Math Statement

Problem 3101

If $2+e^{3 x}=4$ , then solve for $x$ . Note: Round your answer to 2 decimal points and do not include any special characters. For example, if your answer is .1234, enter it as . 12. $\square$

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Problem 3102

$27,28,29,30,31,32,33,34,35$ , and 36 Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
33. $x^{2}+y^{2}=\left(2 x^{2}+2 y^{2}-x\right)^{2},\left(0, \frac{1}{2}\right)$ (cardioid)

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Problem 3103

$\underline{27}, \underline{28}, \underline{29}, \underline{30}, \underline{31}, \underline{32}, \underline{33}, \underline{34}, \underline{35}$ , and $\underline{36}$ Use implicit differentiation to find an equation of the tangent line to the curve at the given point. 3.
31. $x^{2}-x y-y^{2}=1,(2,1)$ (hyperbola) Answer 4

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Problem 3104

In Exercises 3 and 4 , solve for $y$ in terms of $x$ .
3. $\frac{y^{2}}{9}+\frac{x^{2}}{4}=1$
4. $\frac{x^{2}}{36}+\frac{y^{2}}{25}=1$

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Problem 3105

a. Rewrite the equation $4 x+y+3=0$ in slope-intercept form. b. Give the slope and $y$ -intercept. c. Use the slope and $y$ -intercept to graph the linear function. a. The slope-intercept form of the equation is $\square$ (Simplify your answer. Use integers or fractions for any numbers in the equation.) b. The slope of the equation of the line is $\square$ and the $y$ -intercept is $\square$ . (Type integers or fractions.)

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Problem 3106

Find $R$ and $\theta$ given the components $R_{x}=17.57$ and $R_{y}=6.94$ . $\mathrm{R}=\square$ (Round to the nearest hundredth as needed.)

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Problem 3107

$y=\frac{x-5}{x^{2}-25}$

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Problem 3108

Factor the expression $x^{3} + 3x^{2} - 54x$ .

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Problem 3109

11. $\left(x^{2}-8 x+15\right) \div(x-3)$ $x-5$

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Problem 3110

Complete the table. \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ $f(x)=-|x|+1$ } \\ \hline $x$ & $f(x)$ \\ \hline-5 & $\square$ \\ \hline-3 & $\square$ \\ \hline-1 & $\square$ \\ \hline 1 & $\square$ \\ \hline \end{tabular}

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Problem 3111

Factor the expression $x^{3}-3x^{2}-40x$ .

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Problem 3112

Complete the table. \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ $f(x)=-6|x|+3$ } \\ \hline $x$ & $f(x)$ \\ \hline-1 & $\square$ \\ \hline 0 & $\square$ \\ \hline 1 & $\square$ \\ \hline 2 & $\square$ \\ \hline \end{tabular}

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Problem 3113

11) $\frac{-4(-5)+4}{-1(-4-2)}$

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Problem 3114

XERCICE 1: 6 points À l'aide des théorémes de comparaison, étudier les limites suivantes: a) $\lim _{x \rightarrow+\infty} \frac{x-\sin (x)}{2+\sin (x)}(1,5 \mathrm{pt})$ b) $\lim _{x \rightarrow-\infty} \frac{\cos (x)-x}{2 x+1}(1,5 \mathrm{pt})$

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Problem 3115

Use elimination to solve each system below.
System 1 System 2 $\begin{array}{ll} 3 x-4 y=6 & 3 x-4 y=-3 \\ x+4 y=18 & 4 x-3 y=10 \end{array}$
Enter the values of $x$ and $y$ in the solution for each system in the following tabl \begin{tabular}{|c|c|} \hline \multirow[b]{2}{*}{System 1} & value of $y$ \\ \hline & \\ \hline System 2 & \\ \hline \end{tabular}

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Problem 3116

1. Find the general solution of the following differential equation by the method of undetermined coefficients: $y^{\prime \prime}+2 y^{\prime}-24 y=16-(x+2) e^{4 x}$

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Problem 3117

4. What is the standard form of the equation below? $y=3(x-2)^{2}-5$
Standard Form: $f(x)=a x^{2}+b x+c$

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Problem 3118

Consider the following. $y=\frac{1}{3} \sec (x)$
Find the period. $\square$ Give the equations for two consecutive vertical asymptotes for the graph of the function. (Enter your ans $\square$ $x=\square$

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Problem 3119

Find the error in the calculations below, if there is one: $\begin{array}{l} \text { Line (1): }-6 x+8>-22 \\ \text { Line (2): }-6 x>-30 \\ \text { Line (3): } x<5 \\ \text { Line (4): } \end{array}$ There is no error. The error occurred from line (2) to line (3). The error occurred from line (3) to line (4). The error occurred from line (1) to line (2).

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Problem 3120

Solve for $h$ . $-3(3 h-1) \leq-7 h-5$ $h \leq 4$ $h \geq 1$ $h \geq 4$ $h \leq-\frac{1}{10}$

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Problem 3121

Solve for $x: 2|2 x-4|-5=-3$ No solution. $x=\frac{5}{2}$ or $x=\frac{3}{2}$ $x=\frac{15}{4}$ or $x=\frac{21}{4}$ $x=\frac{5}{2}$ or $x=4$

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Problem 3122

Factor the trinomial completely. $21 y^{2}-46 y+25$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice, A. $21 y^{2}-46 y+25=$ $\square$ (Factor completely.) B. The polynomial is prime.

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Problem 3123

Factor the trinomial, or state that the trinomial is prime. Check the factorization using FOIL multiplication. $10 x^{2}-29 x y+10 y^{2}$
Select the correct choice below and fill in any answer boxes within your choice. A. $10 x^{2}-29 x y+10 y^{2}=$ $\square$ B. The polynomial is prime.

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Problem 3124

Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) $\cos [\arccos (-\sqrt{2})]$

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Problem 3125

movement of the progress bar may be uneven because qu Evaluate the expression $2 x^{2}-y^{1}+3 x^{0}$ for $x=4$ and $y=7$ . 28 60 97 15

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Problem 3126

9. $f(x)=4 x^{4}-17 x^{2}+4$ \begin{tabular}{|l|l|} \hline zero(s): & $y$ -intercept: \\ \hline \end{tabular}

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Problem 3127

10. For $n \geq 1$ , establish that the integer $n\left(7 n^{2}+5\right)$ is of the form $6 k$ .
11. If $n$ is an odd integer, show that $n^{4}+4 n^{2}+11$ is of the form $16 k$ .

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Problem 3128

Simplify the expression. $\left(4 a b^{3}\right)^{2}\left(-3 a^{5}\right)$ $-12 a^{6} b^{6}$ $-12 a^{7} b^{6}$ $-48 a^{10} b^{6}$ $-48 a^{7} b^{6}$

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Problem 3129

Factor the trinomial $4x^2 + 8x - 5$ .

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Problem 3130

For which of the following equations is the value of $x$ equal to 10 ? Select all that apply. A) $x+10=20$ B) $10 x=10$ C) $20 \div x=2$ D) $4 x=10$ E) $20-x=10$

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Problem 3131

Is $50,-50,20$ , or -20 the solution of the equation $15=c-35$ ?

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Problem 3132

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. Assume that the variables represent positive real numbers. $\log _{2}\left(\frac{1}{4} m n^{3}\right)=\square$

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Problem 3133

Multiply. $(5 y-4)(7 y+5)$
Simplify your answer.

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Problem 3134

$\begin{array}{l} f(x)=2 x^{2}-5 x-3 \\ g(x)=2 x^{2}+5 x+2 \end{array}$
Find: $\left(\frac{f}{g}\right)(x)$ $\frac{x+3}{x+2}$ $\frac{x-3}{x+2}$ $x^{2}-1 x-\frac{3}{2}$ $\frac{2 x^{2}-5 x-3}{2 x^{2}+5 x+2}$

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Problem 3135

Read the following description of a relationship:
An electronics store has 19 permanent employees who work all year. The store also hires some temporary employees to work during the busy holiday shopping season.
Let a represent the number of temporary employees and $b$ represent the total number of employees during the holiday shopping season.
Complete the table using the function $b=a+19$ . \begin{tabular}{|c|c|} \hline $a$ & $b$ \\ \hline 1 & $\square$ \\ \hline 3 & $\square$ \\ \hline 5 & 24 \\ \hline 7 & $\square$ \\ \hline \end{tabular}
Save answer

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Problem 3136

Multiply. $(4-3 y)(4+3 y)$
Simplify your answer.

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Problem 3137

2. Solve the following equation for Real Number (s) $x$ $\frac{1}{3 x+5}-\frac{2}{5 x-3}=0$

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Problem 3138

lue for the following expression $\log _{4}(576)+\log _{4}(16)-2 \log _{4}(6)=$

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Problem 3139

Evaluate $x^{2}-2 x+3$ when $x=-3$ 3 0 6 18

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Problem 3140

Simplify: $11 y^{2}+12 y-6 y^{2}-8 y+5 y^{9}$ $9 y^{2}+5$ $5 y^{2}+4 y+5$ $5 y^{2}+4 y+1$ $5 y^{2}+9 y$

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Problem 3141

$f(x)=-x^{2}-2 x-5$
The function has $\square$
Axis of Symmetry: $\square$
Vertex: $\square$
Domain: $\square$ Range: $\square$

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Problem 3142

$x$ and choose the correct solution: $x+5 \geq-1$ $x \geq-4$
$x \geq-6$ $x \geq 4$
$x \geq-6$

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Problem 3143

Prove the triangles below are congruent.
Given: $\angle B \cong \angle D, A C \cong C E$ Prove: $\triangle \mathrm{ACB} \cong \triangle \mathrm{ECD}$ 1) $\angle B \cong \angle D, A C \cong C E$ Given 2) $\angle A C B \cong \angle E C D$ [Choose] 3) $\triangle \mathrm{ACB} \cong \triangle E C D$ [Choose ]

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Problem 3144

(b) $f(x)=-x+3$ $\begin{array}{l} g(x)=x+3 \\ f(g(x))=\square \\ g(f(x))=\square \end{array}$ $f$ and $g$ are inverses of each other $f$ and $g$ are not inverses of each other

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Problem 3145

Solve for $a$ . $-6 a+45 \leq 3$ $a \geq 7$ $a \geq-7$ $a \geq-8$ $a \leq 7$

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Problem 3146

(a) $f(x)=\frac{x+7}{2}$ $\begin{array}{l} g(x)=2 x-7 \\ f(g(x))=\square \\ g(f(x))=\square \end{array}$ $f$ and $g$ are inverses of each other $f$ and $g$ are not inverses of each other

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Problem 3147

Find the amplitude, period, and phase shift of the given function. $y=0.4 \cos 0.2\left(x+\frac{\pi}{10}\right)$
The amplitude is $\square$ (Type an exact answer, using $\pi$ as needed. Use integers or decimal

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Problem 3148

Multiply. State the product in simplest form. $\frac{4}{9 k^{5}} \cdot \frac{3 k^{3}}{8}, k \neq 0$ $\frac{1}{25 x^{8}}$ $\frac{1}{6 k^{2}}$ $\frac{1}{60 k^{2}}$ $\frac{1}{6 \mathrm{k}^{8}}$

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Problem 3149

The movement of the progress bar may be Subtract. State the difference in simplest form. $\frac{7}{4 m}-\frac{4}{3 n}$ $\frac{1}{4 m n}$ $\frac{21 n-16 m}{12 m n}$ $\frac{3}{4 m-3 n}$ $\frac{7 m-3 n}{3 m n}$

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Problem 3150

1. What is the equation, center, and radius of the circle? $\begin{array}{l} x^{2}+2 x+y^{2}+6 y-7=0 \\ x^{2}+2 x+y^{2}+6 y=7 \\ x^{2}+2 x+17 y^{2}+6 y=7+1 \\ (x+1)^{2}+y^{2}+6 y=8 \\ (x+1)^{2}+y^{2}+6 y+9<8+9 \\ (x+1)^{2}+(y+3)^{2}=17 \end{array}$

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Problem 3151

Fer was - 42, Solle the equnsien by -Cempleting the Square". (39) $x^{2}+8 x+3=0$ $\begin{array}{r} x^{2}+8 x+16=-5+16 \\ (x+4)^{2}=11 \end{array}$
Solutions: $\qquad$ 41) $7 x^{2}-18 x=14+10 x$ $8-\frac{1}{2}=9$ $(4)^{2}=16$ 90) $\frac{4 x^{2}}{4}-\frac{56 x}{4}-\frac{20}{4}=\frac{0}{4}$ $\begin{array}{cc} x^{2}-14 x-5=0 & -14-\frac{1}{2}=7 \\ x^{2}-14 x=5 & (-7)^{2}=49 \\ x-7=1 \sqrt{54} & x^{2}-14 x+49=5 x 49 \\ (x-7)^{2}=54 \end{array}$
Solutions: $\qquad$ 42) $\mathrm{x}^{2}-12 \mathrm{x}=-44$
Solutions: $\qquad$ Solutions: $\qquad$

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Problem 3152

The function $g$ is defined as follows for the domain given. $g(x)=2-2 x, \quad \text { domain }=\{-3,-2,1,5\}$
Write the range of $g$ using set notation. Then graph $g$ . $\text { range }=\{8,6,0,-8\}$

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Problem 3153

The function $h$ is defined as follows for the domain given. $h(x)=1-2 x, \quad \text { domain }=\{-1,0,1,2\}$
Write the range of $h$ using set notation. Then graph $h$ . range =

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Problem 3154

(1 pt) Find the inflection points of thefunction $f(x)=e^{-x}\left(34-x^{2}\right)$ . INTERMEDIATE WORK $\begin{array}{l} f^{\prime}(x)=e^{\wedge}-x\left(x^{\wedge} 2-2 x-34\right) \\ f^{\prime \prime}(x)=e^{\wedge}-x\left(-x^{\wedge} 2+32\right) \end{array}$
On what intervals is $f$ concave upward? On what intervals is $f$ concave downward? $\square$ (Give your answer in interval notation, for example: [a,b) U (c,d]. If needed enter $-\infty$ as - infinity and $\infty$ as infinity. ) FINAL ANSWER Inflection points of $f(x)$ are $\square$ (Give your answer as a comma separated list, for example: $\mathbf{a}, \mathbf{b}, \ldots$ )

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Problem 3155

Write the following function in the form $\mathrm{y}=\mathrm{a} \sin [\mathrm{b}(\mathrm{x}-\mathrm{c})]$ . Find the period and phase shift. $y=4 \boldsymbol{\operatorname { s i n }}(2 \pi x+10)$
Write the given function in the form $y=a \sin [b(x-c)]$ . $\mathrm{y}=\square \sin [\square(\mathrm{x}-(\square))]$

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Problem 3156

Convert the following expressions between exponential and logarithmic form. a. $2401=7^{4}$ [1 mark] b. $\quad a=\log _{\mathrm{b}} c$ [1 mark]

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Problem 3157

Solve for $x$ . $\begin{array}{l} 4^{x}=21 \\ x=2.192 \end{array}$ (Type an intejer or a decimal. Round to four decimal places as needed. Use a comma to separate answers as needed.

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Problem 3158

$\begin{array}{l}=\sin (\cos 6 x)+\sin 6 x \cos x \\ =\sin (x+6 x)=\sin 7 x\end{array}$

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Problem 3159

$\frac{1}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}=$

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Problem 3160

$\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}=$

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Problem 3161

$\frac{1}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

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Problem 3162

Express the function (or rule) in words. $f(x)=2 x+9$ Multiply by 9 , then add 2. Add 9, then square the result. Add 9, then multiply the result by 2 . Square, then add 9. Multiply by 2, then add 9.

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Problem 3163

Use the function to evaluate the indicated expressions and simplify. $\begin{array}{l} f(x)=27 x-6 \\ f\left(\frac{x}{3}\right)=\square \\ \frac{f(x)}{3}=\square \end{array}$

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Problem 3164

The number of new members joining Facebook each year in the period from 2005 to the middle of 2008 can be modeled by $m(t)=12 t^{2}-20 t+10 \text { million members per year }(0 \leq t \leq 3.5)$ where $t$ is time in years since the start of 2005.t What was the average number of new members joining Facebook each year from the start of 2005 to the start of $2007 ?$ $\square$ million members per year

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Problem 3165

43. [0.24/0.31 Points] DETAILS MYNOTES SCOLALG7 2.2.083. 3/100 Submissions Used PREVIOUS ANSWERS ASKYOUR TEACHER your answer in dollars.) $\left\{\begin{array}{ll} \square & \text { if } 0<x \leq 1 \\ \square & \text { if } 1<x \leq 2 \\ \square & \text { if } 2<x \leq 3 \\ \square & \text { if } 3<x \leq 3.5 \end{array}\right.$

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Problem 3166

8. Evaluate. Show work a) $-\frac{14}{15} \div \frac{21}{20}$ b) $\left(-1 \frac{2}{5}\right) \div\left(-2 \frac{5}{8}\right)$ a. $\qquad$ b. $\qquad$ 9. Evaluate. Show work. $-\frac{3}{8}-\frac{4}{5} \times \frac{3}{10} \div \frac{2}{5}$ $\frac{4}{b}+\frac{7}{c}$ $\begin{array}{l} =\frac{4}{b} \times \frac{\square}{\square}+\frac{7}{c} \times \frac{\square}{\square} \\ =\frac{4 c}{b c}+\frac{7 b}{b c} \\ =\frac{\square+\square}{b c} \end{array}$
9. $\qquad$

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Problem 3167

16. Use the quadratic formula to find the roots (answers). $3 x^{2}-5 x+3=0$

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Problem 3168

4. State the Quadratic formula and use it to solve the equation: $3 x^{2}+8 x+6=0$

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Problem 3169

Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model: $P(t)=\frac{d}{1+k e^{-c t}}$ where $c, d$ , and $k$ are positive constants. For a certain fish population in a small pond $d=1400, k=13, c=0.2$ , and $t$ is measured in years. The fish were introduced into the pond at time $t=$ (a) How many fish were originally put in the pond?
100 $\qquad$ fish (b) Find the population after 10, 20, and 30 years. (Round your answers to the nearest whole number.)
10 years $\square$ fish 20 years $\square$ fish 30 years 1356 $\square$ fish

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Problem 3170

$\sqrt{-50}$

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Problem 3171

Use Synthetic Division to determine each quotient (and remainder - if necessary). If possible, use the quotients to write the dividend in factored form and list all the zeros. If NOT possible with given divisor, write DNE for all applicable answers. Complete work must be shown for credit! $\left(x^{4}-5 x^{2}+4\right) \div(x+2)$
Quotient: $\square$ Factored Form: $\square$ Zeros: Select an answer $\vee$ $\square$

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Problem 3172

5. Classify each polynomial as a monomial, binomial, or trinomial. State the degree of the polynomial. $5 m^{2}$ Name: Select an answer $~ \sim$
Degree: $\square$ Add Work
Next Question

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Problem 3173

Use the rational zeros theorem to list all possible zeros of the function $f(x)=5 x^{3}+x^{2}+x+7$ . Enter the possible zeros separated by commas. You do not need to factor the polynomial. Add Work Next Question

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Problem 3174

Evaluate $w+(-x)-\frac{2}{3}$ where $w=-\frac{5}{9}$ and $x=\frac{4}{3}$

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Problem 3175

$\sum_{n=1}^{\infty} \frac{n^{3}}{n^{5}}=\frac{1}{n^{2}}$
Converge $\sum_{n=1}^{\infty} \frac{n^{3}-2 n^{2}+n-1}{n^{5}-2}$

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Problem 3176

Calculate the integral of $z e^{2 x+y}$ over the surface of the box with $0 \leq x \leq 4,0 \leq y \leq 9,0 \leq z \leq 8$ . (Express numbers in exact form. Use symbolic notation and fractions where needed.) $\iint_{S} z e^{2 x+y} d S=52 e^{17}-20 e^{9}-20 e^{8}-44$
Incorrect Answer

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Problem 3177

Evaluate $f(x)=-3 x+15$ when $x=-4, x=0$ , and $x=5$ .
When $x=-4, f(x)=$ $\square$ when $x=0, f(x)=$ $\square$ , and when $x=5, f(x)=$ $\square$ .

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Problem 3178

Differentiate the following function. $\begin{array}{l} f(x)=\frac{x-e^{-x}}{1+x e^{-x}} \\ f^{\prime}(x)=\square \end{array}$

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Problem 3179

COS 17ㅈ 12

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Problem 3180

LockDown Browser for Chrom chrome//seltings/adPrivacy Clever/Portal Big ldeas Math:Assessment bigideasmath.com/BIM/stu A. Amplify Curriculum Alexia Lopez Castro. Clever / Log in Alexia Lopez Castro
Determine whether each relation is a function.
Function Not A Function $:(1,2),(1,1),(2,0),(3,-1) \quad::(8,2),(7,2),(6,3),(5,4)$ Nov 15

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Problem 3181

Solve the following system of equations. $\begin{array}{l} x^{2}+y^{2}=16 \\ x+4 y=2 \end{array}$
What are ALL the solutions? Round to 3 decimal places. $\begin{array}{l} (\text { smaller } x \text { coordinate, } \mathrm{y} 1)=(\text { Number }), \text { Number }) \\ (\text { larger } \mathrm{x} \text { coordinate, } \mathrm{y} 2)=(\text { Number }) \end{array}$

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Problem 3182

Inbox-olivia.scales@mscs.us Quiz 4.5 - 4.6 labschool.pearson.com/Student/PlayerTest.aspx?testId=10297943 School Grades and Attenda... Schoology 2024-2025 - 4.6 Que
Determine the amplitude and period of each function. Then gra $y=3 \sin \frac{1}{2} x$ (Type an exact answer in terms of $\pi$ . Use integers or fractions Determine the graph of $y=3 \sin \frac{1}{2} x$ . A. B.

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Problem 3183

$\int \cos ^{3}(4 x) \sin (4 x) d x$

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Problem 3184

[-/1 Points] DETAILS MY NOTES POOLELINALG4 2.1.019.
Solve the given system by back substitution. (If your answer is dependent, use the parameters $s$ and $t$ as necessary.) $\begin{array}{r} x-2 y=1 \\ y=3 \\ {[x, y]=[\square]} \end{array}$ Need Help? Read It

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Problem 3185

luate the integral using the properti $\int_{-9}^{9} x\left(8 x^{2}+7\right)^{3} d x$

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Problem 3186

For the polynomial below, -1 is a zero. $h(x)=x^{3}-3 x^{2}-3 x+1$
Express $h(x)$ as a product of linear factors.

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Problem 3187

33. $\cos ^{6} x-\sin ^{6} x=\cos 2 x\left(1-\frac{1}{4} \sin ^{2} 2 x\right)$

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Problem 3188

Use the Fundamental Theorem to evaluate the definite integral exactly. $\int_{0}^{3} t^{3} d t=$ $\square$

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Problem 3189

$f(x) = \sqrt{x^{2}-4} + \sqrt{x^{2}+9}$

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Problem 3190

Differentiate the following function. $y=\frac{3 \ln (4 x)}{\sqrt{x}}$
$\frac{d}{d x}\left(\frac{3 \ln (4 x)}{\sqrt{x}}\right)=$ $\square$

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Problem 3191

Differentiate the function $y=\ln \left(2 x^{2}-7 x+1\right)$ $y^{\prime}=\frac{1}{\frac{d}{d x}\left[2 x^{2}-7 x+1\right]}$ D. $y^{\prime}=\frac{1}{2 x^{2}-7 x+1} \cdot \frac{d}{d x}\left[2 x^{2}-7 x+1\right]$ $y^{\prime}=$ $\square$

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Problem 3192

Differentiate the function $y=\left(x^{2}+9\right) \ln \left(x^{2}+9\right)$ $y^{\prime}=$

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Problem 3193

3. $h(x)=7-2 x$ $7-2(-9)=1$

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Problem 3194

Convert to Standard Form $y=\frac{2}{3} x-9$ $\square$ $\square$ $\square$ $\square$

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Problem 3195

Change to Standard Form: $y=-\frac{2}{3} x-4$ $\square$ $x$ $\square$ $+$ $\square$ $y=$ $\square$

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Problem 3196

1. A T-shirt at a department store costs $\$ 7.50$ . The total cost, in dollars, of $a$ T-shirts is given by the function $C(a)=7.5 a$ . a. Complete the table of values for 4 T -shirts. \begin{tabular}{|l|c|c|c|c|} \hline T-shirts & 1 & 2 & 3 & 4 \\ \hline Cost $(\$)$ & & & & \\ \hline \end{tabular} b. Determine the common difference. c. What does the variable $a$ represent? What are the reasonable domain values for $a$ ?

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Problem 3197

If $t$ is in years, and $t=0$ is January 1,2020 , worldwide energy consumption, $r$ , in exajoules ( $10^{18}$ joules) per year, ${ }^{1}$ is modeled by $r=583.9 e^{0.013 t}$ (a) Write a definite integral for the total energy use between the start of 2020 and the start of 2031.
Total energy used $=$ $\square$ $\square$ $d t$ exajoules

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Problem 3198

Differentiate the following function. $y=\frac{x^{4} \ln x}{4}$ D. $\frac{d}{d x}\left[\frac{x^{4} \ln x}{4}\right]=\frac{d}{d x}\left[\frac{x^{4}}{4}\right] \cdot \ln x+\frac{d}{d x}\left[\frac{x^{4}}{4}\right] \cdot \ln x$ $\frac{d}{d x}\left(\frac{x^{4} \ln x}{4}\right)=$ $\square$

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Problem 3199

Differentiate the following function. $y=\frac{4 \ln (3 x)}{\sqrt{x}}$ D. $\frac{d}{d x}\left[\frac{4 \ln (3 x)}{\sqrt{x}}\right]=\frac{v^{\wedge} d x^{[\cdots l \text { I } /]}}{(\sqrt{x})^{2}}$ $\frac{d}{d x}\left(\frac{4 \ln (3 x)}{\sqrt{x}}\right)=$

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Problem 3200

Differentiate the following function. $y=\frac{4 \ln (3 x)}{\sqrt{x}}$ $\frac{d}{d x}\left(\frac{4 \ln (3 x)}{\sqrt{x}}\right)=$

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Math Statement

Problem 3101

If 2+e3x=42+e^{3 x}=42+e3x=4, then solve for xxx. Note: Round your answer to 2 decimal points and do not include any special characters. For example, if your answer is .1234, enter it as . 12. □\square□

Problem 3102

Problem 3103

Problem 3104

In Exercises 3 and 4 , solve for yyy in terms of xxx.3. y29+x24=1\frac{y^{2}}{9}+\frac{x^{2}}{4}=19y2​+4x2​=14. x236+y225=1\frac{x^{2}}{36}+\frac{y^{2}}{25}=136x2​+25y2​=1

Problem 3105

Problem 3106

Find RRR and θ\thetaθ given the components Rx=17.57R_{x}=17.57Rx​=17.57 and Ry=6.94R_{y}=6.94Ry​=6.94. R=□\mathrm{R}=\squareR=□ (Round to the nearest hundredth as needed.)

Problem 3107

y=x−5x2−25y=\frac{x-5}{x^{2}-25}y=x2−25x−5​

Problem 3108

Factor the expression x3+3x2−54xx^{3} + 3x^{2} - 54xx3+3x2−54x.

Problem 3109

11. (x2−8x+15)÷(x−3)\left(x^{2}-8 x+15\right) \div(x-3)(x2−8x+15)÷(x−3) x−5x-5x−5

Problem 3110

Complete the table. \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{f(x)=−∣x∣+1f(x)=-|x|+1f(x)=−∣x∣+1} \\ \hlinexxx & f(x)f(x)f(x) \\ \hline-5 & □\square□ \\ \hline-3 & □\square□ \\ \hline-1 & □\square□ \\ \hline 1 & □\square□ \\ \hline \end{tabular}

Problem 3111

Factor the expression x3−3x2−40xx^{3}-3x^{2}-40xx3−3x2−40x.

Problem 3112

Complete the table. \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{f(x)=−6∣x∣+3f(x)=-6|x|+3f(x)=−6∣x∣+3} \\ \hlinexxx & f(x)f(x)f(x) \\ \hline-1 & □\square□ \\ \hline 0 & □\square□ \\ \hline 1 & □\square□ \\ \hline 2 & □\square□ \\ \hline \end{tabular}

Problem 3113

11) −4(−5)+4−1(−4−2)\frac{-4(-5)+4}{-1(-4-2)}−1(−4−2)−4(−5)+4​

Problem 3114

Problem 3115

Problem 3116

1. Find the general solution of the following differential equation by the method of undetermined coefficients: y′′+2y′−24y=16−(x+2)e4xy^{\prime \prime}+2 y^{\prime}-24 y=16-(x+2) e^{4 x}y′′+2y′−24y=16−(x+2)e4x

Problem 3117

4. What is the standard form of the equation below? y=3(x−2)2−5y=3(x-2)^{2}-5y=3(x−2)2−5Standard Form: f(x)=ax2+bx+cf(x)=a x^{2}+b x+cf(x)=ax2+bx+c

Problem 3118

Consider the following. y=13sec⁡(x)y=\frac{1}{3} \sec (x)y=31​sec(x)Find the period. □\square□ Give the equations for two consecutive vertical asymptotes for the graph of the function. (Enter your ans □\square□ x=□x=\squarex=□

Problem 3119

Problem 3120

Solve for hhh. −3(3h−1)≤−7h−5-3(3 h-1) \leq-7 h-5−3(3h−1)≤−7h−5 h≤4h \leq 4h≤4 h≥1h \geq 1h≥1 h≥4h \geq 4h≥4 h≤−110h \leq-\frac{1}{10}h≤−101​

Problem 3121

Solve for x:2∣2x−4∣−5=−3x: 2|2 x-4|-5=-3x:2∣2x−4∣−5=−3 No solution. x=52x=\frac{5}{2}x=25​ or x=32x=\frac{3}{2}x=23​ x=154x=\frac{15}{4}x=415​ or x=214x=\frac{21}{4}x=421​ x=52x=\frac{5}{2}x=25​ or x=4x=4x=4

Problem 3122

Factor the trinomial completely. 21y2−46y+2521 y^{2}-46 y+2521y2−46y+25Select the correct choice below and, if necessary, fill in the answer box to complete your choice, A. 21y2−46y+25=21 y^{2}-46 y+25=21y2−46y+25= □\square□ (Factor completely.) B. The polynomial is prime.

Problem 3123

Problem 3124

Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) cos⁡[arccos⁡(−2)]\cos [\arccos (-\sqrt{2})]cos[arccos(−2​)]

Problem 3125

movement of the progress bar may be uneven because qu Evaluate the expression 2x2−y1+3x02 x^{2}-y^{1}+3 x^{0}2x2−y1+3x0 for x=4x=4x=4 and y=7y=7y=7. 28 60 97 15

Problem 3126

9. f(x)=4x4−17x2+4f(x)=4 x^{4}-17 x^{2}+4f(x)=4x4−17x2+4 \begin{tabular}{|l|l|} \hline zero(s): & yyy-intercept: \\ \hline \end{tabular}

Problem 3127

10. For n≥1n \geq 1n≥1, establish that the integer n(7n2+5)n\left(7 n^{2}+5\right)n(7n2+5) is of the form 6k6 k6k.11. If nnn is an odd integer, show that n4+4n2+11n^{4}+4 n^{2}+11n4+4n2+11 is of the form 16k16 k16k.

Problem 3128

Simplify the expression. (4ab3)2(−3a5)\left(4 a b^{3}\right)^{2}\left(-3 a^{5}\right)(4ab3)2(−3a5) −12a6b6-12 a^{6} b^{6}−12a6b6 −12a7b6-12 a^{7} b^{6}−12a7b6 −48a10b6-48 a^{10} b^{6}−48a10b6 −48a7b6-48 a^{7} b^{6}−48a7b6

Problem 3129

Factor the trinomial 4x2+8x−54x^2 + 8x - 54x2+8x−5.

Problem 3130

For which of the following equations is the value of xxx equal to 10 ? Select all that apply. A) x+10=20x+10=20x+10=20 B) 10x=1010 x=1010x=10 C) 20÷x=220 \div x=220÷x=2 D) 4x=104 x=104x=10 E) 20−x=1020-x=1020−x=10

Problem 3131

Is 50,−50,2050,-50,2050,−50,20, or -20 the solution of the equation 15=c−3515=c-3515=c−35 ?

Problem 3132

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. Assume that the variables represent positive real numbers. log⁡2(14mn3)=□\log _{2}\left(\frac{1}{4} m n^{3}\right)=\squarelog2​(41​mn3)=□

Problem 3133

Multiply. (5y−4)(7y+5)(5 y-4)(7 y+5)(5y−4)(7y+5)Simplify your answer.

Problem 3134

Problem 3135

Problem 3136

Multiply. (4−3y)(4+3y)(4-3 y)(4+3 y)(4−3y)(4+3y)Simplify your answer.

Problem 3137

2. Solve the following equation for Real Number (s) xxx 13x+5−25x−3=0\frac{1}{3 x+5}-\frac{2}{5 x-3}=03x+51​−5x−32​=0

Problem 3138

lue for the following expression log⁡4(576)+log⁡4(16)−2log⁡4(6)=\log _{4}(576)+\log _{4}(16)-2 \log _{4}(6)=log4​(576)+log4​(16)−2log4​(6)=

Problem 3139

Evaluate x2−2x+3x^{2}-2 x+3x2−2x+3 when x=−3x=-3x=−3 3 0 6 18

Problem 3140

Simplify: 11y2+12y−6y2−8y+5y911 y^{2}+12 y-6 y^{2}-8 y+5 y^{9}11y2+12y−6y2−8y+5y9 9y2+59 y^{2}+59y2+5 5y2+4y+55 y^{2}+4 y+55y2+4y+5 5y2+4y+15 y^{2}+4 y+15y2+4y+1 5y2+9y5 y^{2}+9 y5y2+9y

Problem 3141

f(x)=−x2−2x−5f(x)=-x^{2}-2 x-5f(x)=−x2−2x−5The function has □\square□Axis of Symmetry: □\square□Vertex: □\square□Domain: □\square□ Range: □\square□

Problem 3142

xxx and choose the correct solution: x+5≥−1x+5 \geq-1x+5≥−1 x≥−4x \geq-4x≥−4 x≥−6x \geq-6x≥−6 x≥4x \geq 4x≥4 x≥−6x \geq-6x≥−6

Problem 3143

Problem 3144

(b) f(x)=−x+3f(x)=-x+3f(x)=−x+3 g(x)=x+3f(g(x))=□g(f(x))=□\begin{array}{l} g(x)=x+3 \\ f(g(x))=\square \\ g(f(x))=\square \end{array}g(x)=x+3f(g(x))=□g(f(x))=□​ fff and ggg are inverses of each other fff and ggg are not inverses of each other

Problem 3145

If $2+e^{3 x}=4$ , then solve for $x$ . Note: Round your answer to 2 decimal points and do not include any special characters. For example, if your answer is .1234, enter it as . 12. $\square$

In Exercises 3 and 4 , solve for $y$ in terms of $x$ .
3. $\frac{y^{2}}{9}+\frac{x^{2}}{4}=1$
4. $\frac{x^{2}}{36}+\frac{y^{2}}{25}=1$

Find $R$ and $\theta$ given the components $R_{x}=17.57$ and $R_{y}=6.94$ . $\mathrm{R}=\square$ (Round to the nearest hundredth as needed.)

$y=\frac{x-5}{x^{2}-25}$

Factor the expression $x^{3} + 3x^{2} - 54x$ .

11. $\left(x^{2}-8 x+15\right) \div(x-3)$ $x-5$

Complete the table. \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ $f(x)=-|x|+1$ } \\ \hline $x$ & $f(x)$ \\ \hline-5 & $\square$ \\ \hline-3 & $\square$ \\ \hline-1 & $\square$ \\ \hline 1 & $\square$ \\ \hline \end{tabular}

Factor the expression $x^{3}-3x^{2}-40x$ .

Complete the table. \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ $f(x)=-6|x|+3$ } \\ \hline $x$ & $f(x)$ \\ \hline-1 & $\square$ \\ \hline 0 & $\square$ \\ \hline 1 & $\square$ \\ \hline 2 & $\square$ \\ \hline \end{tabular}

11) $\frac{-4(-5)+4}{-1(-4-2)}$

1. Find the general solution of the following differential equation by the method of undetermined coefficients: $y^{\prime \prime}+2 y^{\prime}-24 y=16-(x+2) e^{4 x}$

4. What is the standard form of the equation below? $y=3(x-2)^{2}-5$
Standard Form: $f(x)=a x^{2}+b x+c$

Consider the following. $y=\frac{1}{3} \sec (x)$
Find the period. $\square$ Give the equations for two consecutive vertical asymptotes for the graph of the function. (Enter your ans $\square$ $x=\square$

Solve for $h$ . $-3(3 h-1) \leq-7 h-5$ $h \leq 4$ $h \geq 1$ $h \geq 4$ $h \leq-\frac{1}{10}$

Solve for $x: 2|2 x-4|-5=-3$ No solution. $x=\frac{5}{2}$ or $x=\frac{3}{2}$ $x=\frac{15}{4}$ or $x=\frac{21}{4}$ $x=\frac{5}{2}$ or $x=4$

Factor the trinomial completely. $21 y^{2}-46 y+25$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice, A. $21 y^{2}-46 y+25=$ $\square$ (Factor completely.) B. The polynomial is prime.

Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) $\cos [\arccos (-\sqrt{2})]$

movement of the progress bar may be uneven because qu Evaluate the expression $2 x^{2}-y^{1}+3 x^{0}$ for $x=4$ and $y=7$ . 28 60 97 15

9. $f(x)=4 x^{4}-17 x^{2}+4$ \begin{tabular}{|l|l|} \hline zero(s): & $y$ -intercept: \\ \hline \end{tabular}

10. For $n \geq 1$ , establish that the integer $n\left(7 n^{2}+5\right)$ is of the form $6 k$ .
11. If $n$ is an odd integer, show that $n^{4}+4 n^{2}+11$ is of the form $16 k$ .

Simplify the expression. $\left(4 a b^{3}\right)^{2}\left(-3 a^{5}\right)$ $-12 a^{6} b^{6}$ $-12 a^{7} b^{6}$ $-48 a^{10} b^{6}$ $-48 a^{7} b^{6}$

Factor the trinomial $4x^2 + 8x - 5$ .

For which of the following equations is the value of $x$ equal to 10 ? Select all that apply. A) $x+10=20$ B) $10 x=10$ C) $20 \div x=2$ D) $4 x=10$ E) $20-x=10$

Is $50,-50,20$ , or -20 the solution of the equation $15=c-35$ ?

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. Assume that the variables represent positive real numbers. $\log _{2}\left(\frac{1}{4} m n^{3}\right)=\square$

Multiply. $(5 y-4)(7 y+5)$
Simplify your answer.

Multiply. $(4-3 y)(4+3 y)$
Simplify your answer.

2. Solve the following equation for Real Number (s) $x$ $\frac{1}{3 x+5}-\frac{2}{5 x-3}=0$

lue for the following expression $\log _{4}(576)+\log _{4}(16)-2 \log _{4}(6)=$

Evaluate $x^{2}-2 x+3$ when $x=-3$ 3 0 6 18

Simplify: $11 y^{2}+12 y-6 y^{2}-8 y+5 y^{9}$ $9 y^{2}+5$ $5 y^{2}+4 y+5$ $5 y^{2}+4 y+1$ $5 y^{2}+9 y$

$f(x)=-x^{2}-2 x-5$
The function has $\square$
Axis of Symmetry: $\square$
Vertex: $\square$
Domain: $\square$ Range: $\square$

$x$ and choose the correct solution: $x+5 \geq-1$ $x \geq-4$
$x \geq-6$ $x \geq 4$
$x \geq-6$

(b) $f(x)=-x+3$ $\begin{array}{l} g(x)=x+3 \\ f(g(x))=\square \\ g(f(x))=\square \end{array}$ $f$ and $g$ are inverses of each other $f$ and $g$ are not inverses of each other

Solve for $a$ . $-6 a+45 \leq 3$ $a \geq 7$ $a \geq-7$ $a \geq-8$ $a \leq 7$

(a) $f(x)=\frac{x+7}{2}$ $\begin{array}{l} g(x)=2 x-7 \\ f(g(x))=\square \\ g(f(x))=\square \end{array}$ $f$ and $g$ are inverses of each other $f$ and $g$ are not inverses of each other

Find the amplitude, period, and phase shift of the given function. $y=0.4 \cos 0.2\left(x+\frac{\pi}{10}\right)$
The amplitude is $\square$ (Type an exact answer, using $\pi$ as needed. Use integers or decimal

Multiply. State the product in simplest form. $\frac{4}{9 k^{5}} \cdot \frac{3 k^{3}}{8}, k \neq 0$ $\frac{1}{25 x^{8}}$ $\frac{1}{6 k^{2}}$ $\frac{1}{60 k^{2}}$ $\frac{1}{6 \mathrm{k}^{8}}$

The function $h$ is defined as follows for the domain given. $h(x)=1-2 x, \quad \text { domain }=\{-1,0,1,2\}$
Write the range of $h$ using set notation. Then graph $h$ . range =

Convert the following expressions between exponential and logarithmic form. a. $2401=7^{4}$ [1 mark] b. $\quad a=\log _{\mathrm{b}} c$ [1 mark]

Solve for $x$ . $\begin{array}{l} 4^{x}=21 \\ x=2.192 \end{array}$ (Type an intejer or a decimal. Round to four decimal places as needed. Use a comma to separate answers as needed.

$\begin{array}{l}=\sin (\cos 6 x)+\sin 6 x \cos x \\ =\sin (x+6 x)=\sin 7 x\end{array}$

$\frac{1}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}=$

$\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}=$

$\frac{1}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Express the function (or rule) in words. $f(x)=2 x+9$ Multiply by 9 , then add 2. Add 9, then square the result. Add 9, then multiply the result by 2 . Square, then add 9. Multiply by 2, then add 9.

Use the function to evaluate the indicated expressions and simplify. $\begin{array}{l} f(x)=27 x-6 \\ f\left(\frac{x}{3}\right)=\square \\ \frac{f(x)}{3}=\square \end{array}$

16. Use the quadratic formula to find the roots (answers). $3 x^{2}-5 x+3=0$

4. State the Quadratic formula and use it to solve the equation: $3 x^{2}+8 x+6=0$

$\sqrt{-50}$

5. Classify each polynomial as a monomial, binomial, or trinomial. State the degree of the polynomial. $5 m^{2}$ Name: Select an answer $~ \sim$
Degree: $\square$ Add Work
Next Question

Use the rational zeros theorem to list all possible zeros of the function $f(x)=5 x^{3}+x^{2}+x+7$ . Enter the possible zeros separated by commas. You do not need to factor the polynomial. Add Work Next Question

Evaluate $w+(-x)-\frac{2}{3}$ where $w=-\frac{5}{9}$ and $x=\frac{4}{3}$