Browse Math problems in the Studdy Learning Bank!

Problem 9201

Solve the quadratic equation $x^{2} + \frac{1}{2}x + \frac{1}{16} = \frac{4}{9}$ , then factor the left side to find the solution.

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Problem 9202

Graph the quadratic equation $y = 8 - x^2$ and find 7 integer solutions in the range $-3 \leq x \leq 3$ .

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Problem 9203

Simplify the expression $\sqrt[4]{\frac{x^{3}}{256}}$ using the quotient rule, assuming all variables are positive real numbers.

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Problem 9204

Find the mean, median, and mode of the test scores: $84, 79, 77, 73, 79, 65, 75$ .

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Problem 9205

Solve for $x$ in the equation $10=1.35 \sqrt{x}$ .

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Problem 9206

Find the equation of the line passing through the points $(-7,0)$ and $(13,0)$ .

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Problem 9207

Find the integral that represents the length of the curve $f(x) = \cos x, 0 \leq x \leq \pi$ .

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Problem 9208

Perform basic arithmetic operations: (a) $-355-(-139)$ , (b) $\frac{-24+42}{-6}$ , (c) $13-(-5)$ , (d) $-216+138$ , (e) $-125-(-341)$ .

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Problem 9209

Find the average of the numbers $16, 8, 21, 16$ . Round to one decimal place if necessary.

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Problem 9210

Find the values of $m$ for which the integral $\int_{0}^{8} x^{m} d x$ converges.

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Problem 9211

Solve the quadratic equation $4x^2 = 7x + 6$ and find the discriminant $b^2 - 4ac$ . (Simplify your answer)

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Problem 9212

Find the value of $a$ that is 0.4% of 40.

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Problem 9213

Find the inverse function $f^{-1}(x)$ of $f(x) = 5^x$ . The inverse is $f^{-1}(x) = \log_5 x$ .

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Problem 9214

Find the missing operator that makes the equation $(6 \times 2) \, ? \, 4 = 8$ true.

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Problem 9215

Find the solutions to the quadratic equation $1=12x^2+11x$ . Round answers to two decimal places and separate with a comma.

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Problem 9216

Plant's height $H$ (cm) after $M$ months: $H = 53 + M$ . Plant's height after 13 months: $53 + 13 = 66$ cm.

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Problem 9217

Solve the rational equation and find the solution set, excluding values that make the equation undefined. $\frac{5}{x}+\frac{4}{5}=\frac{12}{6x}-\frac{17}{5}$

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Problem 9218

Solve the inequality $-\frac{10}{3} \geq 8x$ for the value of $x$ .

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Problem 9219

Ladder on wall: top slips down as base moves away at 5 m/s. Find (29) rate of top when 5 m from ground, and (30) rate of area change when top is 5 m from ground.

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Problem 9220

What is the remainder when $24$ is divided by $5$ ?

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Problem 9221

Find the difference between 4.8 and -8.7.

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Problem 9222

Solve for real number $w$ where $\sqrt{w}=5$ .

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Problem 9223

Solve the absolute value equation $\left|\frac{2 x-3}{5}\right|=11$ .

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Problem 9224

Evaluate the expression $-8+4$ and choose the correct answer from the options given.

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Problem 9225

Multiply the given rational expressions, simplify, and express the result as a rational expression. $\frac{y^2-4}{y^2-2y} \cdot \frac{y}{y^2+10y+16}, y \neq -8, -2, 0, 2$

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Problem 9226

Solve for $j$ in the proportion $\frac{20}{j}=\frac{32}{48}$ .

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Problem 9227

Find the value of $x$ in the equation $4(6x-9.5)=46$ . The possible solutions are $x=-1.5$ , $x=0.3$ , $x=1.79$ , and $x=3.5$ .

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Problem 9228

Construct a grouped frequency distribution for the ages of presidents at inauguration, using classes of width 5 starting from 41-45. Provide the frequency value for each class.
$41 - 45: \square$ $46 - 50: \square$ $51 - 55: \square$ $56 - 60: \square$ $61 - 65: \square$ $66 - 70: \square$

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Problem 9229

Simplify the expression $(-7)^{2}$ .

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Problem 9230

Find the value of 3/4 of 12.

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Problem 9231

Solve the linear equation $\frac{x}{-5} - 8.75 = -10$ for $x$ .

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Problem 9232

Divide $152$ by $4$ . Write out the times table of the divisor to assist with the calculation.

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Problem 9233

Use the second derivative test to find local extrema of $f(x) = -\frac{5x^3}{3} + 10x^2 + 25x$ in $(-5,8)$ . The local maxima occur at $x = \frac{10}{5}$ . The local minima occur at $\varnothing$ .

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Problem 9234

Predict the number of squirrels on a nature preserve with 8 coyotes using the linear model $y=-5x+60$ .

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Problem 9235

Find the function $(r-p)(x)$ where $r(x) = -7x$ and $p(x) = x^2 + 3x$ , and write the domain in interval notation.

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Problem 9236

Solve for $x$ in $2x^2 = 50$ . Options: a) $\pm 0.2$ , b) $\pm 7.07$ , c) $\pm 5$ , d) $\pm 12.5$ .

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Problem 9237

Subtract and simplify the expression $\frac{8}{x^{2}-8 x}-\frac{x}{8 x-64}$ .

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Problem 9238

Simplify the product of two polynomials $(7-14p)(7+14p)$ and determine the degree of the result.

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Problem 9239

Calculate $k$ when $j=3$ . $k=4j+2$ . Options: a) 12, b) 9, c) 6, d) 14.

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Problem 9240

(a) Solve $2(x+2)-5=9$ . (b) Write as single fraction $\frac{2x+1}{3}+\frac{3x-2}{6}$ . (c) Rearrange $T=2\pi\sqrt{\frac{L}{8}}$ to find $L$ . (d) (I) Show $f(x)=x^3-13x+12$ can be written as $(x-1)(x^2+x-12)$ . (II) Completely factorise $f(x)$ .

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Problem 9241

Find the meaning of $f(x)$ and $x$ in the equation $f(x)=7x+15$ which tracks Luke's exercise over the summer.

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Problem 9242

Solve the equation $(c+2)^{2}-5=-21$ and select the correct solution.

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Problem 9243

Approximate the sum of the series $\sum_{n=1}^{\infty}(-1)^{n} \frac{2}{3 n^{4}}$ with error < 0.001.

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Problem 9244

Find the point of intersection of the lines $y=2x-4$ and $y=-x+5$ .

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Problem 9245

Find the price of a used book sold at a bookstore, where the owner buys them for $\$ 2.25$ each and resells them for $300\%$ of the purchase price.

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Problem 9246

Find the value of $x$ that makes $\frac{1}{x}+\frac{4}{3x}-\frac{5}{6x}+1=0$ .

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Problem 9247

Determine the number of college students who got news from only social media using a Venn diagram. Given: 94 students surveyed, 32 from news websites, 25 from social media, and 11 from both.
$n($ News websites only $)=21$ $n($ Social media only $)=\boxed{14}$

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Problem 9248

Find the value of $x+\sqrt{x}$ for $x=0, 0.01, 0.36, 0.64, 1, 25, 100, 3600$ .

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Problem 9249

Find the equation representing the discount price for senior citizens given a 12% discount. $discount\ price = (original\ price)(1-0.12)$

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Problem 9250

Find the equation with solutions $x=7+i$ and $x=7-i$ , written in standard form.

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Problem 9251

Find the values of $y$ that make the expression $\frac{4}{15-3y}$ undefined.

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Problem 9252

Find the derivative of $y=2 x^{2}(3-2 x)$ using the product rule.

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Problem 9253

Determine the limit of the sequence $\left\{\left(\frac{n+n^{2}}{2 n^{2}}\right)^{n}\right\}$ .

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Problem 9254

Find the integer between $\frac{11 \pi}{5}$ and $\sqrt{58}$ .

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Problem 9255

Simplify the improper fraction $\frac{16}{2}$ .

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Problem 9256

Solve the linear equation $3x + 4 = 13$ for the value of $x$ .

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Problem 9257

Estimate the total number of plastic widgets sold in the first 6 weeks given the sales function $P(t)=7000 t e^{-0.3 t}$ .

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Problem 9258

Find the width of a rectangle with length 10 cm longer than width, if total perimeter is 220 cm.
$x$ cm width, $x+10$ cm length, total perimeter $2(x+x+10)=220$ . Solve for $x$ .

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Problem 9259

Solve for $u$ where $u(u-6)=0$ . Write the solutions as integers or simplified fractions.

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Problem 9260

Multiply the given rational expressions and simplify the result, excluding the values $p = -2, 3, 6$ .

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Problem 9261

Find the possible number of real roots for a linear polynomial with real coefficients. Options: 0, 1, 2.

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Problem 9262

Solve the system of linear equations $y = -x + 1$ and $x - 2y = 4$ .

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Problem 9263

Determine the type of function represented by the equation $y=x(30-2x)(10-2x)$ .

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Problem 9264

Factor the first numerator, then multiply the resulting fractions.
$\frac{x^{2}+3 x}{3 x-1} \cdot \frac{15 x^{2}-5 x}{17 x^{3}+51 x^{2}}=\frac{(x+3)(x)}{3 x-1} \cdot \frac{5 x(3 x-1)}{17 x^{3}+51 x^{2}}$

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Problem 9265

Solve for y in the quadratic equation $19y^2 + 39y + 2 = 0$ . Write each solution as an integer, proper fraction, or improper fraction, separated by commas.

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Problem 9266

Find the logarithm base 3 of 243.

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Problem 9267

Describe the end behavior of $g(x) = -\frac{1}{x^2}$ . As $x \to \pm\infty$ , $g(x)$ goes to 0 or $\pm\infty$ .

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Problem 9268

Simplify the expression $2y - 5y$ .

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Problem 9269

Solve for $k$ given $8k + 2m = 3m + k$ with solutions $k = 70m, k = 7m, k = \frac{7}{\sqrt{m}}, k = \frac{m}{7}$ .

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Problem 9270

Solve the quadratic equation $35v^2 + 43v = 0$ for $v$ . Express each solution as an integer, proper fraction, or improper fraction, separated by commas.

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Problem 9271

What is the ordered pair that is a reflection over the x-axis of $(7,3)$ ? $(-7,3)$ , $(3,-7)$ , $(-3,-7)$

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Problem 9272

Solve for $x$ in the equation $\frac{2x}{5} = \frac{x^2 - 5x}{5x}$ .

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Problem 9273

Find the difference between $(d-9)$ and $(3d-1)$ .

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Problem 9274

Solve for $e$ where $\frac{e}{5}=x$ and $e=$

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Problem 9275

Write the expression as a function of $x$ : $\cos\left(\frac{\pi}{4}-x\right)$ .

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Problem 9276

Find the complete solution to $Ax=b$ for $A=\begin{bmatrix} 1&2&2&2\\ 2&4&6&8\\ 3&6&8&10 \end{bmatrix}, \mathbf{b}=\begin{bmatrix} 5\\1\\6 \end{bmatrix}$ .

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Problem 9277

Determine the sample size needed to estimate the proportion of a population with a genetic marker, with 99% confidence and 1.5% margin of error, given the expected proportion is 80%.
$n = \frac{z^{2}_{\alpha/2} p^{} (1 - p^{})}{E^{2}}$

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Problem 9278

Find the odd one out in the given sets. Explain your reasoning. Sets: $5,8,2,1,2,6$ , $15,18,12,11,0,16$ , $58,21,26$ , $9,4,1,3,7,5$ .

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Problem 9279

Solve the system of linear inequalities $-3n+1 > 7$ or $n+1 > 5$ to find the possible values of $n$ .

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Problem 9280

Find the value of $81^{3/4}$ .

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Problem 9281

Find the critical t-value for a 90% confidence level with a sample size of 11.

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Problem 9282

Convert 43 pounds to kilograms using the conversion $1$ kg $=2.2$ lbs. (Round to the nearest tenth.)

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Problem 9283

Find an equation to represent the total number of movies $n$ that Aldo will watch in $m$ months, given he plans to watch 3 movies each month.

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Problem 9284

Find the excluded value for the rational function $y=\frac{6 x+1}{9 x-4}$ .

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Problem 9285

Simplify the expression $4 \ln x + 8 \ln y$ .

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Problem 9286

1. Find the equation with solution $k=-3$ . A. $2k-5=-1$ B. $k-3=6$ C. $3k-3=-6$ D. $4k+1=-11$
2. Anthony is 4 years older than his brother Felix. Their ages sum to 42. What equation can be used to find their ages? A. $4f=42$ B. $4f+f=42$ C. $f+f+4=42$ D. $4f+f+4=42$

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Problem 9287

Verify the identity: $\frac{2 \cos 2x}{\sin 2x} = \cot x - \tan x$ .

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Problem 9288

Find the secant line equation $y=mx+b$ passing through points $(-3, f(-3))$ and $(2, f(2))$ where $f(x)=x^{3}-5$ .

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Problem 9289

Find the rank of the $3 \times 4$ matrix $A = \begin{bmatrix} 2 & 0 & -2 & 4 \\ 1 & 1 & 2 & 3 \\ 0 & 1 & 3 & 1 \end{bmatrix}$ .

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Problem 9290

Find the equation for a cubic function with roots at $-8, 3$ , and $\frac{4}{3}$ .

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Problem 9291

Simplify the expression $3-\frac{3}{10 y^{2}}$ and express the answer as a single fraction in simplest form.

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Problem 9292

Express $\ln \sqrt[4]{5}$ as a product.

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Problem 9293

Find the number of positive and negative real zeros of $g(x)=x^{3}+5x^{2}+9x-8$ .

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Problem 9294

Calculate the distance travelled by a $11\,\mathrm{cm}$ pendulum swinging $84^\circ$ , given in $\mathrm{cm}$ to 1 d.p.

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Problem 9295

Find the value of the expression $19(5+12)$ .

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Problem 9296

A woman is watching a rocket 13 miles high, standing 4 miles from the launch pad. Find the angle she is looking up from the horizontal, rounded to 2 decimal places.
$\tan^{-1}\left(\frac{13}{4}\right)$

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Problem 9297

Find the equation(s) of the vertical asymptote(s) of the rational function $g(t) = \frac{t^{2} - 5}{3t^{2} + 4t - 3}$ .

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Problem 9298

Differentiate the function $g(t) = \frac{2 - 5t}{7t + 8}$ to find $g'(t)$ .

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Problem 9299

Find the linear approximation of $y=e^{5x}\ln(x)$ at $x=1$ . $L(x)=e^5\ln(1)+\frac{5e^5\ln(1)+e^5}{1}(x-1)$

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Problem 9300

Represent "7 times a number s is 84" as an equation: $7s = 84$

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Math

Problem 9201

Solve the quadratic equation x2+12x+116=49x^{2} + \frac{1}{2}x + \frac{1}{16} = \frac{4}{9}x2+21​x+161​=94​, then factor the left side to find the solution.

Problem 9202

Graph the quadratic equation y=8−x2y = 8 - x^2y=8−x2 and find 7 integer solutions in the range −3≤x≤3-3 \leq x \leq 3−3≤x≤3.

Problem 9203

Simplify the expression x32564\sqrt[4]{\frac{x^{3}}{256}}4256x3​​ using the quotient rule, assuming all variables are positive real numbers.

Problem 9204

Find the mean, median, and mode of the test scores: 84,79,77,73,79,65,7584, 79, 77, 73, 79, 65, 7584,79,77,73,79,65,75.

Problem 9205

Solve for xxx in the equation 10=1.35x10=1.35 \sqrt{x}10=1.35x​.

Problem 9206

Find the equation of the line passing through the points (−7,0)(-7,0)(−7,0) and (13,0)(13,0)(13,0).

Problem 9207

Find the integral that represents the length of the curve f(x)=cos⁡x,0≤x≤πf(x) = \cos x, 0 \leq x \leq \pif(x)=cosx,0≤x≤π.

Problem 9208

Perform basic arithmetic operations: (a) −355−(−139)-355-(-139)−355−(−139), (b) −24+42−6\frac{-24+42}{-6}−6−24+42​, (c) 13−(−5)13-(-5)13−(−5), (d) −216+138-216+138−216+138, (e) −125−(−341)-125-(-341)−125−(−341).

Problem 9209

Find the average of the numbers 16,8,21,1616, 8, 21, 1616,8,21,16. Round to one decimal place if necessary.

Problem 9210

Find the values of mmm for which the integral ∫08xmdx\int_{0}^{8} x^{m} d x∫08​xmdx converges.

Problem 9211

Solve the quadratic equation 4x2=7x+64x^2 = 7x + 64x2=7x+6 and find the discriminant b2−4acb^2 - 4acb2−4ac. (Simplify your answer)

Problem 9212

Find the value of aaa that is 0.4% of 40.

Problem 9213

Find the inverse function f−1(x)f^{-1}(x)f−1(x) of f(x)=5xf(x) = 5^xf(x)=5x. The inverse is f−1(x)=log⁡5xf^{-1}(x) = \log_5 xf−1(x)=log5​x.

Problem 9214

Find the missing operator that makes the equation (6×2) ? 4=8(6 \times 2) \, ? \, 4 = 8(6×2)?4=8 true.

Problem 9215

Find the solutions to the quadratic equation 1=12x2+11x1=12x^2+11x1=12x2+11x. Round answers to two decimal places and separate with a comma.

Problem 9216

Plant's height HHH (cm) after MMM months: H=53+MH = 53 + MH=53+M. Plant's height after 13 months: 53+13=6653 + 13 = 6653+13=66 cm.

Problem 9217

Solve the rational equation and find the solution set, excluding values that make the equation undefined. 5x+45=126x−175\frac{5}{x}+\frac{4}{5}=\frac{12}{6x}-\frac{17}{5}x5​+54​=6x12​−517​

Problem 9218

Solve the inequality −103≥8x-\frac{10}{3} \geq 8x−310​≥8x for the value of xxx.

Problem 9219

Ladder on wall: top slips down as base moves away at 5 m/s. Find (29) rate of top when 5 m from ground, and (30) rate of area change when top is 5 m from ground.

Problem 9220

What is the remainder when 242424 is divided by 555?

Problem 9221

Find the difference between 4.8 and -8.7.

Problem 9222

Solve for real number www where w=5\sqrt{w}=5w​=5.

Problem 9223

Solve the absolute value equation ∣2x−35∣=11\left|\frac{2 x-3}{5}\right|=11∣∣​52x−3​∣∣​=11.

Problem 9224

Evaluate the expression −8+4-8+4−8+4 and choose the correct answer from the options given.

Problem 9225

Multiply the given rational expressions, simplify, and express the result as a rational expression. y2−4y2−2y⋅yy2+10y+16,y≠−8,−2,0,2\frac{y^2-4}{y^2-2y} \cdot \frac{y}{y^2+10y+16}, y \neq -8, -2, 0, 2y2−2yy2−4​⋅y2+10y+16y​,y=−8,−2,0,2

Problem 9226

Solve for jjj in the proportion 20j=3248\frac{20}{j}=\frac{32}{48}j20​=4832​.

Problem 9227

Find the value of xxx in the equation 4(6x−9.5)=464(6x-9.5)=464(6x−9.5)=46. The possible solutions are x=−1.5x=-1.5x=−1.5, x=0.3x=0.3x=0.3, x=1.79x=1.79x=1.79, and x=3.5x=3.5x=3.5.

Problem 9228

Problem 9229

Simplify the expression (−7)2(-7)^{2}(−7)2.

Problem 9230

Find the value of 3/4 of 12.

Problem 9231

Solve the linear equation x−5−8.75=−10\frac{x}{-5} - 8.75 = -10−5x​−8.75=−10 for xxx.

Problem 9232

Divide 152152152 by 444. Write out the times table of the divisor to assist with the calculation.

Problem 9233

Use the second derivative test to find local extrema of f(x)=−5x33+10x2+25xf(x) = -\frac{5x^3}{3} + 10x^2 + 25xf(x)=−35x3​+10x2+25x in (−5,8)(-5,8)(−5,8). The local maxima occur at x=105x = \frac{10}{5}x=510​. The local minima occur at ∅\varnothing∅.

Problem 9234

Predict the number of squirrels on a nature preserve with 8 coyotes using the linear model y=−5x+60y=-5x+60y=−5x+60.

Problem 9235

Find the function (r−p)(x)(r-p)(x)(r−p)(x) where r(x)=−7xr(x) = -7xr(x)=−7x and p(x)=x2+3xp(x) = x^2 + 3xp(x)=x2+3x, and write the domain in interval notation.

Problem 9236

Solve for xxx in 2x2=502x^2 = 502x2=50. Options: a) ±0.2\pm 0.2±0.2, b) ±7.07\pm 7.07±7.07, c) ±5\pm 5±5, d) ±12.5\pm 12.5±12.5.

Problem 9237

Subtract and simplify the expression 8x2−8x−x8x−64\frac{8}{x^{2}-8 x}-\frac{x}{8 x-64}x2−8x8​−8x−64x​.

Problem 9238

Simplify the product of two polynomials (7−14p)(7+14p)(7-14p)(7+14p)(7−14p)(7+14p) and determine the degree of the result.

Problem 9239

Calculate kkk when j=3j=3j=3. k=4j+2k=4j+2k=4j+2. Options: a) 12, b) 9, c) 6, d) 14.

Problem 9240

Problem 9241

Solve the quadratic equation $x^{2} + \frac{1}{2}x + \frac{1}{16} = \frac{4}{9}$ , then factor the left side to find the solution.

Graph the quadratic equation $y = 8 - x^2$ and find 7 integer solutions in the range $-3 \leq x \leq 3$ .

Simplify the expression $\sqrt[4]{\frac{x^{3}}{256}}$ using the quotient rule, assuming all variables are positive real numbers.

Find the mean, median, and mode of the test scores: $84, 79, 77, 73, 79, 65, 75$ .

Solve for $x$ in the equation $10=1.35 \sqrt{x}$ .

Find the equation of the line passing through the points $(-7,0)$ and $(13,0)$ .

Find the integral that represents the length of the curve $f(x) = \cos x, 0 \leq x \leq \pi$ .

Perform basic arithmetic operations: (a) $-355-(-139)$ , (b) $\frac{-24+42}{-6}$ , (c) $13-(-5)$ , (d) $-216+138$ , (e) $-125-(-341)$ .

Find the average of the numbers $16, 8, 21, 16$ . Round to one decimal place if necessary.

Find the values of $m$ for which the integral $\int_{0}^{8} x^{m} d x$ converges.

Solve the quadratic equation $4x^2 = 7x + 6$ and find the discriminant $b^2 - 4ac$ . (Simplify your answer)

Find the value of $a$ that is 0.4% of 40.

Find the inverse function $f^{-1}(x)$ of $f(x) = 5^x$ . The inverse is $f^{-1}(x) = \log_5 x$ .

Find the missing operator that makes the equation $(6 \times 2) \, ? \, 4 = 8$ true.

Find the solutions to the quadratic equation $1=12x^2+11x$ . Round answers to two decimal places and separate with a comma.

Plant's height $H$ (cm) after $M$ months: $H = 53 + M$ . Plant's height after 13 months: $53 + 13 = 66$ cm.

Solve the rational equation and find the solution set, excluding values that make the equation undefined. $\frac{5}{x}+\frac{4}{5}=\frac{12}{6x}-\frac{17}{5}$

Solve the inequality $-\frac{10}{3} \geq 8x$ for the value of $x$ .

What is the remainder when $24$ is divided by $5$ ?

Solve for real number $w$ where $\sqrt{w}=5$ .

Solve the absolute value equation $\left|\frac{2 x-3}{5}\right|=11$ .

Evaluate the expression $-8+4$ and choose the correct answer from the options given.

Multiply the given rational expressions, simplify, and express the result as a rational expression. $\frac{y^2-4}{y^2-2y} \cdot \frac{y}{y^2+10y+16}, y \neq -8, -2, 0, 2$

Solve for $j$ in the proportion $\frac{20}{j}=\frac{32}{48}$ .

Find the value of $x$ in the equation $4(6x-9.5)=46$ . The possible solutions are $x=-1.5$ , $x=0.3$ , $x=1.79$ , and $x=3.5$ .

Simplify the expression $(-7)^{2}$ .

Solve the linear equation $\frac{x}{-5} - 8.75 = -10$ for $x$ .

Divide $152$ by $4$ . Write out the times table of the divisor to assist with the calculation.

Use the second derivative test to find local extrema of $f(x) = -\frac{5x^3}{3} + 10x^2 + 25x$ in $(-5,8)$ . The local maxima occur at $x = \frac{10}{5}$ . The local minima occur at $\varnothing$ .

Predict the number of squirrels on a nature preserve with 8 coyotes using the linear model $y=-5x+60$ .

Find the function $(r-p)(x)$ where $r(x) = -7x$ and $p(x) = x^2 + 3x$ , and write the domain in interval notation.

Solve for $x$ in $2x^2 = 50$ . Options: a) $\pm 0.2$ , b) $\pm 7.07$ , c) $\pm 5$ , d) $\pm 12.5$ .

Subtract and simplify the expression $\frac{8}{x^{2}-8 x}-\frac{x}{8 x-64}$ .

Simplify the product of two polynomials $(7-14p)(7+14p)$ and determine the degree of the result.

Calculate $k$ when $j=3$ . $k=4j+2$ . Options: a) 12, b) 9, c) 6, d) 14.

Find the meaning of $f(x)$ and $x$ in the equation $f(x)=7x+15$ which tracks Luke's exercise over the summer.

Solve the equation $(c+2)^{2}-5=-21$ and select the correct solution.

Approximate the sum of the series $\sum_{n=1}^{\infty}(-1)^{n} \frac{2}{3 n^{4}}$ with error < 0.001.

Find the point of intersection of the lines $y=2x-4$ and $y=-x+5$ .

Find the price of a used book sold at a bookstore, where the owner buys them for $\$ 2.25$ each and resells them for $300\%$ of the purchase price.

Find the value of $x$ that makes $\frac{1}{x}+\frac{4}{3x}-\frac{5}{6x}+1=0$ .

Determine the number of college students who got news from only social media using a Venn diagram. Given: 94 students surveyed, 32 from news websites, 25 from social media, and 11 from both.
$n($ News websites only $)=21$ $n($ Social media only $)=\boxed{14}$

Find the value of $x+\sqrt{x}$ for $x=0, 0.01, 0.36, 0.64, 1, 25, 100, 3600$ .

Find the equation representing the discount price for senior citizens given a 12% discount. $discount\ price = (original\ price)(1-0.12)$

Find the equation with solutions $x=7+i$ and $x=7-i$ , written in standard form.

Find the values of $y$ that make the expression $\frac{4}{15-3y}$ undefined.

Find the derivative of $y=2 x^{2}(3-2 x)$ using the product rule.

Determine the limit of the sequence $\left\{\left(\frac{n+n^{2}}{2 n^{2}}\right)^{n}\right\}$ .

Find the integer between $\frac{11 \pi}{5}$ and $\sqrt{58}$ .

Simplify the improper fraction $\frac{16}{2}$ .

Solve the linear equation $3x + 4 = 13$ for the value of $x$ .

Estimate the total number of plastic widgets sold in the first 6 weeks given the sales function $P(t)=7000 t e^{-0.3 t}$ .

Find the width of a rectangle with length 10 cm longer than width, if total perimeter is 220 cm.
$x$ cm width, $x+10$ cm length, total perimeter $2(x+x+10)=220$ . Solve for $x$ .

Solve for $u$ where $u(u-6)=0$ . Write the solutions as integers or simplified fractions.

Multiply the given rational expressions and simplify the result, excluding the values $p = -2, 3, 6$ .

Solve the system of linear equations $y = -x + 1$ and $x - 2y = 4$ .

Determine the type of function represented by the equation $y=x(30-2x)(10-2x)$ .

Solve for y in the quadratic equation $19y^2 + 39y + 2 = 0$ . Write each solution as an integer, proper fraction, or improper fraction, separated by commas.

Describe the end behavior of $g(x) = -\frac{1}{x^2}$ . As $x \to \pm\infty$ , $g(x)$ goes to 0 or $\pm\infty$ .

Simplify the expression $2y - 5y$ .

Solve for $k$ given $8k + 2m = 3m + k$ with solutions $k = 70m, k = 7m, k = \frac{7}{\sqrt{m}}, k = \frac{m}{7}$ .

Solve the quadratic equation $35v^2 + 43v = 0$ for $v$ . Express each solution as an integer, proper fraction, or improper fraction, separated by commas.

What is the ordered pair that is a reflection over the x-axis of $(7,3)$ ? $(-7,3)$ , $(3,-7)$ , $(-3,-7)$

Solve for $x$ in the equation $\frac{2x}{5} = \frac{x^2 - 5x}{5x}$ .

Find the difference between $(d-9)$ and $(3d-1)$ .

Solve for $e$ where $\frac{e}{5}=x$ and $e=$