Problem 2240

Expand (6−x)2(6-x)^{2}(6−x)2 using special product of binomials and choose correct answer: (A) 36+12x−x236+12x-x^{2}36+12x−x2 (B) 36−12x+x236-12x+x^{2}36−12x+x2 (C) 6−36x−x26-36x-x^{2}6−36x−x2 (D) 6−12x+x26-12x+x^{2}6−12x+x2

Problem 2241

Reduce the ratio 0.13:0.0520.13: 0.0520.13:0.052 to its smallest terms.

Solve the equation $4(4x-3)=2(3x+3)$ for the given variable. Express the solution in reduced fractional form.

Find the range of the quadratic function $f(x)=-6(x-7)^{2}+5$ .

Find the smallest nonnegative angle $\theta_C$ coterminal with $\theta = -\pi/20$ .

Find the two integers whose sum is $10$ and the sum of their squares is minimized.

Solve the linear equation $3(3-4x) = 3(5x+1)$ and verify the solution.

Determine the amplitude, period, and phase shift of $y=\cos(x-\pi/4)$ . The amplitude is $1$ , the period is $2\pi$ , and the phase shift is $-\pi/4$ .

Solve the equation $\frac{7}{x} + \frac{1}{4} = \frac{5}{x} + \frac{1}{3}$ and check the solution.

Find the indefinite integral of $5x^3$ .

Simplify the expression $-2(-8 x+10)+9 x$ .

Solve linear equation $3(2x-1)-3=0$ for $x$

Solve for $x$ where $\frac{x}{4}-2=-10$ .

Find the value of $x$ in the equation $\frac{6a}{7b} = \frac{x}{-14b}$ .

Solve for $\theta$ given the equation $5+4\cos\theta=6$ .

Find the value of $d$ given the relationship $d=2.5 r$ and $r=64$ .

Show that $y=\sin(t)$ solves the ODE $(\frac{dy}{dt})^2=1-y^2$ . Justify your answer in terms of $t$ .

Determine the length of Teresa's workout plans A and B given the number of clients and total training hours on Friday and Saturday. Plan A: $\square$ hour(s) Plan B: $\square$ hour(s)

Evaluate the definite integral of $0.25e^{-0.25x}$ .

Find the largest integer value of $t$ that satisfies the inequality $\frac{t}{4} + 2 < 11$ .

Solve the equation $6(t+12)=114$ by applying the Distributive Property. Determine the first and last operations needed.

Find the value of $9^3$ .

Find the total temperature change when the temperature increases by $2^{\circ} \mathrm{C}$ each hour for $9 \mathrm{~h}$ .

Find the value of the sine function evaluated at $\frac{2 \pi}{3}$ .

Find the change in the function $f(x) = 7 - 6x$ from $x = 5$ to $x = 7$ .

Solve the inequality $x^2 - 169 < 0$

Jared's bicycle rides: given distances and times, find the missing time for 40 miles, assuming constant speed.
\begin{tabular}{|c|c|} \hline Miles (x) & Minutes (y) \\ \hline 6 & 45 \\ \hline 17 & 127.5 \\ \hline 40 & \\ \hline \end{tabular}

Find the solutions of the system of linear inequalities $8x + 5y > 40$ and $-6x + 2y \geq -18$ .

Solve for the variable $v$ in the equation $1.4 = -6v + 20.6$ .

Solve the equation $24+0.44x=19+1.69x$ and select the correct answer from the options provided.

Translate Chau's height decreased by 16 is 60 into an equation using variable $c$ to represent Chau's height.

Simplify expressions like $a^3$ , $6yx$ , $4x^2$ , $15x^2y$ , and $-4y^2z^2$ .

Determine the tire lifespan warranty that will replace no more than $10\%$ of tires, given a normal distribution with $\mu=47,700$ miles and $\sigma=2,000$ miles.

Identify whether $7-8(x+3)$ is an expression or an equation.

Expand $(6-x)^{2}$ using special product of binomials and choose correct answer: (A) $36+12x-x^{2}$ (B) $36-12x+x^{2}$ (C) $6-36x-x^{2}$ (D) $6-12x+x^{2}$

Reduce the ratio $0.13: 0.052$ to its smallest terms.

Find the value of $x$ that satisfies the equation $\frac{2 x}{x-2}-1=\frac{4}{x-2}$ .

Calculate the daily energy consumption of a light bulb that uses $7650$ watt-hours in $4$ days and $6$ hours.

Find the distance between the point $(-2,7)$ and the line $6x + 4y + 1 = 0$ .

Find the value of $y=a b^{x}$ given $a=1600, b=.25, x=12$ , rounded to 7 decimal places.

Find all complex solutions to the cubic equation $f(x) = x^3 - 8x^2 + 21x - 20$ .

Solve the equation $-4 x = 16 x^{2}$ for $x$ .

Evaluate $y=x^5$ when $x=4$ . Round the result to five decimal places.

Find the value of $a^{2} + 3b/c - 2d$ when $a=3, b=8, c=2$ , and $d=5$ .

Determine the nature of the roots based on the discriminant value of $64$ .

Which transformation turns a figure around a point? $\{1\text{. reflection}, 2\text{. translation}, 3\text{. rotation}, 4\text{. none of the above}\}$

Find the value of $(-870 \div 5) \cdot(-6)$ .

Multiplicar y simplificar: $(z-10)(z+10)$

Evaluate $\frac{\sqrt{x-3}}{9}$ when $x=12$ . Options: A) $\frac{1}{3}$ B) 1 C) 3 D) 81.

Find the equation of the line passing through the point $(4,5)$ and parallel to the $x$ -axis.

Solve for the value of $v$ that satisfies the equation $5.2-(2 \div v)=5.1$ .

Resolver para $g$ donde $9g=W$ .

Write a quadratic function $h$ with zeros at -4 and -5.

Prove that the function $f(x)=x^{7}+8 x-2$ has at most one real root using Rolle's Theorem. Show it has exactly one using the Intermediate Value Theorem.

A plane flies 2316 mi with the wind and 2004 mi against the wind. Find the wind speed $\square \mathrm{mph}$ given the plane's cruising speed is $540 \mathrm{mph}$ .

Classic Movie DVDs are on sale from June 19-25. 60 titles available. 2 for $\$ 15.00$ , 3 for $\$ 20.00$ , or 5 for $\$ 30.00$ with coupon. After June 25, $\$ 8.50$ each. Cost of 5 DVDs on June 26 is $\$ 32.50$ .

Solve the equation $\frac{8}{x}+\frac{7}{6 x}=\frac{-5}{6}$ for $x$ .

Find a vector $\vec{b}$ with opposite direction of $\vec{a}$ and $|\vec{b}|=3$ , where $\vec{a}$ is a nonzero vector.

Solve for $x$ in the equation $\frac{x+3}{4}=\frac{5}{2}$ . Simplify the solution.

Find the exact value of $\cot \frac{-11 \pi}{6}$ .

Find the integer closest to $x$ such that $2^{x} = 100$ .

Find complex solutions of $9 x^3 - 17 x^2 + 43 x + 5 = 0$ using possible rational roots: $\pm 1, \pm 1/3, \pm 1/9, \pm 5, \pm 5/3, \pm 5/9$ .

Solve the absolute value equation: $|2x+1| = 9$

Solve for $x$ in the equation $\frac{3}{8} x=48$ . Simplify the solution.

Solve the equation $10-c=-3$ and express the solution as an integer or simplified fraction.

Solve the linear equation $12p - 0.7 = 5p + 3.2$ for the variable $p$ .

Find the average velocity of an object moving along a vertical line with position $L(t)=-3t^2+t+8$ (m) at time $t$ (s) for the given intervals: [3s, 9s], [2s, 7s], [5s, 8s].