Natural Numbers

Problem 201

Find the value of $x$ such that the sum of the arithmetic sequence $3n+5$ from $n=3$ to $n=x$ equals 711.

See Solution

Problem 202

Solve for $y$ where $\frac{y}{6}=\frac{4}{8}$ . Simplify the solution $y$ .

See Solution

Problem 203

Determine if $x+8>8$ has $0$ as a solution.

See Solution

Problem 204

Find the values of $x$ and $y$ that satisfy the linear equation $x + 2 = 3y$ .

See Solution

Problem 205

Solve for the amount of money left after buying 4 tires that each cost $\$ 41$ plus $\$ 2.25$ tax and weigh 25 pounds, given you have $\$ 269$ to spend. The piece of given information that is not necessary is the weight of the tires.

See Solution

Problem 206

Find the value of $x$ in the equation $5(2x + 8) = 4(3x + 2)$ .

See Solution

Problem 207

Find the value of $x$ that satisfies the equation $8(2.5 x+3.2)=3+(-x+1.6)$ . If $g(x)=f(x)+k$ , what are the possible values of $k$ ?

See Solution

Problem 208

Solve the equation $-2v-18=0$ and express the solution as an integer, simplified fraction, or decimal to 2 decimal places.

See Solution

Problem 209

Solve for $L$ in $P=2L+2W$ . Describe error in classmate's solution that equates $P-W=L$ .

See Solution

Problem 210

Find the actual length (in km) of a road that measures $12 \mathrm{~cm}$ on a map with a scale of $1 \mathrm{~cm} = 6 \mathrm{~km}$ .

See Solution

Problem 211

Multiply the given equation by the LCD to eliminate denominators. The resulting equation is $(x+2)(x-3) = (x-2)(x-3)$

See Solution

Problem 212

Chinedu solves 2 math problems per minute. Find the explicit formula for the sequence $f(n)$ representing the number of problems left to solve at the start of the $n^{\text{th}}$ minute.
$f(n) = 30 - 2n$

See Solution

Problem 213

An arrow is shot upward at 80 ft/s from a 25 ft platform. The path is $h=-16t^{2}+80t+25$ , where $h$ is height and $t$ is time. Find the maximum height.

See Solution

Problem 214

Simplify the expression $3 x^{3} y^{2} \times 5 x^{4} y^{3}$ .

See Solution

Problem 215

Find the value of $x$ using cross-multiplication: $\frac{64}{15} = \frac{40}{x}$ .

See Solution

Problem 216

Solve the equation $-4x-20=0$ and express the answer as an integer, simplified fraction, or decimal rounded to two decimal places.

See Solution

Problem 217

Find the values of $A$ and $B$ that make the piecewise function $f(x)$ differentiable at $x=0$ , where $f(x) = x^2 + 1$ for $x \geq 0$ , and $f(x) = A \sin x + B \cos x$ for $x < 0$ .

See Solution

Problem 218

Match each expression with its quotient: $(x^2 - 3x - 18) / (x + 3)$ , $(x^3 - x^2 - 5x - 3) / (x^2 + 2x + 1)$ , $x - 6$ , $(x^3 - 4x^2 + 4x - 3) / (x - 3)$ , $x^2 - x + 1$ , $x - 3$ .

See Solution

Problem 219

Solve for $x$ in the equation $(a^{2x})^{x-8} = a^{-4} \cdot a^{22}$ .

See Solution

Problem 220

Find the roots of the quadratic function $y=4x^2+2x-30$ by factoring the equation $0=4x^2+2x-30$ .

See Solution

Problem 221

Solve for the value of $x$ in the equation $x-10=12$ .

See Solution

Problem 222

Solve the differential equation $3 y y' = 5 x$ .

See Solution

Problem 223

Determine if the piecewise function $y = \begin{cases} x^2 & x < 2 \\ 4 & x \geq 2 \end{cases}$ is continuous or discontinuous.

See Solution

Problem 224

Evaluate $2|-x|$ when $x=10$ . Options: $210$ , $-20$ , $-210$ , $20$ .

See Solution

Problem 225

Solve the linear equation $-12=117x-45$ for the value of $x$ .

See Solution

Problem 226

Solve the quadratic equation $-4x^2 - 4x + 8 = 0$ to find the value of $x$ .

See Solution

Problem 227

Is $4x - 9 = 2x - 3$ true when $x = 3$ ? Yes or No

See Solution

Problem 228

Find the range of values for $x$ that satisfy the inequality $-21 < 8x + 3$ . Choose the correct response.

See Solution

Problem 229

Find the value of $c$ in the proportion $\frac{65}{75} = \frac{39}{c}$ .

See Solution

Problem 230

Evaluate the integral $\int \frac{9}{8+9 x} d x$ for $x \neq -\frac{8}{9}$ . Type the exact answer.

See Solution

Problem 231

Solve $5-\frac{8}{3}=\frac{y}{3}$ ; multiply both sides by $3$ to get $15-8=y$ .

See Solution

Problem 232

Solve the quadratic equation $x^{2} - x = 1$ for real values of $x$ .

See Solution

Problem 233

To find the value that completes the square on $x^{2} - \frac{2}{7} x$ , add $\left(\frac{2}{7}\right)^{2} = \frac{4}{49}$ .

See Solution

Problem 234

Determine if $f(x) = 5 \tan x$ is even, odd, or neither. Verify algebraically.

See Solution

Problem 235

Find the positive values of $x$ that satisfy the equation $2xy + 4 = 34$ , where $y = 3$ .

See Solution

Problem 236

Solve for $x$ in the equation $64+31=54x+48-68x$ . Express the answer as an integer, simplified fraction, or decimal rounded to two places.

See Solution

Problem 237

Simplify the expression $\frac{\sec x-\csc x}{\sec x+\csc x}$ and show it is equal to $\frac{\tan x-1}{\tan x+1}$ .

See Solution

Problem 238

Find the roots of the polynomial equation $9x^3 + 13x^2 = 8x + 15$ by factoring or using other methods.

See Solution

Problem 239

Determine if $\frac{-1}{3} < \frac{4}{3}$ is true or false. If false, rewrite as true statement.

See Solution

Problem 240

Simplify the given complex number expression and express the result in the form $a + bi$ .
$(5 + 2i)^2 + (2 - i)^2$

See Solution

Problem 241

Solve $\frac{x}{4}-\frac{3}{4}=16$ . Which property was used to add $\frac{3}{4}$ to both sides?

See Solution

Problem 242

Solve the equation $9 = 9x - 3x + 21$ and express the solution as an integer, simplified fraction, or decimal rounded to two decimal places.

See Solution

Problem 243

Find the ones digit of the number $1,427$ .

See Solution

Problem 244

Solve and check each linear equation: $7x-5=72$ , $6x-3=63$ , $11x-(6x-5)=40$ , $5x-(2x-10)=35$ , $2x-7=6+x$ , $3x+5=2x+13$ , $7x+4=x+16$ , $13x+14=12x-5$ .

See Solution

Problem 245

Solve the equation $-11=2n-5n+16$ and express the answer as an integer, simplified fraction, or decimal rounded to two decimal places.

See Solution

Problem 246

7a) Find $v$ when $u=4$ and $t=3$ for $v=u+10t$ . 7b) Solve for $u$ in $v=u+10t$ . 12) Solve for $m$ in $s=\frac{hm}{4}$ .

See Solution

Problem 247

Find the height and width of a 10-gallon aquarium that is 2 inches taller than it is wide, with a length of 23 inches and a volume of 1840 cubic inches.
Height: $\square \square$ inches Width: $\square \square$ inches

See Solution

Problem 248

If a quadratic equation has a negative discriminant, it has $\textbf{two complex solutions}$ .

See Solution

Problem 249

Solve for the value of $y$ such that $6 \geq 18 - 2y$ .

See Solution

Problem 250

Find the correct equation to verify the solution $205-110=95$ .

See Solution

Problem 251

Solve for $r$ where $-1 r-5 < -4$ .

See Solution

Problem 252

Solve for $8x+7$ given $4x+9=10$ . Options: (A) 2, (B) 9, (C) 15, (D) 20, (E) 27.

See Solution

Problem 253

Find the sum of weights: $7.50 g + 5.26 g + 8.6 g + \underline{10 g}$ .

See Solution

Problem 254

Find the value of the expression $5x + 5x$ .

See Solution

Problem 255

Solve the rational equation $\frac{x-2}{2x} + 1 = \frac{x+1}{x}$ . Find the value(s) of $x$ that make the denominator(s) zero, which are the $\varnothing$ restrictions on the variable.

See Solution

Problem 256

Find the sum of the numbers $42, 75, 189, 301$ , and $728$ .

See Solution

Problem 257

Find the exact value of $\sec(14\pi)$ without using a calculator. Select the correct choice: A. $\sec(14\pi)=\square$ (Type an exact answer, using radicals as needed. Rationalize the denominator) or B. The answer is undefined.

See Solution

Problem 258

Find the amount of type A coffee used in a 158-pound coffee blend that costs $815.60 total, given type A costs$ 5.80/lb and type B costs $4.60/lb.

See Solution

Problem 259

Find the annual return percentage for a stock purchased at $70 per share, sold after 4 years for$ 8200, with 100 shares.

See Solution

Problem 260

Determine the inflection points and extrema of the function $f(x) = \frac{1}{8} x^{3} + \frac{3}{4} x^{2}$ . Sketch the graph.

See Solution

Problem 261

Find the change in the number of commercial radio stations playing a particular genre of music from 2005 to 2015. The absolute change is $\left| 744 - 398 \right| = 346$ . The relative change is $\left( \frac{398 - 744}{744} \right) \times 100 = -46.5\%$ .

See Solution

Problem 262

Find the expressions for $(r \cdot s)(x)$ and $(r+s)(x)$ , then evaluate $(r-s)(3)$ .

See Solution

Problem 263

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

See Solution

Problem 264

Solve the linear equation $2x - 9y = -38$ and find the value of $y$ when $x = -10$ .

See Solution

Problem 265

Find rational roots of $f(x) = 2x^3 - 4x^2 - 8x + 16$ . Determine $y$ -intercept and sketch graph crossing all intercepts.

See Solution

Problem 266

The university's physical plant receives daily requests to replace fluorescent lightbulbs. The distribution of requests follows a normal distribution with $\mu=59$ and $\sigma=10$ . Using the Empirical Rule, find the percentage of requests between 39 and 59.
ans = 68.27%

See Solution

Problem 267

Luke swam $3 \times 45 = 135$ meters in 45 seconds. The point on the line is (45, $135$ ).

See Solution

Problem 268

Solve the linear equation $-8y - 6 = -2y$ and simplify the solution.

See Solution

Problem 269

Find the value of $p$ using the equation $6\left(\frac{d}{3}-5\right)=34$ . Determine the final operation needed if you apply the Distributive Property first.

See Solution

Problem 270

Solve for $x$ in the equation $4-5x = -5x+4$ , if possible. Check the solution.

See Solution

Problem 271

Solve the linear equation $-x + 7y = 8$ and find the value of $y$ when $x = 6$ .

See Solution

Problem 272

Circle the picture representing each equation, then solve: $\frac{1}{2} \times \frac{3}{6}$ , $\frac{1}{2} \times \frac{1}{3}$ , $\frac{2}{5} \times \frac{3}{4}$ . Use grid to model and solve: $\frac{5}{6} \times \frac{5}{6}$ , $\frac{3}{7} \times \frac{2}{4}$ .

See Solution

Problem 273

Find the value of $4 \times 3^3$ by expressing it as a single term with a coefficient and power.

See Solution

Problem 274

Solve for the side length of an equilateral triangle fence with a perimeter of $183 \mathrm{cm}$ after increasing each side by $7 \mathrm{cm}$ .
a) $s + 7 + s + 7 + s + 7 = 183$ b) Determine the length of each side of the old fence.

See Solution

Problem 275

Solve the linear equation $2.1(16y - 10.3) = 18.42y - 36.81$ to find the value of $y$ .

See Solution

Problem 276

Find the width of a storage container with length 14.7 cm and width $3.5 \times$ length.

See Solution

Problem 277

Arrange the numbers from left to right on a number line: $-2.76, -2.57, -2.5, -1.85, -1.58, 2.5, 2.85$ .

See Solution

Problem 278

Find the solution to the inequality $\log_{10}x > \log_{10}(x-1)$ .

See Solution

Problem 279

Solve the absolute value equation $|x-4|=4$ for the value(s) of $x$ .

See Solution

Problem 280

Find the inverse of $\left[\begin{array}{rr}4 & -3 \\ -8 & 7\end{array}\right]$ , then use it to solve two linear systems.

See Solution

Problem 281

Find the value of $y$ given the equation $y=4-(-2^{2})$ .

See Solution

Problem 282

Solve the equation $129=15x+9$ . (1 point)

See Solution

Problem 283

Find the unit tangent vector and length of the curve $\mathbf{r}(t) = 6t^3\mathbf{i} + 2t^3\mathbf{j} - 3t^3\mathbf{k}$ for $1 \leq t \leq 2$ . The unit tangent vector is $(\frac{6}{7})\mathbf{i} + (\frac{2}{7})\mathbf{j} + (-\frac{3}{7})\mathbf{k}$ , and the length is $9\sqrt{7}$ units.

See Solution

Problem 284

Find the value of $a$ that satisfies the equation $-(a-3)+2a=-12$ .

See Solution

Problem 285

Find the angle, in degrees, whose secant is -5.48. Round the result to the nearest hundredth.

See Solution

Problem 286

Find the missing binomial term to complete the factorization: $2s^{4} - 2s = 2s(s^{2} + s + 1)$ .

See Solution

Problem 287

Find the derivative of $\left(\frac{e^{2-x}}{x+2}\right)$ .

See Solution

Problem 288

Find the values of $a$ and $b$ in the function $P(t) = a b^t$ that models the number of bacteria in a lab experiment, given the function $P(t) = 47(1.112)^{5t}$ . Round the final values of $a$ and $b$ to 4 decimal places.

See Solution

Problem 289

Find the time to fill a vat with two pipes, one filling in 3 hours, the other emptying in 8 hours, when both are left open.

See Solution

Problem 290

A transformer has $6$ primary and $5$ secondary turns. The primary voltage is $10$ volts. What type of transformer is this?

See Solution

Problem 291

Solve for x in the linear equation $6x + 5 = 47$ .

See Solution

Problem 292

Find the x-intercepts of the function $y=-2(x-1)(x+5)$ .

See Solution

Problem 293

Find the rectangular field dimensions that maximize the enclosed area given 800 feet of fencing to create 3 identical smaller plots. Express answers as reduced fractions.

See Solution

Problem 294

Simplify $\sqrt{36 x^{18}}$ when $x>0$ .

See Solution

Problem 295

Find the value of $-34+2(x-7)$ when $x=-1$ .

See Solution

Problem 296

Simplify the expression $\frac{5 x}{x+3} \div \frac{x^{2}-8 x+15}{x^{2}-9}$ .

See Solution

Problem 297

Solve for the number of large boxes shipped given the equation $3a + 4b = 25$ and that the customer had 3 small boxes shipped.

See Solution

Problem 298

Find the missing variable $v$ given $r=16 \mathrm{m}, \omega=\frac{3 \pi}{4}$ rad/s using $v=r\omega$ .

See Solution

Problem 299

Find $z$ when $x=10$ and $y=3$ , given that $z$ varies directly as $x$ and inversely as $y^2$ , and $z=60$ when $x=8$ and $y=8$ . Round answer to two decimal places.

See Solution

Problem 300

Find the product $\$(f \cdot g)(x)\$$ if $\$f(x)=11 x+2\$$ and $\$g(x)=5 x\$$ .

See Solution

1 2 3 4 5 6 ...28

Natural Numbers

Problem 201

Find the value of xxx such that the sum of the arithmetic sequence 3n+53n+53n+5 from n=3n=3n=3 to n=xn=xn=x equals 711.

Problem 202

Solve for yyy where y6=48\frac{y}{6}=\frac{4}{8}6y​=84​. Simplify the solution yyy.

Problem 203

Determine if x+8>8x+8>8x+8>8 has 000 as a solution.

Problem 204

Find the values of xxx and yyy that satisfy the linear equation x+2=3yx + 2 = 3yx+2=3y.

Problem 205

Solve for the amount of money left after buying 4 tires that each cost $41\$ 41$41 plus $2.25\$ 2.25$2.25 tax and weigh 25 pounds, given you have $269\$ 269$269 to spend. The piece of given information that is not necessary is the weight of the tires.

Problem 206

Find the value of xxx in the equation 5(2x+8)=4(3x+2)5(2x + 8) = 4(3x + 2)5(2x+8)=4(3x+2).

Problem 207

Find the value of xxx that satisfies the equation 8(2.5x+3.2)=3+(−x+1.6)8(2.5 x+3.2)=3+(-x+1.6)8(2.5x+3.2)=3+(−x+1.6). If g(x)=f(x)+kg(x)=f(x)+kg(x)=f(x)+k, what are the possible values of kkk?

Problem 208

Solve the equation −2v−18=0-2v-18=0−2v−18=0 and express the solution as an integer, simplified fraction, or decimal to 2 decimal places.

Problem 209

Solve for LLL in P=2L+2WP=2L+2WP=2L+2W. Describe error in classmate's solution that equates P−W=LP-W=LP−W=L.

Problem 210

Find the actual length (in km) of a road that measures 12 cm12 \mathrm{~cm}12 cm on a map with a scale of 1 cm=6 km1 \mathrm{~cm} = 6 \mathrm{~km}1 cm=6 km.

Problem 211

Multiply the given equation by the LCD to eliminate denominators. The resulting equation is (x+2)(x−3)=(x−2)(x−3)(x+2)(x-3) = (x-2)(x-3)(x+2)(x−3)=(x−2)(x−3)

Problem 212

Chinedu solves 2 math problems per minute. Find the explicit formula for the sequence f(n)f(n)f(n) representing the number of problems left to solve at the start of the nthn^{\text{th}}nth minute.f(n)=30−2nf(n) = 30 - 2nf(n)=30−2n

Problem 213

An arrow is shot upward at 80 ft/s from a 25 ft platform. The path is h=−16t2+80t+25h=-16t^{2}+80t+25h=−16t2+80t+25, where hhh is height and ttt is time. Find the maximum height.

Problem 214

Simplify the expression 3x3y2×5x4y33 x^{3} y^{2} \times 5 x^{4} y^{3}3x3y2×5x4y3.

Problem 215

Find the value of xxx using cross-multiplication: 6415=40x\frac{64}{15} = \frac{40}{x}1564​=x40​.

Problem 216

Solve the equation −4x−20=0-4x-20=0−4x−20=0 and express the answer as an integer, simplified fraction, or decimal rounded to two decimal places.

Problem 217

Find the values of AAA and BBB that make the piecewise function f(x)f(x)f(x) differentiable at x=0x=0x=0, where f(x)=x2+1f(x) = x^2 + 1f(x)=x2+1 for x≥0x \geq 0x≥0, and f(x)=Asin⁡x+Bcos⁡xf(x) = A \sin x + B \cos xf(x)=Asinx+Bcosx for x<0x < 0x<0.

Problem 218

Problem 219

Solve for xxx in the equation (a2x)x−8=a−4⋅a22(a^{2x})^{x-8} = a^{-4} \cdot a^{22}(a2x)x−8=a−4⋅a22.

Problem 220

Find the roots of the quadratic function y=4x2+2x−30y=4x^2+2x-30y=4x2+2x−30 by factoring the equation 0=4x2+2x−300=4x^2+2x-300=4x2+2x−30.

Problem 221

Solve for the value of xxx in the equation x−10=12x-10=12x−10=12.

Problem 222

Solve the differential equation 3yy′=5x3 y y' = 5 x3yy′=5x.

Problem 223

Determine if the piecewise function y={x2x<24x≥2y = \begin{cases} x^2 & x < 2 \\ 4 & x \geq 2 \end{cases}y={x24​x<2x≥2​ is continuous or discontinuous.

Problem 224

Evaluate 2∣−x∣2|-x|2∣−x∣ when x=10x=10x=10. Options: 210210210, −20-20−20, −210-210−210, 202020.

Problem 225

Solve the linear equation −12=117x−45-12=117x-45−12=117x−45 for the value of xxx.

Problem 226

Solve the quadratic equation −4x2−4x+8=0-4x^2 - 4x + 8 = 0−4x2−4x+8=0 to find the value of xxx.

Problem 227

Is 4x−9=2x−34x - 9 = 2x - 34x−9=2x−3 true when x=3x = 3x=3? Yes or No

Problem 228

Find the range of values for xxx that satisfy the inequality −21<8x+3-21 < 8x + 3−21<8x+3. Choose the correct response.

Problem 229

Find the value of ccc in the proportion 6575=39c\frac{65}{75} = \frac{39}{c}7565​=c39​.

Problem 230

Evaluate the integral ∫98+9xdx\int \frac{9}{8+9 x} d x∫8+9x9​dx for x≠−89x \neq -\frac{8}{9}x=−98​. Type the exact answer.

Problem 231

Solve 5−83=y35-\frac{8}{3}=\frac{y}{3}5−38​=3y​; multiply both sides by 333 to get 15−8=y15-8=y15−8=y.

Problem 232

Solve the quadratic equation x2−x=1x^{2} - x = 1x2−x=1 for real values of xxx.

Problem 233

To find the value that completes the square on x2−27xx^{2} - \frac{2}{7} xx2−72​x, add (27)2=449\left(\frac{2}{7}\right)^{2} = \frac{4}{49}(72​)2=494​.

Problem 234

Determine if f(x)=5tan⁡xf(x) = 5 \tan xf(x)=5tanx is even, odd, or neither. Verify algebraically.

Problem 235

Find the positive values of xxx that satisfy the equation 2xy+4=342xy + 4 = 342xy+4=34, where y=3y = 3y=3.

Problem 236

Solve for xxx in the equation 64+31=54x+48−68x64+31=54x+48-68x64+31=54x+48−68x. Express the answer as an integer, simplified fraction, or decimal rounded to two places.

Problem 237

Simplify the expression sec⁡x−csc⁡xsec⁡x+csc⁡x\frac{\sec x-\csc x}{\sec x+\csc x}secx+cscxsecx−cscx​ and show it is equal to tan⁡x−1tan⁡x+1\frac{\tan x-1}{\tan x+1}tanx+1tanx−1​.

Problem 238

Find the roots of the polynomial equation 9x3+13x2=8x+159x^3 + 13x^2 = 8x + 159x3+13x2=8x+15 by factoring or using other methods.

Problem 239

Determine if −13<43\frac{-1}{3} < \frac{4}{3}3−1​<34​ is true or false. If false, rewrite as true statement.

Problem 240

Simplify the given complex number expression and express the result in the form a+bia + bia+bi.(5+2i)2+(2−i)2(5 + 2i)^2 + (2 - i)^2(5+2i)2+(2−i)2

Find the value of $x$ such that the sum of the arithmetic sequence $3n+5$ from $n=3$ to $n=x$ equals 711.

Solve for $y$ where $\frac{y}{6}=\frac{4}{8}$ . Simplify the solution $y$ .

Determine if $x+8>8$ has $0$ as a solution.

Find the values of $x$ and $y$ that satisfy the linear equation $x + 2 = 3y$ .

Solve for the amount of money left after buying 4 tires that each cost $\$ 41$ plus $\$ 2.25$ tax and weigh 25 pounds, given you have $\$ 269$ to spend. The piece of given information that is not necessary is the weight of the tires.

Find the value of $x$ in the equation $5(2x + 8) = 4(3x + 2)$ .

Find the value of $x$ that satisfies the equation $8(2.5 x+3.2)=3+(-x+1.6)$ . If $g(x)=f(x)+k$ , what are the possible values of $k$ ?

Solve the equation $-2v-18=0$ and express the solution as an integer, simplified fraction, or decimal to 2 decimal places.

Solve for $L$ in $P=2L+2W$ . Describe error in classmate's solution that equates $P-W=L$ .

Find the actual length (in km) of a road that measures $12 \mathrm{~cm}$ on a map with a scale of $1 \mathrm{~cm} = 6 \mathrm{~km}$ .

Multiply the given equation by the LCD to eliminate denominators. The resulting equation is $(x+2)(x-3) = (x-2)(x-3)$

Chinedu solves 2 math problems per minute. Find the explicit formula for the sequence $f(n)$ representing the number of problems left to solve at the start of the $n^{\text{th}}$ minute.
$f(n) = 30 - 2n$

An arrow is shot upward at 80 ft/s from a 25 ft platform. The path is $h=-16t^{2}+80t+25$ , where $h$ is height and $t$ is time. Find the maximum height.

Simplify the expression $3 x^{3} y^{2} \times 5 x^{4} y^{3}$ .

Find the value of $x$ using cross-multiplication: $\frac{64}{15} = \frac{40}{x}$ .

Solve the equation $-4x-20=0$ and express the answer as an integer, simplified fraction, or decimal rounded to two decimal places.

Find the values of $A$ and $B$ that make the piecewise function $f(x)$ differentiable at $x=0$ , where $f(x) = x^2 + 1$ for $x \geq 0$ , and $f(x) = A \sin x + B \cos x$ for $x < 0$ .

Solve for $x$ in the equation $(a^{2x})^{x-8} = a^{-4} \cdot a^{22}$ .

Find the roots of the quadratic function $y=4x^2+2x-30$ by factoring the equation $0=4x^2+2x-30$ .

Solve for the value of $x$ in the equation $x-10=12$ .

Solve the differential equation $3 y y' = 5 x$ .

Determine if the piecewise function $y = \begin{cases} x^2 & x < 2 \\ 4 & x \geq 2 \end{cases}$ is continuous or discontinuous.

Evaluate $2|-x|$ when $x=10$ . Options: $210$ , $-20$ , $-210$ , $20$ .

Solve the linear equation $-12=117x-45$ for the value of $x$ .

Solve the quadratic equation $-4x^2 - 4x + 8 = 0$ to find the value of $x$ .

Is $4x - 9 = 2x - 3$ true when $x = 3$ ? Yes or No

Find the range of values for $x$ that satisfy the inequality $-21 < 8x + 3$ . Choose the correct response.

Find the value of $c$ in the proportion $\frac{65}{75} = \frac{39}{c}$ .

Evaluate the integral $\int \frac{9}{8+9 x} d x$ for $x \neq -\frac{8}{9}$ . Type the exact answer.

Solve $5-\frac{8}{3}=\frac{y}{3}$ ; multiply both sides by $3$ to get $15-8=y$ .

Solve the quadratic equation $x^{2} - x = 1$ for real values of $x$ .

To find the value that completes the square on $x^{2} - \frac{2}{7} x$ , add $\left(\frac{2}{7}\right)^{2} = \frac{4}{49}$ .

Determine if $f(x) = 5 \tan x$ is even, odd, or neither. Verify algebraically.

Find the positive values of $x$ that satisfy the equation $2xy + 4 = 34$ , where $y = 3$ .

Solve for $x$ in the equation $64+31=54x+48-68x$ . Express the answer as an integer, simplified fraction, or decimal rounded to two places.

Simplify the expression $\frac{\sec x-\csc x}{\sec x+\csc x}$ and show it is equal to $\frac{\tan x-1}{\tan x+1}$ .

Find the roots of the polynomial equation $9x^3 + 13x^2 = 8x + 15$ by factoring or using other methods.

Determine if $\frac{-1}{3} < \frac{4}{3}$ is true or false. If false, rewrite as true statement.

Simplify the given complex number expression and express the result in the form $a + bi$ .
$(5 + 2i)^2 + (2 - i)^2$

Solve $\frac{x}{4}-\frac{3}{4}=16$ . Which property was used to add $\frac{3}{4}$ to both sides?

Solve the equation $9 = 9x - 3x + 21$ and express the solution as an integer, simplified fraction, or decimal rounded to two decimal places.

Find the ones digit of the number $1,427$ .

Solve the equation $-11=2n-5n+16$ and express the answer as an integer, simplified fraction, or decimal rounded to two decimal places.

7a) Find $v$ when $u=4$ and $t=3$ for $v=u+10t$ . 7b) Solve for $u$ in $v=u+10t$ . 12) Solve for $m$ in $s=\frac{hm}{4}$ .

Find the height and width of a 10-gallon aquarium that is 2 inches taller than it is wide, with a length of 23 inches and a volume of 1840 cubic inches.
Height: $\square \square$ inches Width: $\square \square$ inches

If a quadratic equation has a negative discriminant, it has $\textbf{two complex solutions}$ .

Solve for the value of $y$ such that $6 \geq 18 - 2y$ .

Find the correct equation to verify the solution $205-110=95$ .

Solve for $r$ where $-1 r-5 < -4$ .

Solve for $8x+7$ given $4x+9=10$ . Options: (A) 2, (B) 9, (C) 15, (D) 20, (E) 27.

Find the sum of weights: $7.50 g + 5.26 g + 8.6 g + \underline{10 g}$ .

Find the value of the expression $5x + 5x$ .

Solve the rational equation $\frac{x-2}{2x} + 1 = \frac{x+1}{x}$ . Find the value(s) of $x$ that make the denominator(s) zero, which are the $\varnothing$ restrictions on the variable.

Find the sum of the numbers $42, 75, 189, 301$ , and $728$ .

Find the exact value of $\sec(14\pi)$ without using a calculator. Select the correct choice: A. $\sec(14\pi)=\square$ (Type an exact answer, using radicals as needed. Rationalize the denominator) or B. The answer is undefined.

Find the amount of type A coffee used in a 158-pound coffee blend that costs $815.60 total, given type A costs$ 5.80/lb and type B costs $4.60/lb.

Find the annual return percentage for a stock purchased at $70 per share, sold after 4 years for$ 8200, with 100 shares.

Determine the inflection points and extrema of the function $f(x) = \frac{1}{8} x^{3} + \frac{3}{4} x^{2}$ . Sketch the graph.

Find the expressions for $(r \cdot s)(x)$ and $(r+s)(x)$ , then evaluate $(r-s)(3)$ .

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

Solve the linear equation $2x - 9y = -38$ and find the value of $y$ when $x = -10$ .

Find rational roots of $f(x) = 2x^3 - 4x^2 - 8x + 16$ . Determine $y$ -intercept and sketch graph crossing all intercepts.

The university's physical plant receives daily requests to replace fluorescent lightbulbs. The distribution of requests follows a normal distribution with $\mu=59$ and $\sigma=10$ . Using the Empirical Rule, find the percentage of requests between 39 and 59.
ans = 68.27%

Luke swam $3 \times 45 = 135$ meters in 45 seconds. The point on the line is (45, $135$ ).

Solve the linear equation $-8y - 6 = -2y$ and simplify the solution.

Find the value of $p$ using the equation $6\left(\frac{d}{3}-5\right)=34$ . Determine the final operation needed if you apply the Distributive Property first.

Solve for $x$ in the equation $4-5x = -5x+4$ , if possible. Check the solution.

Solve the linear equation $-x + 7y = 8$ and find the value of $y$ when $x = 6$ .

Find the value of $4 \times 3^3$ by expressing it as a single term with a coefficient and power.

Solve for the side length of an equilateral triangle fence with a perimeter of $183 \mathrm{cm}$ after increasing each side by $7 \mathrm{cm}$ .
a) $s + 7 + s + 7 + s + 7 = 183$ b) Determine the length of each side of the old fence.