Natural Numbers

Problem 901

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

See Solution

Problem 902

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

See Solution

Problem 903

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.

See Solution

Problem 904

Find the logarithm base 3 of 243.

See Solution

Problem 905

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

See Solution

Problem 906

Simplify the expression $2y - 5y$ .

See Solution

Problem 907

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

See Solution

Problem 908

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

See Solution

Problem 909

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

See Solution

Problem 910

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

See Solution

Problem 911

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

See Solution

Problem 912

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

See Solution

Problem 913

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

See Solution

Problem 914

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

See Solution

Problem 915

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%.
$n = \frac{z^{2}_{\alpha/2} p^{} (1 - p^{})}{E^{2}}$

See Solution

Problem 916

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

See Solution

Problem 917

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

See Solution

Problem 918

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

See Solution

Problem 919

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

See Solution

Problem 920

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

See Solution

Problem 921

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

See Solution

Problem 922

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.

See Solution

Problem 923

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

See Solution

Problem 924

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. $4f+f+4=42$

See Solution

Problem 925

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

See Solution

Problem 926

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

See Solution

Problem 927

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

See Solution

Problem 928

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

See Solution

Problem 929

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

See Solution

Problem 930

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

See Solution

Problem 931

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

See Solution

Problem 932

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

See Solution

Problem 933

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

See Solution

Problem 934

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.
$\tan^{-1}\left(\frac{13}{4}\right)$

See Solution

Problem 935

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

See Solution

Problem 936

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

See Solution

Problem 937

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

See Solution

Problem 938

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

See Solution

Problem 939

Rewrite $\frac{1}{10,000}$ as a power of 10.

See Solution

Problem 940

Find the value of $u$ given the equation $4=\frac{u}{6.4}$ .

See Solution

Problem 941

Find the real number $u$ such that $\sqrt{u} = 10$ .

See Solution

Problem 942

Expand $f(x+a)$ and $f(a)$ , then find the difference $f(x+a)-f(a)$ without factoring.

See Solution

Problem 943

Solve for $x$ in the equation $7(x+2)^{3}-4=2621$ and simplify the solution.

See Solution

Problem 944

Write logarithm of $0.00000001$ in base 10.

See Solution

Problem 945

Distribute the negative sign outside the parentheses: $-(5g - 5.5)$

See Solution

Problem 946

Find the midquartile of football league passer ratings, where Midquartile = $(Q_{1} + Q_{3})/2$ . The ratings are: 99.7, 95.7, 89.2, 84.7, 83.3, 82.4, 78.5, 77.8, 76.3, 74.4.

See Solution

Problem 947

Find the products that are negative when $x$ is negative.

See Solution

Problem 948

Find the quotient of the long division of $90.24$ .

See Solution

Problem 949

Simplify the absolute value expression $|6.75|$ .

See Solution

Problem 950

Determinar si los pares ordenados $(x, y)$ son soluciones de $y = -4x - 6$ .

See Solution

Problem 951

Dee bought 7 bags of flour. He used 1/2 the total on Monday and 11/4 bags on Tuesday. How much flour is left?
$7(64/4) - (3.5 + 2.75)$

See Solution

Problem 952

Find the approximate value of $\cot \frac{\pi}{12}$ using a calculator.

See Solution

Problem 953

Find the y-intercept of the function with the given $(x,y)$ coordinates: $(-14,-5)$ , $(-8,-2.8)$ , $(0,-1.25)$ , $(3.1,0)$ .

See Solution

Problem 954

Find the surface area of a $5 \mathrm{~cm}$ cube. Options: A) $25 \mathrm{~cm}^{2}$ , B) $30 \mathrm{~cm}^{2}$ , C) $125 \mathrm{~cm}^{2}$ , D) $150 \mathrm{~cm}^{2}$ .

See Solution

Problem 955

Find two decimals with product near $6.2$ . Which numbers satisfy this?

See Solution

Problem 956

A hiker hikes at a steady rate on a mountain. Which student wrote the correct equation $y = -125x + 5,775$ to represent the linear relationship between hours hiked $(x)$ and altitude $(y)$ ?

See Solution

Problem 957

Solve $f=D+A$ for $A$ , accounting for capitalization.

See Solution

Problem 958

The graph $y=500(0.85)^{x}$ represents the amount of drug (in mg) left in a patient's system $x$ hours after administration. Find the $y$ -intercept.

See Solution

Problem 959

Derive the function $f(x) = \ln 3x^2$ .

See Solution

Problem 960

The equation $6 \sec^2 \theta \tan \theta = 8 \tan \theta$ has the solution set $\{0, \pi/2\}$ .

See Solution

Problem 961

Find the Laplace transform of $3te^{5t}$ using a table of Laplace transforms. Integration by parts may be useful.

See Solution

Problem 962

Solve the quadratic equation $\left(x^{2}-8\right)^{2}-2\left(x^{2}-8\right)=-1$ and provide all solutions.

See Solution

Problem 963

Find the domain, range, intercepts, and asymptotes of the exponential function $f(x) = 3 \cdot 6^{x}$ . Describe the end behavior.

See Solution

Problem 964

Solve for P in the equation $A=P+\operatorname{Pr} t$ . Options: a) $P=A-r t$ , b) $P=\frac{A-r t}{2}$ , c) $P=\frac{A}{1+r t}$ , d) $P=\frac{A}{2 r t}$ .

See Solution

Problem 965

Determine the domain of an exponential function: $y>0$ , $y<0$ , all real numbers, $y\geq 0$ , or $y\leq 0$ .

See Solution

Problem 966

Find $\Delta y$ , $dy=f'(x)dx$ , and $dy$ for $y=2x^3$ , $x=4$ , and $\Delta x=0.08$ . a) $\Delta y=\boxed{1.6384}$ b) $dy=f'(x)dx=\boxed{96}dx$ c) $dy=\boxed{7.68}$

See Solution

Problem 967

Convert weight to fraction. $10.4 = \square$ (Type integer, proper fraction, or mixed number).

See Solution

Problem 968

Convert the given radian measures to degrees and determine the quadrant of the terminal side. a) $\frac{7 \pi}{5}$ degrees, Quad b) $-\frac{11 \pi}{12}$ degrees, Quad

See Solution

Problem 969

Find the trigonometric ratio of a right triangle with $BC=4$ and $AC=8$ . Match the values to the appropriate trigonometric ratios.

See Solution

Problem 970

Find the value of $p r - r$ when $p = -7$ and $r = \frac{1}{2}$ .

See Solution

Problem 971

Find the area of a regular hexagon with side length $18$ .

See Solution

Problem 972

Find the value of $m$ that satisfies the equation $6m-8=2(m+5)$ .

See Solution

Problem 973

Solve for $u$ in the equation $-\frac{6}{5}u=-42$ . Simplify the solution as much as possible.

See Solution

Problem 974

Find the range of the given set of ordered pairs: $\{(7,2),(-4,-5),(0,4),(10,0)\}$ .

See Solution

Problem 975

Solve the linear equation $\frac{3 x-13}{9}+\frac{x+11}{18}=\frac{10}{9}$ for $x$ .

See Solution

Problem 976

1. Given $p=5-2i$ and $q=-3+7i$ , write each expression in the form $a+bi$ : a. $p+q-p\times q$ b. $p-q-p\div q$
2. a. Solve the equation $\sqrt{2x+1}-4=-1$ . b. Explain why $\sqrt{2x+1}+4=-1$ has no real solution.

See Solution

Problem 977

Find the number of brothers Lou has given that Carla has $x$ fewer brothers than Lou.

See Solution

Problem 978

Calculate the expression $-2.5-\frac{1}{2}$ .

See Solution

Problem 979

Find the value of $x$ in the equation $e^{x}=5$ . The correct statements are: $x=\ln 5$ , $x=\log _{5} e$ , and to the nearest hundredth, $x \approx 1.61$ .

See Solution

Problem 980

Complete the square for $g(x) = -4x^2 + 16x - 13$ . Find the domain, vertex, range, and graph the function.

See Solution

Problem 981

Find the ratio of $x$ to $y$ if $7y - x = 4y$ .

See Solution

Problem 982

Evaluate the given expressions as fractions: $\frac{-5}{4^{2}}$ and $\left(-\frac{1}{2}\right)^{3}$ .

See Solution

Problem 983

Solve the linear equation $4x + 3 - x - 9 = 0$ using the balance method.

See Solution

Problem 984

Match the example with the step used to solve $5x + 3 - 4x = 9 \rightarrow x + 3 = 9$ .

See Solution

Problem 985

Determine the mean and standard deviation of the sampling distribution of the proportion of voters supporting a candidate in a county, given the population proportion and sample size.
Mean: $\mu_{\widehat{p}}=0.2700$ Standard error: $\sigma_{\widehat{p}}=0.0226$

See Solution

Problem 986

Find $x$ and $NQ$ given $NS=2x+7$ and $SQ=5x-23$ .

See Solution

Problem 987

Find $y$ for $x=0$ in the linear equation $x + 5y = 15$ .

See Solution

Problem 988

Encontre o grau e o coeficiente principal do polinômio $-5+3x^2+2x^3+10x$ .

See Solution

Problem 989

Multiply fractions using prime factorization and canceling common factors: $\frac{21}{4} \times \frac{2}{-9} \times \frac{3}{5} \times \frac{-6}{15}$ .

See Solution

Problem 990

Find the differential $dy$ for $y=e^{x/4}$ and evaluate $dy$ for $x=0, dx=0.05$ .

See Solution

Problem 991

Subtract complex numbers $(2+3i)$ and $(-3-i)$ and simplify the result in the form $a + bi$ .

See Solution

Problem 992

Find the value of $-9 \times 2.2$

See Solution

Problem 993

Solve for the value of $x$ in the equation $(x-2)^{\frac{3}{4}}=8$ .

See Solution

Problem 994

Find the correct quotient when dividing $1 2 0$ by $3.636$ .

See Solution

Problem 995

Solve the quadratic expression $36 x^{2} + 30 x + 9$ . Identify the special case that can be used.

See Solution

Problem 996

Identify the hole, vertical asymptote, horizontal asymptote, and domain of the rational function $f(x) = \frac{x^2 + 9x + 20}{x^2 + 3x - 4}$ .

See Solution

Problem 997

Find the value of $a$ if the solutions to the equation $|x+a| = 4$ are $-2$ and $6$ .

See Solution

Problem 998

Solve the equation by graphing the related function: $-x^{2}-5=0$

See Solution

Problem 999

Solve for $x$ in the equation $\frac{1}{2}(\sqrt{x})^{5}=16$ , checking for extraneous solutions.

See Solution

Problem 1000

Find the value of $g$ that satisfies the equation $6 g(6 g+1)=0$ . Express the solution(s) as an integer or a simplified fraction.

See Solution

1 ...7 8 9 10 11 12 13 ...28

Natural Numbers

Problem 901

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

Problem 902

Problem 903

Solve for y in the quadratic equation 19y2+39y+2=019y^2 + 39y + 2 = 019y2+39y+2=0. Write each solution as an integer, proper fraction, or improper fraction, separated by commas.

Problem 904

Find the logarithm base 3 of 243.

Problem 905

Describe the end behavior of g(x)=−1x2g(x) = -\frac{1}{x^2}g(x)=−x21​. As x→±∞x \to \pm\inftyx→±∞, g(x)g(x)g(x) goes to 0 or ±∞\pm\infty±∞.

Problem 906

Simplify the expression 2y−5y2y - 5y2y−5y.

Problem 907

Solve for kkk given 8k+2m=3m+k8k + 2m = 3m + k8k+2m=3m+k with solutions k=70m,k=7m,k=7m,k=m7k = 70m, k = 7m, k = \frac{7}{\sqrt{m}}, k = \frac{m}{7}k=70m,k=7m,k=m​7​,k=7m​.

Problem 908

Solve the quadratic equation 35v2+43v=035v^2 + 43v = 035v2+43v=0 for vvv. Express each solution as an integer, proper fraction, or improper fraction, separated by commas.

Problem 909

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

Problem 910

Solve for xxx in the equation 2x5=x2−5x5x\frac{2x}{5} = \frac{x^2 - 5x}{5x}52x​=5xx2−5x​.

Problem 911

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

Problem 912

Solve for eee where e5=x\frac{e}{5}=x5e​=x and e=e=e=

Problem 913

Write the expression as a function of xxx: cos⁡(π4−x)\cos\left(\frac{\pi}{4}-x\right)cos(4π​−x).

Problem 914

Find the complete solution to Ax=bAx=bAx=b for A=[1222246836810],b=[516]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}A=⎣⎡​123​246​268​2810​⎦⎤​,b=⎣⎡​516​⎦⎤​.

Problem 915

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=zα/22p∗(1−p∗)E2n = \frac{z^{2}_{\alpha/2} p^{*} (1 - p^{*})}{E^{2}}n=E2zα/22​p∗(1−p∗)​

Problem 916

Find the odd one out in the given sets. Explain your reasoning. Sets: 5,8,2,1,2,65,8,2,1,2,65,8,2,1,2,6, 15,18,12,11,0,1615,18,12,11,0,1615,18,12,11,0,16, 58,21,2658,21,2658,21,26, 9,4,1,3,7,59,4,1,3,7,59,4,1,3,7,5.

Problem 917

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

Problem 918

Find the value of 813/481^{3/4}813/4.

Problem 919

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

Problem 920

Convert 43 pounds to kilograms using the conversion 111 kg =2.2=2.2=2.2 lbs. (Round to the nearest tenth.)

Problem 921

Find the excluded value for the rational function y=6x+19x−4y=\frac{6 x+1}{9 x-4}y=9x−46x+1​.

Problem 922

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

Problem 923

Simplify the expression 4ln⁡x+8ln⁡y4 \ln x + 8 \ln y4lnx+8lny.

Problem 924

Problem 925

Verify the identity: 2cos⁡2xsin⁡2x=cot⁡x−tan⁡x\frac{2 \cos 2x}{\sin 2x} = \cot x - \tan xsin2x2cos2x​=cotx−tanx.

Problem 926

Find the secant line equation y=mx+by=mx+by=mx+b passing through points (−3,f(−3))(-3, f(-3))(−3,f(−3)) and (2,f(2))(2, f(2))(2,f(2)) where f(x)=x3−5f(x)=x^{3}-5f(x)=x3−5.

Problem 927

Find the rank of the 3×43 \times 43×4 matrix A=[20−2411230131]A = \begin{bmatrix} 2 & 0 & -2 & 4 \\ 1 & 1 & 2 & 3 \\ 0 & 1 & 3 & 1 \end{bmatrix}A=⎣⎡​210​011​−223​431​⎦⎤​.

Problem 928

Find the equation for a cubic function with roots at −8,3-8, 3−8,3, and 43\frac{4}{3}34​.

Problem 929

Simplify the expression 3−310y23-\frac{3}{10 y^{2}}3−10y23​ and express the answer as a single fraction in simplest form.

Problem 930

Express ln⁡54\ln \sqrt[4]{5}ln45​ as a product.

Problem 931

Find the number of positive and negative real zeros of g(x)=x3+5x2+9x−8g(x)=x^{3}+5x^{2}+9x-8g(x)=x3+5x2+9x−8.

Problem 932

Calculate the distance travelled by a 11 cm11\,\mathrm{cm}11cm pendulum swinging 84∘84^\circ84∘, given in cm\mathrm{cm}cm to 1 d.p.

Problem 933

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

Problem 934

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(134)\tan^{-1}\left(\frac{13}{4}\right)tan−1(413​)

Problem 935

Find the equation(s) of the vertical asymptote(s) of the rational function g(t)=t2−53t2+4t−3g(t) = \frac{t^{2} - 5}{3t^{2} + 4t - 3}g(t)=3t2+4t−3t2−5​.

Problem 936

Differentiate the function g(t)=2−5t7t+8g(t) = \frac{2 - 5t}{7t + 8}g(t)=7t+82−5t​ to find g′(t)g'(t)g′(t).

Problem 937

Find the linear approximation of y=e5xln⁡(x)y=e^{5x}\ln(x)y=e5xln(x) at x=1x=1x=1. L(x)=e5ln⁡(1)+5e5ln⁡(1)+e51(x−1)L(x)=e^5\ln(1)+\frac{5e^5\ln(1)+e^5}{1}(x-1)L(x)=e5ln(1)+15e5ln(1)+e5​(x−1)

Problem 938

Represent "7 times a number s is 84" as an equation: 7s=847s = 847s=84

Problem 939

Rewrite 110,000\frac{1}{10,000}10,0001​ as a power of 10.

Problem 940

Find the value of uuu given the equation 4=u6.44=\frac{u}{6.4}4=6.4u​.

Problem 941

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 $e=$

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

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

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%.
$n = \frac{z^{2}_{\alpha/2} p^{} (1 - p^{})}{E^{2}}$

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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.
$\tan^{-1}\left(\frac{13}{4}\right)$

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

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

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

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

Rewrite $\frac{1}{10,000}$ as a power of 10.

Find the value of $u$ given the equation $4=\frac{u}{6.4}$ .

Find the real number $u$ such that $\sqrt{u} = 10$ .

Expand $f(x+a)$ and $f(a)$ , then find the difference $f(x+a)-f(a)$ without factoring.

Solve for $x$ in the equation $7(x+2)^{3}-4=2621$ and simplify the solution.

Write logarithm of $0.00000001$ in base 10.

Distribute the negative sign outside the parentheses: $-(5g - 5.5)$

Find the midquartile of football league passer ratings, where Midquartile = $(Q_{1} + Q_{3})/2$ . The ratings are: 99.7, 95.7, 89.2, 84.7, 83.3, 82.4, 78.5, 77.8, 76.3, 74.4.

Find the products that are negative when $x$ is negative.

Find the quotient of the long division of $90.24$ .

Simplify the absolute value expression $|6.75|$ .

Determinar si los pares ordenados $(x, y)$ son soluciones de $y = -4x - 6$ .

Dee bought 7 bags of flour. He used 1/2 the total on Monday and 11/4 bags on Tuesday. How much flour is left?
$7(64/4) - (3.5 + 2.75)$

Find the approximate value of $\cot \frac{\pi}{12}$ using a calculator.

Find the y-intercept of the function with the given $(x,y)$ coordinates: $(-14,-5)$ , $(-8,-2.8)$ , $(0,-1.25)$ , $(3.1,0)$ .

Find the surface area of a $5 \mathrm{~cm}$ cube. Options: A) $25 \mathrm{~cm}^{2}$ , B) $30 \mathrm{~cm}^{2}$ , C) $125 \mathrm{~cm}^{2}$ , D) $150 \mathrm{~cm}^{2}$ .

Find two decimals with product near $6.2$ . Which numbers satisfy this?

A hiker hikes at a steady rate on a mountain. Which student wrote the correct equation $y = -125x + 5,775$ to represent the linear relationship between hours hiked $(x)$ and altitude $(y)$ ?

Solve $f=D+A$ for $A$ , accounting for capitalization.

The graph $y=500(0.85)^{x}$ represents the amount of drug (in mg) left in a patient's system $x$ hours after administration. Find the $y$ -intercept.

Derive the function $f(x) = \ln 3x^2$ .

The equation $6 \sec^2 \theta \tan \theta = 8 \tan \theta$ has the solution set $\{0, \pi/2\}$ .

Find the Laplace transform of $3te^{5t}$ using a table of Laplace transforms. Integration by parts may be useful.

Solve the quadratic equation $\left(x^{2}-8\right)^{2}-2\left(x^{2}-8\right)=-1$ and provide all solutions.

Find the domain, range, intercepts, and asymptotes of the exponential function $f(x) = 3 \cdot 6^{x}$ . Describe the end behavior.

Solve for P in the equation $A=P+\operatorname{Pr} t$ . Options: a) $P=A-r t$ , b) $P=\frac{A-r t}{2}$ , c) $P=\frac{A}{1+r t}$ , d) $P=\frac{A}{2 r t}$ .

Determine the domain of an exponential function: $y>0$ , $y<0$ , all real numbers, $y\geq 0$ , or $y\leq 0$ .

Find $\Delta y$ , $dy=f'(x)dx$ , and $dy$ for $y=2x^3$ , $x=4$ , and $\Delta x=0.08$ . a) $\Delta y=\boxed{1.6384}$ b) $dy=f'(x)dx=\boxed{96}dx$ c) $dy=\boxed{7.68}$

Convert weight to fraction. $10.4 = \square$ (Type integer, proper fraction, or mixed number).

Convert the given radian measures to degrees and determine the quadrant of the terminal side. a) $\frac{7 \pi}{5}$ degrees, Quad b) $-\frac{11 \pi}{12}$ degrees, Quad

Find the trigonometric ratio of a right triangle with $BC=4$ and $AC=8$ . Match the values to the appropriate trigonometric ratios.

Find the value of $p r - r$ when $p = -7$ and $r = \frac{1}{2}$ .

Find the area of a regular hexagon with side length $18$ .

Find the value of $m$ that satisfies the equation $6m-8=2(m+5)$ .

Solve for $u$ in the equation $-\frac{6}{5}u=-42$ . Simplify the solution as much as possible.

Find the range of the given set of ordered pairs: $\{(7,2),(-4,-5),(0,4),(10,0)\}$ .