Browse Math Statement problems Studdy Solved!

Problem 3001

Find the derivative of the function $f(x)=\log _{2}\left(x^{2}-3\right)$ . (Express numbers in exact form. Use symbolic notation and fractions where needed.) $f^{\prime}(x)=\sqrt{\frac{1}{x^{2}-3} \cdot 2 x}$
Incorrect Answer

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Problem 3002

rement of the progress bar may be uneven because questions can be worth more or less (inciuc
Factor out the Greatest Common Factor (GCF): $64 d^{5}-24 d^{2}$ $8 d\left(8 d^{4}-3 d\right)$ $8 d^{2}\left(8 d^{3}-3\right)$ $8 d^{2} \cdot 8 d^{3}-8 d^{2} \cdot 3$ $4 d\left(16 d^{4}-6 d\right)$

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Problem 3003

Find an equation of the hyperbola having foci at $(3,-1-\sqrt{45})$ and $(3,-1+\sqrt{45})$ and asymptotes at $y=2 x-7$ and $y=-2 x+5$ .

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Problem 3004

Write the equation in exponential form. $\log _{2}(8)=3$

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Problem 3005

1) $7(2+5 v)=3 v+14$ $(14+35 v)=3 v+$

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Problem 3006

The equations of two conics are given below. Choose the correct classification for each, and then provide the requested information. \begin{tabular}{|l|l|} \hline (a) $-3 x^{2}-6 x-y-2=0$ & (Choose one) $\nabla$ \\ \hline (b) $-16 x^{2}-4 y^{2}-32 x-8 y+44=0$ & (Choose one) $\boldsymbol{}$ \\ \hline \end{tabular}

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Problem 3007

What is the slope of the line represented by the equation $y=-\frac{1}{2} x+\frac{1}{4}$ ? $-\frac{1}{2}$ $-\frac{1}{4}$ $\frac{1}{4}$ $\frac{1}{2}$

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Problem 3008

Which equation can be solved by using this system of equations? $\left\{\begin{array}{l} y=3 x^{5}-5 x^{3}+2 x^{2}-10 x+4 \\ y=4 x^{4}+6 x^{3}-11 \end{array}\right.$ $3 x^{5}-5 x^{3}+2 x^{2}-10 x+4=0$ $3 x^{5}-5 x^{3}+2 x^{2}-10 x+4=4 x^{4}+6 x^{3}-11$ $3 x^{5}+4 x^{4}+x^{3}+2 x^{2}-10 x-7=0$ $4 x^{4}+6 x^{3}-11=0$

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Problem 3009

A system of equations has two lines with a positive slope, but the slope of each line is different. Which of the following statements is true? The equations are independent. There is not enough information to determine whether the equations are dependent or independent. The lines are perpendicular to each other. The equations are dependent.

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Problem 3010

Solve the following inequalities using the multiplication property of inequalities. If you multiply both sides by a negative number, be sure to reverse the direction of the inequality symbol. Graph the solution set. $3 y<9$ $\square$ $\square$
Clear All $\square$ Draw: $\square$

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Problem 3011

7 Solve this equation $\mathrm{a}=2 \quad \mathrm{~b}=3 \quad \mathrm{c}=7$ $|a x-b| \leq c$

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Problem 3012

The movement of the progress bor moy be uneven because questions can be worth more or less (including zero Solve for $x$ and $y$ : $\begin{array}{l} 5 y-7 x=-9 \\ x=4-2 y \end{array}$ $x=-3, y=-6$ $x=6, y=-1$ $x=1, y=2$ $x=2, y=1$

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Problem 3013

$0=x^{2}+24 x-34$

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Problem 3014

2 State whether or not this parabola has a maximum or minimum, then state $y$ -value of the $\max$ or $\min . \quad \mathrm{y}=-(\mathrm{x}+64)^{\wedge} 2-199$

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Problem 3015

231) $y=\left(2 x^{3}-x^{2}+6 x+1\right)^{3}$

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Problem 3016

Expand and fully simplify $(4 p+3)(2 p+5)+6(p+3)$

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Problem 3017

Find $\frac{d y}{d x}$ by implicit differentiation, if $x^{2}+y^{2}=4$ , $\frac{d y}{d x}=$ $\square$

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Problem 3018

In $\triangle \mathrm{FGH}, f=200 \mathrm{~cm}, g=880 \mathrm{~cm}$ and $\angle \mathrm{H}=149^{\circ}$ . Find the length of $h$ , to the nearest centimeter.
Answer Attempt 4 out of 100 Submit Answer

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Problem 3019

Evaluate the function $f(r)=\sqrt{r+3}-8$ at the given values of the independent varial a. $f(-3)$ b. $\mathrm{f}(78)$ c. $f(x-3)$ a. $f(-3)=-8$ (Simplify your answer.) b. $f(78)=1$ (Simplify your answer.) c. $f(x-3)=\square$ (Simplify your answer.)

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Problem 3020

Find the Least Common Denominator of the fractions: $1 / 6$ and $3 / 5$ 6 5 30 12

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Problem 3021

$3^{7 x-6}=3^{8=4 x}$

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Problem 3022

$\frac{2}{5 x}+\frac{1}{5 x}$

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Problem 3023

$2^{-4} \times 2^{-3}$ A. $\frac{1}{128}$ B. $\frac{1}{256}$ C. $\frac{1}{4}$ D. $\frac{1}{16}$

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Problem 3024

$9(-2)=\left|3 x-x^{3}\right|$

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Problem 3025

$\left(5 m n^{4}\right)^{3} \div\left(5 m^{3} n\right)^{4}$ A. $\frac{n^{8}}{5 m^{9}}$ B. $\frac{5}{m^{9} n^{8}}$ C. $\frac{1}{5 m^{9} n^{8}}$ D. $5 m^{9} n^{8}$

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Problem 3026

For each pair of statements, choose the one that is true. (a) $\{4\} \in\{4,5\}$ $4 \in\{4,5\}$ (b) $\{10,12,14\} \subseteq\{2,4,6,8, \ldots\}$ $\{10,12,14\} \in\{2,4,6,8, \ldots\}$ (c) $q \subseteq\{q, r\}$ $\{q\} \subseteq\{q, r\}$ $\{g\} \in\{e, g, h\}$ (d) $\{g\} \nsubseteq\{e, f, h\}$

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Problem 3027

Subtract. $-\frac{8 a+11 b}{3 a}-\frac{8 a-8 b}{3 a}$
Simplify your answer as much as possible.

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Problem 3028

Solve for the roots in simplest form using the quadratic formula: $3 x^{2}+15=6 x$
Answer Attempt 1 out of 2

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Problem 3029

Solve for $y$ . $4+\frac{7}{y}=\frac{5}{3}$
Simplify your answer as much as possible. $y=$

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Problem 3030

Find $\frac{d y}{d x}$ by implicit differentiation. $e^{y}=4 x-8 y$
Answer: $\frac{d y}{d x}=$

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Problem 3031

Subtract. $\frac{13 a+2}{8 a}-\frac{3 a}{8 a}$
Simplify your answer as much as possible.

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Problem 3032

Consider the function $g(x)=4-2 x^{2}$ a. Find $g(2)$ and $g(-1)$

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Problem 3033

Factor. $r^{2}-81$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $r^{2}-81=$ $\square$ (Factor completely.) B. The polynomial is prime.

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Problem 3034

Factor. $s^{2}-36$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $s^{2}-36=$ $\square$ (Factor completely.) B. The polynomial is prime.

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Problem 3035

Factor completely. $b^{2}-d^{2}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $b^{2}-d^{2}=$ $\square$ B. The binomial is not factorable.

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Problem 3036

2. Consider the function $g(x)=4-2 x^{2}$ a. Find $g(2)$ and $g(-1)$ $\begin{array}{l} g(2)=-4 \\ g(-1)=2 \end{array}$ b. Find the value(s) of $x$ such that $g(x)=-14$
3 and -3 c. Find $g(2 x)$

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Problem 3037

Diviaing rational expressions involving linear expressions
Divide. $\frac{2 x+14}{x+3} \div \frac{6 x+42}{5 x+15}$
Simplify your answer as much as possible.

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Problem 3038

Convert the given unit of weight to the unit indicated. 7.4 dg to mg $7.4 \mathrm{dg}=\square \mathrm{mg}$

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Problem 3039

Convert the given unit of weight to the unit indicated. $\begin{array}{r} 540 \mathrm{mg} \text { to } \mathrm{g} \\ 540 \mathrm{mg}=\square \mathrm{g} \end{array}$ $\square$ g

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Problem 3040

3. $4+x=25 ; \quad x=21$ $\square$
4. The number of blue beads (b) in a bracelet is four times as many as the number of yellow beads (y). Write an equation to represent the number of each type of bead in bracelet with a total of 50 beads. $\square$ $\square$ $\square$ y

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Problem 3041

Simplify this expression: $\left(4 x^{3} y^{-4}\right)^{-2}$ .

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Problem 3042

Find or approximate all points at which the given function equals its average value on the given interval. $f(x)=-\frac{\pi}{6} \sin x \text { on }[-\pi, 0]$
The function is equal to its average value at $x=$ $\square$ (Round to one decimal place as needed. Use a comma to separate answers as needed.)

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Problem 3043

The number of bacteria $\mathrm{P}(\mathrm{t})$ in a certain population increases according to the following function, where time $t$ is measured in hours. $P(t)=2600 e^{0.11 t}$
Find the initial number of bacteria in the population and the number of bacteria after 7 hours. Round your answers to the nearest whole number as necessary.
Initial number: II bacteria
Number after 7 hours: $\square$ bacteria

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Problem 3044

The number of bacteria $\mathrm{P}(\mathrm{t})$ in a certain population increases according to the following function, where time t is measured in hours. $P(t)=2600 e^{0.11 t}$
Find the initial number of bacteria in the population and the number of bacteria after 7 hours. Round your answers to the nearest whole number as necessary.
Initial number: II bacteria
Number after 7 hours: $\square$ bacteria

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Problem 3045

Day 12 \% Name: (9) $\frac{5}{6} \times \frac{3}{9}$ (2) $\frac{7}{9} \times \frac{5}{3}$ $\frac{5}{3} \times \frac{7}{9}$ $3 \times \frac{6}{3}$ - $5.3 \times 3.547$ $1=$ $\qquad$ $\qquad$ $\frac{9}{7} \times \frac{8}{3}$ $6 \times \frac{6}{3}$ $\frac{4}{6} \times \frac{2}{8}$ $\frac{5}{7} \times \frac{6}{4}$ (1I) $\frac{4}{9} \times \frac{6}{7}$ $\frac{3}{2} \times \frac{8}{6}$ $6 \times \frac{8}{2}$ $\frac{9}{9} \times \frac{10}{7}$ $\frac{8}{7} \times \frac{6}{2}$ $\frac{6}{2} \times \frac{5}{9}$ $\frac{5}{8} \times \frac{9}{4}$ (13) $\frac{4}{3} \times \frac{2}{6}$ (13) $\frac{7}{7} \times \frac{6}{5}$ $\frac{4}{3} \times \frac{9}{2}$ $9 \times \frac{9}{6}$ (17) $5 \times \frac{7}{6}$ (2) $\frac{7}{6} \times \frac{5}{6}$ (23) $4 \times \frac{7}{5}$ (24) $\frac{4}{8} \times \frac{9}{5}$ (21) $\frac{3}{8} \times \frac{9}{2}$

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Problem 3046

Use the Fundamental Theorem of Calculus to evaluate the following definite integra $\int_{0}^{\frac{1}{2}} \frac{6 d x}{\sqrt{1-x^{2}}}$ $\int_{0}^{\frac{1}{2}} \frac{6 d x}{\sqrt{1-x^{2}}}=\square$ (Type an exact answer.)

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Problem 3047

349. 9709 m22_qp_12 Q: 11
It is given that a curve has equation $y=k(3 x-k)^{-1}+3 x$ , where $k$ is a constant. (a) Find, in terms of $k$ , the values of $x$ at which there is a stationary point.

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Problem 3048

Use PMT $=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]^{2}}$ to determine the regular payment amount, rounded to the nearest dollar. Your credit card has a balance of $\$ 3400$ and an annual interest rate of $12 \%$ . $Y$ decide to pay off the balance over three years. If there are no further purchases charged to the card, a. How much must you pay each month? b. How much total interest will you pay? a. The monthly payments are approximately $\$$ $\square$ (Do not round until the final answer. Then round to the nearest dollar as needed.)

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Problem 3049

$6(x-9)=-36$

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Problem 3050

16) Solve the equation $\frac{-2}{x+3}=\frac{5}{x+1}$

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Problem 3051

Complete the expressions and select the missing property.
Write each answer as a number, a variable, or the product of a number and a variable. $\begin{aligned} & 7+7 u+5 \\ = & 7 u+\square+5 \\ = & 7 u+\square \end{aligned}$ Add

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Problem 3052

Solve for all values of x . $\left(\frac{1}{8}\right)^{-2 x-24}=\left(\frac{1}{2}\right)^{-2 x^{2}+4 x}$

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Problem 3053

Problem 4 Consider the successive gas phase reactions: $\begin{aligned} 3 \mathrm{~A}(\mathrm{~g}) & \rightleftharpoons 2 \mathrm{~B}(\mathrm{~g}) \\ \mathrm{B}(\mathrm{~g})+\mathrm{C}(\mathrm{~g}) & \rightleftharpoons \mathrm{D}(\mathrm{~g}) \end{aligned}$
The equilibrium constants for these reactions at 500. K are $K_{p, 1}=6.0932$ and $K_{c, 2}=10.0$ . a) What is the value of $K_{c}$ for the overall reaction at $500 . \mathrm{K}$ ? b) What is the value of $K_{p}$ for the overall reaction at $500 . \mathrm{K}$ ?

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Problem 3054

The position of the squirrel can be calculated using the function $p(t)=a t^{2}+b t+c$ .
What is the value of $a$ ?
What is the value of $b$ ?
What is the value of $c$ ?

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Problem 3055

Factor. $x^{2}+6 x-27$

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Problem 3056

Factor. $x^{2}+7 x+10$

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Problem 3057

Solve for $k$ . $\frac{-10}{k-4}=\frac{-3}{k+3}$
There may be 1 or 2 solutions. $k=$ $\square$ or $k=$ $\square$ Submit

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Problem 3058

Question
Factor. $x^{2}-8 x+15$

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Problem 3059

For $f(x)=x-\ln x$ , and $0.1 \leq x \leq 2$ , find the following. (a) Find the values of $x$ for which $f(x)$ has a local maximum.
Enter your answers in the increasing order. $\begin{array}{l} x=i \\ x=i \end{array}$ eTextbook and Media (b) Find the value of $x$ for which $f(x)$ has a local minimum. $x=\mathbf{i}$ eTextbook and Media (c) Find the value of $x$ for which $f(x)$ has a global maximum. $x=$ $\square$

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Problem 3060

Current Attempt in Progress
For $f(x)=x-\ln x$ , and $0.1 \leq x \leq 2$ , find the following. (a) Find the values of $x$ for which $f(x)$ has a local maximum.
Enter your answers in the increasing order. $\begin{array}{l} x=\mathbf{i}|l| \\ \hline x=i \end{array}$

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Problem 3061

For $f(x) = x - \ln x$ , and $0.1 \leq x \leq 2$ , find the value of $x$ for which $f(x)$ has a global minimum.
$x =$ $\square$

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Problem 3062

Divide. $\frac{1}{2} \div \frac{5}{8}=$ $\square$
Submit

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Problem 3063

3. Simplify this expression by combining the like terms. (Show your work below) $3 x^{2}+2 x^{2}+4 y-3+8 y$

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Problem 3064

6. $7 b^{2}-42 b+63=0$

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Problem 3065

3. For which of the following values of $\lambda$ and $\mu$ the system of equ $\begin{array}{l} x+y+z=6 \\ x+2 y+3 z=10 \\ x+2 y+\lambda z=\mu \end{array}$ has no solution a. $\lambda=3$ and $\mu \neq 10$ b. $\lambda \neq 3$ c. $\lambda \neq 3$ and $\mu=10$ d. $\lambda=3$ and $\mu=10$

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Problem 3066

Use long division to divide. $\left(x^{3}+4 x^{2}-3 x-16\right) \div(x-3)$

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Problem 3067

3. a) $\log x+\log (x-4)=1$

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Problem 3068

Factor out the Greatest Common Factor (GCF): $64 d^{5}-32 d^{2}$ $8 d\left(8 d^{4}-4 d\right)$ $32 d\left(2 d^{4}-d\right)$ $32 d^{2} \cdot 2 d^{3}-32 d^{2}$ $32 d^{2}\left(2 d^{3}-1\right)$

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Problem 3069

Use the properties of logarithms to write the following as a single logarithm. $\log (x)-\frac{1}{4} \log (z)+\frac{1}{2} \log (y)$

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Problem 3070

The movement of the progress bar moy be uneven because questions Find the error in the calculations below, if there is one: $\begin{array}{l} \text { Line }(1): 4 x^{3}+2 x^{2}-6 x+3 \\ \begin{array}{l} \text { Line }(2):=2 x^{2}(2 x+1)-3(2 x+1) \\ \text { Line (3): }=2 x^{2}(2 x+1)+(-3)(2 x+1) \\ \text { Line }(4):=\left(2 x^{2}-3\right)(2 x+1) \end{array} \end{array}$ There are no errors. The error occurred from line (2) to line (3). The error occurred from line (3) to line (4). The enror occurred from line (1) to line (2).

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Problem 3071

Find an equation for the inverse function. $\begin{array}{l} f(x)=\log (x-8)+4 \\ f^{-1}(x)=\square \end{array}$ $\square$ $\square \log \square$

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Problem 3072

Suppose $M$ is the midpoint of $\overline{F G}$ . Find the missing measure. $\begin{array}{l} F G=11 x-15.6, M G=10.9 \\ x=\square \end{array}$

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Problem 3073

12. The sequence described by the explicit rule: $f(n)=42-7(n-1)$ \begin{tabular}{l|l} $n$ & $f(x)$ \\ \hline 1 & 42 \\ 2 & 35 \\ 3 & 28 \\ 4 & 21 \end{tabular}
First five terms of the sequence: Domain: $\{1,2,3,4\}$ Range: x - Intercept(s): y - Intercept(s): Interval(s) of increase: non- Interval(s) of decrease: Discrete Continuous/Discontinuous:

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Problem 3074

Find the error in the calculations below, if there is one: Line (1): $-3 y^{3}+9 y^{2}+30 y$ Line (2): $=-3 y\left(y^{2}-3 y-10\right)$ Line (3): $=-3 y\left(y^{2}-5 y+2 y-10\right)$ Line (4): $=-3 y(y(y-5)+2(y-5))$ Line (5): $=-3 y(y+2)(y-5)$ There are no errors. The error occurred from line (1) to line (2). The error occurred from line (3) to line (4). The error occurred from line (2) to line (3).

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Problem 3075

Evaluate the following expressions. Your answer must be an exact angle in radians and in the interval $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ . Example: Enter pi/6 for $\frac{\pi}{6}$ . (a) $\tan ^{-1}(1)=$ $\square$ (b) $\tan ^{-1}(0)=$ $\square$ (c) $\tan ^{-1}\left(\frac{\sqrt{3}}{3}\right)=$ $\square$ Question Help: Video 1 Video 2 Submit Question Jump to Answer

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Problem 3076

The spread of a highly contagious virus in a high school can be described by the logistic function $y=\frac{4500}{1+899 e^{-0.7 x}}$ where $x$ is the number of days after the virus is identified in the school and $y$ is the total number of people who are infected by the virus. (a) What is the upper limit of the number infected by the virus during this period? (b) How much time has gone by when 3000 people are infected? (Round to three decimal places) (c) How many people are infected when the disease is first diagnosed? (d) If you round the number of infect people to the nearest whole number, how long will it take for the maximum number of people to be infected (Round the number of days up to a whole number) (a) The upper limit of the number infected by the virus during the period is $\square$ (b) The number of days that have passed by when 3000 people are infected is $\square$ days (Round to three decimal places) (c) On the day of first diagnosis there are already $\square$ infections (d) Rounding to the nearest whole number, it will take $\square$ days for the maximum number of infections to be reached (Round the number of days up to a whole number)

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Problem 3077

Question 4
Use your calculator to evaluate $\cos ^{-1}(0.06)$ to at least 3 decimal places. Give the answer in radians.

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Problem 3078

Let $f(x)=\csc (g(x))$ . If $g(3)=\frac{1}{6} \pi \quad$ and $g^{\prime}(3)=1$ then determine $f^{\prime}(3)$ .
Your answer must be exact. Use sqrt(x) for $\sqrt{x}$ or switch to equation editor mode. $\begin{array}{l} a^{b} \quad \sin (a) \\ f^{\prime}(3)= \end{array}$

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Problem 3079

Solve for $x .(5 x+6)(3 x-6)=0$ $x=\frac{6}{5}$ or $x=-2$ $x=0$ $x=\frac{-6}{5}$ or $x=2$ $x=-6$ or $x=6$

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Problem 3080

Find the absolute maximum and minimum values of: $f(x)=x^{3}+3 x^{2}-9 x-7 \text { on }[-6,4]$

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Problem 3081

b. $y=\log _{6}(x) \Rightarrow \frac{d y}{d x}=$

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Problem 3082

Simplify the following expression: $4^{\log _{4}(6 \sqrt{3})}$ $6 \sqrt{3}$ $-6 \sqrt{3}$ $4^{6 \sqrt{3}}$ $-4$
4 None of the above

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Problem 3083

$\left(\frac{1}{81}\right)^{2}$

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Problem 3084

Factor the expression by grouping: $2 x^{2}-14 x+3 x-21$ $(2 x+7)(x-3)$ $(2 x-7)(x+3)$ $(2 x+3)(x-7)$ $(2 x-3)(x+7)$

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Problem 3085

Match each equation on the left with its solution on the right. No answer on the right will be used twice. $\begin{array}{l} 2 x+3(x-2)=6(x+1)+x \\ 2 x+3(x-2)=6(x-1)-x \\ 2 x+3(x-2)=6(x-1)+x \\ 2 x+3(x-1)=6(x-1)-x \end{array}$ $x=0$
No solution $x=-6$
All real numbers
Clear Click and hold an item in one column, then drag it to the matching item in the other column. Be sure your target before releasing. The target will highlight or the cursor will change. Need help? Watch this video.

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Problem 3086

e) $(3 x-11)(2 x+1)$

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Problem 3087

The following equation is given. Complete parts (a)-(c). $x^{3}-3 x^{2}-4 x+12=0$ a. List all rational roots that are possible according to the Rational Zero Theorem. $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12$ (Use a comma to separate answers as needed.) b. Use synthetic division to test several possible rational roots in order to identify one actual root.
One rational root of the given equation is $\square$ (Simplify your answer.)

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Problem 3088

Factor. $27-u^{3}$

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Problem 3089

Find all roots of the polynomial equation. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first root. $2 x^{4}-11 x^{3}+27 x^{2}-66 x+90=0$
The solution set of the equation $2 x^{4}-11 x^{3}+27 x^{2}-66 x+90=0$ is $\square$ (Use a comma to separate answers as needed. Type an exact answer, uling radicals and $i$ as needed. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

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Problem 3090

3. Solve the inequality below. $0.6 y-2.3 \geq 6.1$

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Problem 3091

3 Fill in the Blank 5 points $-4 x^{2}+10 x+14=0$
Write the factored form of the quadratic expression. type you answer... type your answer... type your Solve for $x$ . $\mathrm{x}=$ type your answer... type your answer...

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Problem 3092

6. Factor each express a) $x^{2}-121$

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Problem 3093

6. Determine whether the equations below have one solution, no solution, or infinitely many solutions. \begin{tabular}{|l|c|c|c|} \hline & One solution & Not Solution & \begin{tabular}{c} Infinitely Many \\ Solutions \end{tabular} \\ \hline $-10 y+18=-3(5 y-7)+5 y$ & $\square$ & $\square$ & $\square$ \\ \hline $3(a+2)-2 a=\frac{1}{7}(-7 a+42)$ & $\square$ & $\square$ & $\square$ \\ \hline $-4 y-3=\frac{1}{3}(12 y-9)-8 y$ & $\square$ & $\square$ & $\square$ \\ \hline \end{tabular}

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Problem 3094

Find the second-order partial derivative. Find $f_{x y}$ when $f(x, y)=10 x^{2} y^{4}-7 x^{3} y^{5}$ . $160 x y^{3}-21 x^{2} y^{4}$ $80 x y^{3}-21 x^{2} y^{4}$ $80 x y^{3}-105 x^{2} y^{4}$ $160 x y^{3}-105 x^{2} y^{4}$

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Problem 3095

The $x$ coordinate of the vertex is: $x=\frac{-b}{2 a}$ True False

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Problem 3096

$\underline{27}, \underline{28}, \underline{29}, \underline{30}, \underline{31}, \underline{32}, \underline{33}, \underline{34}, \underline{35}$ , and $\underline{36}$ Use implicit differentiation to find an equation of the tangent line the curve at the given point.
27. $y e^{\sin x}=x \cos y,(0,0)$
Answer

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Problem 3097

Compute each of the following indefinite integrals. (a) $\int \frac{1}{(3 x+7)^{7}} d x=$ $\square$ $+C$ (b) $\int \frac{1}{3 x+7} d x=$ $\square$ $+C$

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Problem 3098

التبرين الثراي: (07 نقاطم)

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Problem 3099

Find the equation of the tangent line to $y=2^{x^{2}-3 x+1}$ at $x=4$ . $y=$

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Problem 3100

(5 Points) If a proton $\left(m_{p}=1.67 \times 10^{-27} \mathrm{~kg}\right)$ has a de Broglie wavelength of 14.5 nm , calculate the velocity of the proton.

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Math Statement

Problem 3001

Problem 3002

Problem 3003

Find an equation of the hyperbola having foci at (3,−1−45)(3,-1-\sqrt{45})(3,−1−45​) and (3,−1+45)(3,-1+\sqrt{45})(3,−1+45​) and asymptotes at y=2x−7y=2 x-7y=2x−7 and y=−2x+5y=-2 x+5y=−2x+5.

Problem 3004

Write the equation in exponential form. log⁡2(8)=3\log _{2}(8)=3log2​(8)=3

Problem 3005

1) 7(2+5v)=3v+147(2+5 v)=3 v+147(2+5v)=3v+14 (14+35v)=3v+(14+35 v)=3 v+(14+35v)=3v+

Problem 3006

Problem 3007

What is the slope of the line represented by the equation y=−12x+14y=-\frac{1}{2} x+\frac{1}{4}y=−21​x+41​ ? −12-\frac{1}{2}−21​ −14-\frac{1}{4}−41​ 14\frac{1}{4}41​ 12\frac{1}{2}21​

Problem 3008

Problem 3009

Problem 3010

Problem 3011

7 Solve this equation a=2 b=3c=7\mathrm{a}=2 \quad \mathrm{~b}=3 \quad \mathrm{c}=7a=2 b=3c=7 ∣ax−b∣≤c|a x-b| \leq c∣ax−b∣≤c

Problem 3012

Problem 3013

0=x2+24x−340=x^{2}+24 x-340=x2+24x−34

Problem 3014

2 State whether or not this parabola has a maximum or minimum, then state yyy-value of the max⁡\maxmax or min⁡.y=−(x+64)∧2−199\min . \quad \mathrm{y}=-(\mathrm{x}+64)^{\wedge} 2-199min.y=−(x+64)∧2−199

Problem 3015

231) y=(2x3−x2+6x+1)3y=\left(2 x^{3}-x^{2}+6 x+1\right)^{3}y=(2x3−x2+6x+1)3

Problem 3016

Expand and fully simplify (4p+3)(2p+5)+6(p+3)(4 p+3)(2 p+5)+6(p+3)(4p+3)(2p+5)+6(p+3)

Problem 3017

Find dydx\frac{d y}{d x}dxdy​ by implicit differentiation, if x2+y2=4x^{2}+y^{2}=4x2+y2=4, dydx=\frac{d y}{d x}=dxdy​= □\square□

Problem 3018

In △FGH,f=200 cm,g=880 cm\triangle \mathrm{FGH}, f=200 \mathrm{~cm}, g=880 \mathrm{~cm}△FGH,f=200 cm,g=880 cm and ∠H=149∘\angle \mathrm{H}=149^{\circ}∠H=149∘. Find the length of hhh, to the nearest centimeter.Answer Attempt 4 out of 100 Submit Answer

Problem 3019

Problem 3020

Find the Least Common Denominator of the fractions: 1/61 / 61/6 and 3/53 / 53/5 6 5 30 12

Problem 3021

37x−6=38=4x3^{7 x-6}=3^{8=4 x}37x−6=38=4x

Problem 3022

25x+15x\frac{2}{5 x}+\frac{1}{5 x}5x2​+5x1​

Problem 3023

2−4×2−32^{-4} \times 2^{-3}2−4×2−3 A. 1128\frac{1}{128}1281​ B. 1256\frac{1}{256}2561​ C. 14\frac{1}{4}41​ D. 116\frac{1}{16}161​

Problem 3024

9(−2)=∣3x−x3∣9(-2)=\left|3 x-x^{3}\right|9(−2)=∣∣​3x−x3∣∣​

Problem 3025

(5mn4)3÷(5m3n)4\left(5 m n^{4}\right)^{3} \div\left(5 m^{3} n\right)^{4}(5mn4)3÷(5m3n)4 A. n85m9\frac{n^{8}}{5 m^{9}}5m9n8​ B. 5m9n8\frac{5}{m^{9} n^{8}}m9n85​ C. 15m9n8\frac{1}{5 m^{9} n^{8}}5m9n81​ D. 5m9n85 m^{9} n^{8}5m9n8

Problem 3026

Problem 3027

Subtract. −8a+11b3a−8a−8b3a-\frac{8 a+11 b}{3 a}-\frac{8 a-8 b}{3 a}−3a8a+11b​−3a8a−8b​Simplify your answer as much as possible.

Problem 3028

Solve for the roots in simplest form using the quadratic formula: 3x2+15=6x3 x^{2}+15=6 x3x2+15=6xAnswer Attempt 1 out of 2

Problem 3029

Solve for yyy. 4+7y=534+\frac{7}{y}=\frac{5}{3}4+y7​=35​Simplify your answer as much as possible. y=y=y=

Problem 3030

Find dydx\frac{d y}{d x}dxdy​ by implicit differentiation. ey=4x−8ye^{y}=4 x-8 yey=4x−8yAnswer: dydx=\frac{d y}{d x}=dxdy​=

Problem 3031

Subtract. 13a+28a−3a8a\frac{13 a+2}{8 a}-\frac{3 a}{8 a}8a13a+2​−8a3a​Simplify your answer as much as possible.

Problem 3032

Consider the function g(x)=4−2x2g(x)=4-2 x^{2}g(x)=4−2x2 a. Find g(2)g(2)g(2) and g(−1)g(-1)g(−1)

Problem 3033

Factor. r2−81r^{2}-81r2−81Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. r2−81=r^{2}-81=r2−81= □\square□ (Factor completely.) B. The polynomial is prime.

Problem 3034

Factor. s2−36s^{2}-36s2−36Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. s2−36=s^{2}-36=s2−36= □\square□ (Factor completely.) B. The polynomial is prime.

Problem 3035

Factor completely. b2−d2b^{2}-d^{2}b2−d2Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. b2−d2=b^{2}-d^{2}=b2−d2= □\square□ B. The binomial is not factorable.

Problem 3036

2. Consider the function g(x)=4−2x2g(x)=4-2 x^{2}g(x)=4−2x2 a. Find g(2)g(2)g(2) and g(−1)g(-1)g(−1) g(2)=−4g(−1)=2\begin{array}{l} g(2)=-4 \\ g(-1)=2 \end{array}g(2)=−4g(−1)=2​ b. Find the value(s) of xxx such that g(x)=−14g(x)=-14g(x)=−143 and -3 c. Find g(2x)g(2 x)g(2x)

Problem 3037

Diviaing rational expressions involving linear expressionsDivide. 2x+14x+3÷6x+425x+15\frac{2 x+14}{x+3} \div \frac{6 x+42}{5 x+15}x+32x+14​÷5x+156x+42​Simplify your answer as much as possible.

Problem 3038

Convert the given unit of weight to the unit indicated. 7.4 dg to mg 7.4dg=□mg7.4 \mathrm{dg}=\square \mathrm{mg}7.4dg=□mg

Problem 3039

Convert the given unit of weight to the unit indicated. 540mg to g540mg=□g\begin{array}{r} 540 \mathrm{mg} \text { to } \mathrm{g} \\ 540 \mathrm{mg}=\square \mathrm{g} \end{array}540mg to g540mg=□g​ □\square□ g

Problem 3040

Problem 3041

Simplify this expression: (4x3y−4)−2\left(4 x^{3} y^{-4}\right)^{-2}(4x3y−4)−2.

Problem 3042

Problem 3043

Problem 3044

Problem 3045

Problem 3046

Problem 3047

349. 9709 m22_qp_12 Q: 11It is given that a curve has equation y=k(3x−k)−1+3xy=k(3 x-k)^{-1}+3 xy=k(3x−k)−1+3x, where kkk is a constant. (a) Find, in terms of kkk, the values of xxx at which there is a stationary point.

Find an equation of the hyperbola having foci at $(3,-1-\sqrt{45})$ and $(3,-1+\sqrt{45})$ and asymptotes at $y=2 x-7$ and $y=-2 x+5$ .

Write the equation in exponential form. $\log _{2}(8)=3$

1) $7(2+5 v)=3 v+14$ $(14+35 v)=3 v+$

What is the slope of the line represented by the equation $y=-\frac{1}{2} x+\frac{1}{4}$ ? $-\frac{1}{2}$ $-\frac{1}{4}$ $\frac{1}{4}$ $\frac{1}{2}$

7 Solve this equation $\mathrm{a}=2 \quad \mathrm{~b}=3 \quad \mathrm{c}=7$ $|a x-b| \leq c$

$0=x^{2}+24 x-34$

2 State whether or not this parabola has a maximum or minimum, then state $y$ -value of the $\max$ or $\min . \quad \mathrm{y}=-(\mathrm{x}+64)^{\wedge} 2-199$

231) $y=\left(2 x^{3}-x^{2}+6 x+1\right)^{3}$

Expand and fully simplify $(4 p+3)(2 p+5)+6(p+3)$

Find $\frac{d y}{d x}$ by implicit differentiation, if $x^{2}+y^{2}=4$ , $\frac{d y}{d x}=$ $\square$

In $\triangle \mathrm{FGH}, f=200 \mathrm{~cm}, g=880 \mathrm{~cm}$ and $\angle \mathrm{H}=149^{\circ}$ . Find the length of $h$ , to the nearest centimeter.
Answer Attempt 4 out of 100 Submit Answer

Find the Least Common Denominator of the fractions: $1 / 6$ and $3 / 5$ 6 5 30 12

$3^{7 x-6}=3^{8=4 x}$

$\frac{2}{5 x}+\frac{1}{5 x}$

$2^{-4} \times 2^{-3}$ A. $\frac{1}{128}$ B. $\frac{1}{256}$ C. $\frac{1}{4}$ D. $\frac{1}{16}$

$9(-2)=\left|3 x-x^{3}\right|$

$\left(5 m n^{4}\right)^{3} \div\left(5 m^{3} n\right)^{4}$ A. $\frac{n^{8}}{5 m^{9}}$ B. $\frac{5}{m^{9} n^{8}}$ C. $\frac{1}{5 m^{9} n^{8}}$ D. $5 m^{9} n^{8}$

Subtract. $-\frac{8 a+11 b}{3 a}-\frac{8 a-8 b}{3 a}$
Simplify your answer as much as possible.

Solve for the roots in simplest form using the quadratic formula: $3 x^{2}+15=6 x$
Answer Attempt 1 out of 2

Solve for $y$ . $4+\frac{7}{y}=\frac{5}{3}$
Simplify your answer as much as possible. $y=$

Find $\frac{d y}{d x}$ by implicit differentiation. $e^{y}=4 x-8 y$
Answer: $\frac{d y}{d x}=$

Subtract. $\frac{13 a+2}{8 a}-\frac{3 a}{8 a}$
Simplify your answer as much as possible.

Consider the function $g(x)=4-2 x^{2}$ a. Find $g(2)$ and $g(-1)$

Factor. $r^{2}-81$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $r^{2}-81=$ $\square$ (Factor completely.) B. The polynomial is prime.

Factor. $s^{2}-36$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $s^{2}-36=$ $\square$ (Factor completely.) B. The polynomial is prime.

Factor completely. $b^{2}-d^{2}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $b^{2}-d^{2}=$ $\square$ B. The binomial is not factorable.

2. Consider the function $g(x)=4-2 x^{2}$ a. Find $g(2)$ and $g(-1)$ $\begin{array}{l} g(2)=-4 \\ g(-1)=2 \end{array}$ b. Find the value(s) of $x$ such that $g(x)=-14$
3 and -3 c. Find $g(2 x)$

Diviaing rational expressions involving linear expressions
Divide. $\frac{2 x+14}{x+3} \div \frac{6 x+42}{5 x+15}$
Simplify your answer as much as possible.

Convert the given unit of weight to the unit indicated. 7.4 dg to mg $7.4 \mathrm{dg}=\square \mathrm{mg}$

Convert the given unit of weight to the unit indicated. $\begin{array}{r} 540 \mathrm{mg} \text { to } \mathrm{g} \\ 540 \mathrm{mg}=\square \mathrm{g} \end{array}$ $\square$ g

Simplify this expression: $\left(4 x^{3} y^{-4}\right)^{-2}$ .

349. 9709 m22_qp_12 Q: 11
It is given that a curve has equation $y=k(3 x-k)^{-1}+3 x$ , where $k$ is a constant. (a) Find, in terms of $k$ , the values of $x$ at which there is a stationary point.

$6(x-9)=-36$

16) Solve the equation $\frac{-2}{x+3}=\frac{5}{x+1}$

Complete the expressions and select the missing property.
Write each answer as a number, a variable, or the product of a number and a variable. $\begin{aligned} & 7+7 u+5 \\ = & 7 u+\square+5 \\ = & 7 u+\square \end{aligned}$ Add

Solve for all values of x . $\left(\frac{1}{8}\right)^{-2 x-24}=\left(\frac{1}{2}\right)^{-2 x^{2}+4 x}$

The position of the squirrel can be calculated using the function $p(t)=a t^{2}+b t+c$ .
What is the value of $a$ ?
What is the value of $b$ ?
What is the value of $c$ ?

Factor. $x^{2}+6 x-27$

Factor. $x^{2}+7 x+10$

Solve for $k$ . $\frac{-10}{k-4}=\frac{-3}{k+3}$
There may be 1 or 2 solutions. $k=$ $\square$ or $k=$ $\square$ Submit

Question
Factor. $x^{2}-8 x+15$

For $f(x) = x - \ln x$ , and $0.1 \leq x \leq 2$ , find the value of $x$ for which $f(x)$ has a global minimum.
$x =$ $\square$

Divide. $\frac{1}{2} \div \frac{5}{8}=$ $\square$
Submit

3. Simplify this expression by combining the like terms. (Show your work below) $3 x^{2}+2 x^{2}+4 y-3+8 y$

6. $7 b^{2}-42 b+63=0$

Use long division to divide. $\left(x^{3}+4 x^{2}-3 x-16\right) \div(x-3)$

3. a) $\log x+\log (x-4)=1$

Use the properties of logarithms to write the following as a single logarithm. $\log (x)-\frac{1}{4} \log (z)+\frac{1}{2} \log (y)$

Find an equation for the inverse function. $\begin{array}{l} f(x)=\log (x-8)+4 \\ f^{-1}(x)=\square \end{array}$ $\square$ $\square \log \square$

Suppose $M$ is the midpoint of $\overline{F G}$ . Find the missing measure. $\begin{array}{l} F G=11 x-15.6, M G=10.9 \\ x=\square \end{array}$