Algebra

Problem 30101

Graph the supply $S(q)=p=\frac{3}{2} q$ and demand $D(q)=p=81-\frac{3}{4} q$ . Find equilibrium quantity and price.

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Problem 30102

Solve the equation $d-10-2d+7=8+d-10-3d$ . What is $d$ ? Options: $-5$ , $-1$ , $1$ , $5$ .

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Problem 30103

Solve the inequality: $\frac{x+1}{x-4}>0$ . Provide your answer in interval notation.

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Problem 30104

Find the product of the functions $f(x)=3 x^{2}+5 x$ and $g(x)=7 x+3$ . What is $f(x) g(x)$ ?

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Problem 30105

Find $f(3) g(3)$ for $f(x)=2 x^{2}+4 x+5$ and $g(x)=x^{2}+x+1$ .

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Problem 30106

If $y$ varies directly with $x$ and $y$ is 72 when $x$ is 9, find $y$ when $x$ is 17. $y=[?]$

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Problem 30107

In a race, a turtle has a $7 \mathrm{~km}$ head start, running at $\frac{2 \mathrm{~km}}{\mathrm{hr}}$ , while a rabbit runs at $\frac{7 \mathrm{~km}}{\mathrm{hr}}$ . How long until the rabbit catches the turtle?
1. The distance that the rabbit travels is $7 + 2t$ .
2. The distance that the turtle travels is $7t$ .
The rabbit races $7 + 2t$ km at $\frac{7 \mathrm{~km}}{\mathrm{hr}}$ for time $t$ .

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Problem 30108

Solve the equation $2.8y + 6 + 0.2y = 5y - 14$ . Find the value of $y$ . Options: $-10$ , $-1$ , $1$ , $10$ .

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Problem 30109

Solve for $y$ in the equation: $y + 6 = -3y + 26$ . Options: $-8$ , $-5$ , $5$ , $8$ .

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Problem 30110

Find the function $d(t)$ for a car that travels 372 miles in 6 hours from Lubbock to Austin.

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Problem 30111

Solve the equation: $\frac{2}{3} x - \frac{1}{2} = \frac{1}{3} + \frac{5}{6} x$ . What is $x$ ?

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Problem 30112

Find the product $f(x) g(x)$ for $f(x)=3 x^{2}+4 x+5$ and $g(x)=x^{2}+x+1$ .

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Problem 30113

Find all real zeros of the polynomial $f(x)=2 x^{4}+x^{3}-7 x^{2}-3 x+3$ and factor it over the reals.

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Problem 30114

Find the value of the piecewise function $f(x)$ at $x = -4$ .

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Problem 30115

Find the value of the piecewise function $f(x)$ at $x = -1$ , where $f(x)$ is defined as:
$f(x)=\left\{\begin{array}{lll} 3 x-5 & \text { for } & x<1 \\ 1 & \text { for } & x=1 \\ -2 & \text { for } & 1<x \leq 5 \end{array}\right.$

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Problem 30116

What is the graph of $f(x)=\frac{1}{4}(8)^{x}$ after reflecting it across the $y$ -axis and then the $x$ -axis?

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Problem 30117

Evaluate the following compositions: $(f \circ g)(1)$ , $(f \circ g)(-1)$ , $(g \circ f)(0)$ , $(g \circ f)(-1)$ , $(g \circ g)(-2)$ , $(f \circ f)(-1)$ . Use values from $f(x)$ and $g(x)$ : $f(-3)=-6$ , $f(-2)=-4$ , $f(-1)=-2$ , $f(0)=-1$ , $f(1)=2$ , $f(2)=4$ , $f(3)=6$ , $g(-3)=6$ , $g(-2)=2$ , $g(-1)=0$ , $g(0)=-1$ , $g(1)=0$ , $g(2)=2$ , $g(3)=6$ .

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Problem 30118

Find the value of the piecewise function $f(x)$ at $x = -1$ :
$f(x)=\left\{\begin{array}{lll} 2 x+8 & \text { for } & -5 \leq x<-1 \\ -6 & \text { for } & x=-1 \\ x+5 & \text { for } & -1<x \leq 2 \end{array}\right.$

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Problem 30119

Rewrite $f(x)=x^{2}+6 x$ in vertex form and find its roots (i.e. $x$ -intercepts).

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Problem 30120

Solve for $p$ : $2.6(5.5 p-12.4)=127.92$ . Use the distributive, addition, and division properties.

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Problem 30121

Find $(f \circ g)(4)$ , $(g \circ f)(2)$ , $(f \circ f)(1)$ , and $(g \circ g)(0)$ for $f(x)=3x$ and $g(x)=6x^2+6$ .

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Problem 30122

A school play sold tickets for \$ 3 (student) and \$ 7 (adult). Total sales were \$ 2,001 with 467 tickets sold. Find counts.

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Problem 30123

Find the composite functions for $f(x)=9x+7$ and $g(x)=x^{2}$ : (a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ . State each domain.

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Problem 30124

Kevin starts with \ $750 in savings and adds \$70 weekly. Write$ S $as a function of$ W $and find$ S$ after 11 weeks.

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Problem 30125

Find the following: (a) $(f \circ g)(4)$ for $f(x)=3x$ and $g(x)=6x^2+6$ (b) $(g \circ f)(2)$ (c) $(f \circ f)(1)$ (d) $(g \circ g)(0)$

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Problem 30126

Lisa bought 100 items: cups at \ $2 and bracelets at \$3, costing \$260. Find the number of cups using:$ $\left\{\begin{array}{l} c+b=100 \\ 2 c+3 b=260 \end{array}\right.$ $

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Problem 30127

A school needs 5 more desks in secondary classrooms than in elementary ones. With 20 elementary and 25 secondary classrooms totaling 1,115 desks, find the number of desks in each secondary classroom.

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Problem 30128

A pond starts with 700 liters and water is added at 35 liters/min. Write $W$ as a function of $T$ and find $W$ after 14 mins.

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Problem 30129

Justin's total pay $P$ is given by $P = 2100 + 70N$ . Find $P$ if he sells 28 copies: $P = 2100 + 70(28)$ .

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Problem 30130

Find composite functions for $f(x)=9x+7$ and $g(x)=x^{2}$ : (a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ . State their domains.

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Problem 30131

Find the solutions for the system: $2y=4x+12$ and $y=2x-6$ .

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Problem 30132

Solve the equations: 4x - 3y = 8 and 2x + y = 11. Find the value of $y$ . Choices: $-\frac{8}{3}$ , $-6$ , $14$ , $\frac{14}{5}$ .

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Problem 30133

How many zeros does the function $f(x)=x(x-1)(2 x+4)^{2}$ have? (1 point) Options: 2, 4, 3.

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Problem 30134

Find the composite functions for $f(x)=2x+3$ and $g(x)=x^{2}$ and state their domains: (a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ .

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Problem 30135

A road starts at 54 miles, increasing by 2 miles daily. Find the equation $L = 54 + 2D$ and total length after 36 days.

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Problem 30136

The Sugar Sweet Company has a total cost $C = 7500 + 175S$ . Find the cost to transport 19 tons of sugar.

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Problem 30137

Find the composite functions for $f(x)=6x+8$ and $g(x)=x^{2}$ :
(a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ . State their domains.

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Problem 30138

Solve for $x$ in the equation: $x - 6 = -13$ .

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Problem 30139

Sam starts with \ $350 and adds \$30 weekly. Write the equation for total savings$ S $after$ W $weeks and find$ S$ after 18 weeks.

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Problem 30140

Find $g(x)=3x+2$ for $x = -1, 0, 2, 3, 5$ and complete the function table with the values of $g(x)$ .

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Problem 30141

A pond starts with 300 liters and fills at 29 liters/min. Write $W$ in terms of $T$ and find $W$ after 17 minutes.

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Problem 30142

Solve for $x$ in the equation: $-10.1 = x + 5.3$ .

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Problem 30143

Given $f(x)=5x+8$ and $g(x)=x^{2}$ , find the composite functions and their domains: (a) $f \circ g$ (b) $g \circ f$ (c) $f \circ f$ (d) $g \circ g$ Find and simplify each expression and state the domain.

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Problem 30144

Find values of $g(x)=3x+2$ for $x=-1, 0, 2, 3, 5$ . Complete the function table.

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Problem 30145

Find values of $f(x)=4x+4$ for $x=-1, 0, 1, 2, 5$ .

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Problem 30146

Find the composite functions for $f(x)=8x+4$ and $g(x)=x^{2}$ : (a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ . Also, state the domain for each function.

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Problem 30147

A school play sold 500 tickets for \$1480. Student tickets are \$2, adult tickets are \$5. How many of each type?

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Problem 30148

Find $f(-6)$ for $f(x)=2x+2$ and $g(-3)$ for $g(x)=-2x^{3}-5$ . Simplify your answers.

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Problem 30149

Solve the equations: $-2x + 3y = 8$ and $5x - 2y = -9$ . Choose the correct solution from the options provided.

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Problem 30150

Find the composite functions for $f(x)=4x+7$ and $g(x)=x^{2}$ , and state their domains: (a) $f \circ g$ (b) $g \circ f$ (c) $f \circ f$ (d) $g \circ g$

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Problem 30151

Solve the equations: $-3x + 4y = 13$ and $5x - 3y = -18$ . Choose the correct solution from the options provided.

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Problem 30152

For $f(x)=8x+3$ and $g(x)=x^{2}$ , find the composite functions: (a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ and their domains.

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Problem 30153

Find the composite functions for $f(x)=8x+3$ and $g(x)=x^{2}$ , and state their domains:
(a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ .

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Problem 30154

42 is 6 times more than 7.

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Problem 30155

Find composite functions for $f(x)=\sqrt{x}$ and $g(x)=8x+1$ : (a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ .

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Problem 30156

Calculate moles of $\mathrm{CH}_{3} \mathrm{OH}$ in $150.0 \mathrm{~mL}$ of $0.210 \mathrm{M} \mathrm{CH}_{3} \mathrm{OH}$ .

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Problem 30157

A rectangle's length is $5 \mathrm{ft}$ more than twice the width, with an area of $42 \mathrm{ft}^{2}$ . Find its dimensions.

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Problem 30158

Find the functions: a. $(f \circ g)(x)$ ; b. $(g \circ f)(x)$ ; c. $(f \circ g)(2)$ ; d. $(g \circ f)(2)$ for $f(x)=6-x$ and $g(x)=2x^2+x+9$ .

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Problem 30159

Select the graph of $f(x)=-2$ and compare it with its parent function $f(x)=0$ .

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Problem 30160

A pond's water amount $W$ (liters) is given by $W=35T+600$ for time $T$ (minutes) in [0, 90]. Find domain and range sets.

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Problem 30161

A publishing company has $C=25N+700$ for costs. Find the domain and range values for $N$ (0 to 300) and $C$ .

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Problem 30162

Calculate $f+g$ , $f-g$ , $fg$ , and $\frac{f}{g}$ for $f(x)=4x-9$ , $g(x)=x-2$ . Find their domains.

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Problem 30163

An airplane's fuel tank holds 300 gallons. If $W=7F+4000$ , describe the domain and range values. Choose the best sets.

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Problem 30164

Find the secant line for $f(x)=\frac{5}{x}$ between $x=4$ and $x=5$ , and the tangent line at $x=4$ .

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Problem 30165

Let $x$ be the weight bench-pressed by other competitors. Write the inequality: $x \leq 400 - 23$ .

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Problem 30166

Find the weight of an airplane with 70 gallons of fuel, given it weighs 2012 lbs at 20 gallons and 2208 lbs at 55 gallons.

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Problem 30167

Chau drives to Dallas. After 43 min, he has 47 miles left; after 65 min, 30.5 miles. How far after 71 min?

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Problem 30168

Solve for $y$ : $3(4y - 1) = 2\left(5y + \frac{1}{2}\right)$ . What is $y$ ?

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Problem 30169

Rewrite the cost of the software product as an inequality: $235 < x < 370$ .

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Problem 30170

Find the monthly cost for 75 minutes of calls if 55 mins costs \$13.63 and 91 mins costs \$17.95.

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Problem 30171

How many years does light take to travel $3.65 \times 10^{8}$ miles if a light year is $5.87 \times 10^{12}$ miles?

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Problem 30172

A weight-lifting winner bench-pressed 400 lbs; others pressed at least 23 lbs less.
a. Write the inequality for others' weights: $x \leq 377$ . b. Can someone bench-press 379 lbs? No, 379 lbs is not a solution.

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Problem 30173

Find the height from which a marble falls in 3 seconds using the formula $s=16 t^{2}$ . What is the height $s$ ?

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Problem 30174

A forest area of $2700 \mathrm{~km}^{2}$ decreases by $3.75\%$ yearly. Find the area after 13 years, rounded to the nearest km.

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Problem 30175

Find Revenue, Cost, and Profit for selling $x$ thousand items with price \ $3.00, fixed cost \$143,185, and variable cost$ -3x^{2}+3480x-100$.

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Problem 30176

Factor completely: $x^{3} y + 12 x^{2} y^{2} + 27 x y^{3}$

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Problem 30177

A student drops a marble from a $180 \mathrm{~cm}$ ramp, reaching $80.0 \mathrm{~cm/s}$ . How long to reach the bottom?

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Problem 30178

In a weight-lifting contest, the winner bench-pressed 400 lbs. Other competitors lifted at least 23 lbs less.
a. Write the inequality for their weights: $x \leq 377$ . b. Can someone lift 379 lbs? No, 379 lbs is not a solution to the inequality. Explain.

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Problem 30179

Factor completely: $3 x^{2}-21 x+30$

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Problem 30180

ASK YOUR TEACHER
A contestant in a winter games event pushes a $41.0-\mathrm{kg}$ block of ice across a frozen lake with a force of 25 N at $28.0^{\circ}$ below the horizontal as shown in Figure (a) below, and it moves with an acceleration of $0.540 \mathrm{~m} / \mathrm{s}^{2}$ to the right. (a) (b) (a) What is the normal force exerted by the lake surface on the block of ice? $\square$ N surface on the block of ite? $\square$ Tutorial

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Problem 30181

4. Given $f(x)=3 x^{2}+17$ , find $f(-5)$

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Problem 30182

? Question Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the expressions with their simplified forms.
Tiles $\frac{1}{2}$ $5 \sqrt{3}$ $2 \sqrt{5}$ $4 \sqrt{5}$ 4
Pairs $\sqrt{2} \cdot \sqrt{8}$ $\qquad$ $\sqrt{80}$ $\frac{\sqrt{5}}{\sqrt{20}}$ $\qquad$ $\square$ $\square$ $\sqrt{20}$ $\qquad$

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Problem 30183

Tiles $5 \sqrt{3}$ $2 \sqrt{5}$
Pairs $\begin{array}{cc} \sqrt{2} \cdot \sqrt{8} & \longrightarrow \\ \sqrt{80} & \longrightarrow \\ \frac{\sqrt{5}}{\sqrt{20}} & \longrightarrow \\ \sqrt{20} \end{array}$

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Problem 30184

Part A $3 \pi+\frac{2 \pi}{3}$
Space used (includes formatting): $0 / 30000$ Submit
Part B $3 \sqrt{5}+15 \sqrt{5}$

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Problem 30185

Perform the operation and combine to one fraction. $\frac{2 x+1}{x}+\frac{5 x}{x+9}$

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Problem 30186

What is the slope of this line?
Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$

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Problem 30187

Expressions with Irrational Numbers: Tutorial ? Question Drag each expression to the correct location. Estimate the value of each irrational expression to the nearest integer. $\begin{array}{lllll} -3 \sqrt{4} \cdot \sqrt{3}+2 \sqrt{9} \cdot \sqrt{3} & \frac{-\sqrt{20}}{-\sqrt{21}} & \frac{2 \sqrt{2}+3 \sqrt{2}}{5 \sqrt{2}} & -\frac{3 \pi}{3 \sqrt{10}} & 4 \cdot 3 \sqrt{2}-2 \sqrt{2} \cdot \sqrt{36} \end{array}$ $-\frac{3 \pi}{3 \sqrt{10}}$

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Problem 30188

Which representation has the same rate of change of $y$ with respect to $x$ as the equation $x+$ $2 y=6$ ? (A) $y=-\frac{1}{2} x+2$

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Problem 30189

Darin's great aunt lives in a retirement home. Darin visits her to help plant green beans in a garden. So far they have planted 6 rows with 72 green bean stalks. They plant the same number of green bean stalks in each row.
What is the constant of proportionality in this relationship? 6 12 72 78

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Problem 30190

6) white $(4-5 x)-(2 x-16)$

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Problem 30191

Rewrite in simplest terms: $-9 a-2(9 a-5)$
Answer Attempt 1 out of 2 $\square$ Submit Answer

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Problem 30192

15. Higher Order Thinking Explain whether $8 t-3 y-4 t$ is equivalent to $7 t+(-3 t)-3 y$ .

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Problem 30193

15. Construct Arguments A baseball team gets 3 outs for each inning it comes up to bat. So far this season, Silvio's team has batted in 45 innings, $n$ , and has made 135 outs, $t$ . What is the dependent variable? Explain.

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Problem 30194

assessment.peardeck.com Tube Math 2 Final Review Fall 2024 Fall 2024 Pear Assessment Pakas en las Rakas - Junior H BOOKMARK CHECK ANSWER
53 What is the absolute value function represented by the graph below? Give your answer in vertex form $(y=a|x-h|+k)$

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Problem 30195

Ms. Driva Reck drove from her home to a service station at $48 \mathrm{~km} / \mathrm{h}$ . She returned home by bicycle at $16 \mathrm{~km} / \mathrm{h}$ . The entire trip took 4 hours. How far was the service station from Ms. Reck's home?

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Problem 30196

How would you describe the opposite of a number in your own words?

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Problem 30197

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. $y=-x^{2}+6 x$

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Problem 30198

$f(x)=2 x^{3}+15 x^{2}+4 x-21$
Identify the $y$ -intercept of the function. $-21$
Identify all real roots. Use commas to separate $\square$

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Problem 30199

Solve the system of linear equations by elimination. $\begin{array}{l} x+y=2 \\ 2 x+7 y=9 \end{array}$

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Problem 30200

CRITICAL THINKING Tell whether the statement is always, sometimes, or never true. The absolute value of a negative number is positive.
The statement is $\square$ always true.
Explain.

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Algebra

Problem 30101

Graph the supply S(q)=p=32qS(q)=p=\frac{3}{2} qS(q)=p=23​q and demand D(q)=p=81−34qD(q)=p=81-\frac{3}{4} qD(q)=p=81−43​q. Find equilibrium quantity and price.

Problem 30102

Solve the equation d−10−2d+7=8+d−10−3dd-10-2d+7=8+d-10-3dd−10−2d+7=8+d−10−3d. What is ddd? Options: −5-5−5, −1-1−1, 111, 555.

Problem 30103

Solve the inequality: x+1x−4>0\frac{x+1}{x-4}>0x−4x+1​>0. Provide your answer in interval notation.

Problem 30104

Find the product of the functions f(x)=3x2+5xf(x)=3 x^{2}+5 xf(x)=3x2+5x and g(x)=7x+3g(x)=7 x+3g(x)=7x+3. What is f(x)g(x)f(x) g(x)f(x)g(x)?

Problem 30105

Find f(3)g(3)f(3) g(3)f(3)g(3) for f(x)=2x2+4x+5f(x)=2 x^{2}+4 x+5f(x)=2x2+4x+5 and g(x)=x2+x+1g(x)=x^{2}+x+1g(x)=x2+x+1.

Problem 30106

If yyy varies directly with xxx and yyy is 72 when xxx is 9, find yyy when xxx is 17. y=[?]y=[?]y=[?]

Problem 30107

Problem 30108

Solve the equation 2.8y+6+0.2y=5y−142.8y + 6 + 0.2y = 5y - 142.8y+6+0.2y=5y−14. Find the value of yyy. Options: −10-10−10, −1-1−1, 111, 101010.

Problem 30109

Solve for yyy in the equation: y+6=−3y+26y + 6 = -3y + 26y+6=−3y+26. Options: −8-8−8, −5-5−5, 555, 888.

Problem 30110

Find the function d(t)d(t)d(t) for a car that travels 372 miles in 6 hours from Lubbock to Austin.

Problem 30111

Solve the equation: 23x−12=13+56x\frac{2}{3} x - \frac{1}{2} = \frac{1}{3} + \frac{5}{6} x32​x−21​=31​+65​x. What is xxx?

Problem 30112

Find the product f(x)g(x)f(x) g(x)f(x)g(x) for f(x)=3x2+4x+5f(x)=3 x^{2}+4 x+5f(x)=3x2+4x+5 and g(x)=x2+x+1g(x)=x^{2}+x+1g(x)=x2+x+1.

Problem 30113

Find all real zeros of the polynomial f(x)=2x4+x3−7x2−3x+3f(x)=2 x^{4}+x^{3}-7 x^{2}-3 x+3f(x)=2x4+x3−7x2−3x+3 and factor it over the reals.

Problem 30114

Find the value of the piecewise function f(x)f(x)f(x) at x=−4x = -4x=−4.

Problem 30115

Problem 30116

What is the graph of f(x)=14(8)xf(x)=\frac{1}{4}(8)^{x}f(x)=41​(8)x after reflecting it across the yyy-axis and then the xxx-axis?

Problem 30117

Problem 30118

Problem 30119

Rewrite f(x)=x2+6xf(x)=x^{2}+6 xf(x)=x2+6x in vertex form and find its roots (i.e. xxx-intercepts).

Problem 30120

Solve for ppp: 2.6(5.5p−12.4)=127.922.6(5.5 p-12.4)=127.922.6(5.5p−12.4)=127.92. Use the distributive, addition, and division properties.

Problem 30121

Find (f∘g)(4)(f \circ g)(4)(f∘g)(4), (g∘f)(2)(g \circ f)(2)(g∘f)(2), (f∘f)(1)(f \circ f)(1)(f∘f)(1), and (g∘g)(0)(g \circ g)(0)(g∘g)(0) for f(x)=3xf(x)=3xf(x)=3x and g(x)=6x2+6g(x)=6x^2+6g(x)=6x2+6.

Problem 30122

A school play sold tickets for \$ 3 (student) and \$ 7 (adult). Total sales were \$ 2,001 with 467 tickets sold. Find counts.

Problem 30123

Find the composite functions for f(x)=9x+7f(x)=9x+7f(x)=9x+7 and g(x)=x2g(x)=x^{2}g(x)=x2: (a) f∘gf \circ gf∘g, (b) g∘fg \circ fg∘f, (c) f∘ff \circ ff∘f, (d) g∘gg \circ gg∘g. State each domain.

Problem 30124

Kevin starts with \750insavingsandadds$70weekly.Write750 in savings and adds \$70 weekly. Write 750insavingsandadds$70weekly.WriteSasafunctionof as a function of asafunctionofWandfind and find andfindS$ after 11 weeks.

Problem 30125

Find the following: (a) (f∘g)(4)(f \circ g)(4)(f∘g)(4) for f(x)=3xf(x)=3xf(x)=3x and g(x)=6x2+6g(x)=6x^2+6g(x)=6x2+6 (b) (g∘f)(2)(g \circ f)(2)(g∘f)(2) (c) (f∘f)(1)(f \circ f)(1)(f∘f)(1) (d) (g∘g)(0)(g \circ g)(0)(g∘g)(0)

Problem 30126

Problem 30127

A school needs 5 more desks in secondary classrooms than in elementary ones. With 20 elementary and 25 secondary classrooms totaling 1,115 desks, find the number of desks in each secondary classroom.

Problem 30128

A pond starts with 700 liters and water is added at 35 liters/min. Write WWW as a function of TTT and find WWW after 14 mins.

Problem 30129

Justin's total pay PPP is given by P=2100+70NP = 2100 + 70NP=2100+70N. Find PPP if he sells 28 copies: P=2100+70(28)P = 2100 + 70(28)P=2100+70(28).

Problem 30130

Find composite functions for f(x)=9x+7f(x)=9x+7f(x)=9x+7 and g(x)=x2g(x)=x^{2}g(x)=x2: (a) f∘gf \circ gf∘g, (b) g∘fg \circ fg∘f, (c) f∘ff \circ ff∘f, (d) g∘gg \circ gg∘g. State their domains.

Problem 30131

Find the solutions for the system: 2y=4x+122y=4x+122y=4x+12 and y=2x−6y=2x-6y=2x−6.

Problem 30132

Solve the equations: 4x - 3y = 8 and 2x + y = 11. Find the value of yyy. Choices: −83-\frac{8}{3}−38​, −6-6−6, 141414, 145\frac{14}{5}514​.

Problem 30133

How many zeros does the function f(x)=x(x−1)(2x+4)2f(x)=x(x-1)(2 x+4)^{2}f(x)=x(x−1)(2x+4)2 have? (1 point) Options: 2, 4, 3.

Problem 30134

Find the composite functions for f(x)=2x+3f(x)=2x+3f(x)=2x+3 and g(x)=x2g(x)=x^{2}g(x)=x2 and state their domains: (a) f∘gf \circ gf∘g, (b) g∘fg \circ fg∘f, (c) f∘ff \circ ff∘f, (d) g∘gg \circ gg∘g.

Problem 30135

A road starts at 54 miles, increasing by 2 miles daily. Find the equation L=54+2DL = 54 + 2DL=54+2D and total length after 36 days.

Problem 30136

The Sugar Sweet Company has a total cost C=7500+175SC = 7500 + 175SC=7500+175S. Find the cost to transport 19 tons of sugar.

Problem 30137

Find the composite functions for f(x)=6x+8f(x)=6x+8f(x)=6x+8 and g(x)=x2g(x)=x^{2}g(x)=x2: (a) f∘gf \circ gf∘g, (b) g∘fg \circ fg∘f, (c) f∘ff \circ ff∘f, (d) g∘gg \circ gg∘g. State their domains.

Problem 30138

Solve for xxx in the equation: x−6=−13x - 6 = -13x−6=−13.

Problem 30139

Sam starts with \350andadds$30weekly.Writetheequationfortotalsavings350 and adds \$30 weekly. Write the equation for total savings 350andadds$30weekly.WritetheequationfortotalsavingsSafter after afterWweeksandfind weeks and find weeksandfindS$ after 18 weeks.

Problem 30140

Find g(x)=3x+2g(x)=3x+2g(x)=3x+2 for x=−1,0,2,3,5x = -1, 0, 2, 3, 5x=−1,0,2,3,5 and complete the function table with the values of g(x)g(x)g(x).

Problem 30141

A pond starts with 300 liters and fills at 29 liters/min. Write WWW in terms of TTT and find WWW after 17 minutes.

Problem 30142

Solve for xxx in the equation: −10.1=x+5.3-10.1 = x + 5.3−10.1=x+5.3.

Graph the supply $S(q)=p=\frac{3}{2} q$ and demand $D(q)=p=81-\frac{3}{4} q$ . Find equilibrium quantity and price.

Solve the equation $d-10-2d+7=8+d-10-3d$ . What is $d$ ? Options: $-5$ , $-1$ , $1$ , $5$ .

Solve the inequality: $\frac{x+1}{x-4}>0$ . Provide your answer in interval notation.

Find the product of the functions $f(x)=3 x^{2}+5 x$ and $g(x)=7 x+3$ . What is $f(x) g(x)$ ?

Find $f(3) g(3)$ for $f(x)=2 x^{2}+4 x+5$ and $g(x)=x^{2}+x+1$ .

If $y$ varies directly with $x$ and $y$ is 72 when $x$ is 9, find $y$ when $x$ is 17. $y=[?]$

Solve the equation $2.8y + 6 + 0.2y = 5y - 14$ . Find the value of $y$ . Options: $-10$ , $-1$ , $1$ , $10$ .

Solve for $y$ in the equation: $y + 6 = -3y + 26$ . Options: $-8$ , $-5$ , $5$ , $8$ .

Find the function $d(t)$ for a car that travels 372 miles in 6 hours from Lubbock to Austin.

Solve the equation: $\frac{2}{3} x - \frac{1}{2} = \frac{1}{3} + \frac{5}{6} x$ . What is $x$ ?

Find the product $f(x) g(x)$ for $f(x)=3 x^{2}+4 x+5$ and $g(x)=x^{2}+x+1$ .

Find all real zeros of the polynomial $f(x)=2 x^{4}+x^{3}-7 x^{2}-3 x+3$ and factor it over the reals.

Find the value of the piecewise function $f(x)$ at $x = -4$ .

What is the graph of $f(x)=\frac{1}{4}(8)^{x}$ after reflecting it across the $y$ -axis and then the $x$ -axis?

Rewrite $f(x)=x^{2}+6 x$ in vertex form and find its roots (i.e. $x$ -intercepts).

Solve for $p$ : $2.6(5.5 p-12.4)=127.92$ . Use the distributive, addition, and division properties.

Find $(f \circ g)(4)$ , $(g \circ f)(2)$ , $(f \circ f)(1)$ , and $(g \circ g)(0)$ for $f(x)=3x$ and $g(x)=6x^2+6$ .

Find the composite functions for $f(x)=9x+7$ and $g(x)=x^{2}$ : (a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ . State each domain.

Kevin starts with \ $750 in savings and adds \$70 weekly. Write$ S $as a function of$ W $and find$ S$ after 11 weeks.

Find the following: (a) $(f \circ g)(4)$ for $f(x)=3x$ and $g(x)=6x^2+6$ (b) $(g \circ f)(2)$ (c) $(f \circ f)(1)$ (d) $(g \circ g)(0)$

A pond starts with 700 liters and water is added at 35 liters/min. Write $W$ as a function of $T$ and find $W$ after 14 mins.

Justin's total pay $P$ is given by $P = 2100 + 70N$ . Find $P$ if he sells 28 copies: $P = 2100 + 70(28)$ .

Find composite functions for $f(x)=9x+7$ and $g(x)=x^{2}$ : (a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ . State their domains.

Find the solutions for the system: $2y=4x+12$ and $y=2x-6$ .

Solve the equations: 4x - 3y = 8 and 2x + y = 11. Find the value of $y$ . Choices: $-\frac{8}{3}$ , $-6$ , $14$ , $\frac{14}{5}$ .

How many zeros does the function $f(x)=x(x-1)(2 x+4)^{2}$ have? (1 point) Options: 2, 4, 3.

Find the composite functions for $f(x)=2x+3$ and $g(x)=x^{2}$ and state their domains: (a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ .

A road starts at 54 miles, increasing by 2 miles daily. Find the equation $L = 54 + 2D$ and total length after 36 days.

The Sugar Sweet Company has a total cost $C = 7500 + 175S$ . Find the cost to transport 19 tons of sugar.

Find the composite functions for $f(x)=6x+8$ and $g(x)=x^{2}$ :
(a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ . State their domains.

Solve for $x$ in the equation: $x - 6 = -13$ .

Sam starts with \ $350 and adds \$30 weekly. Write the equation for total savings$ S $after$ W $weeks and find$ S$ after 18 weeks.

Find $g(x)=3x+2$ for $x = -1, 0, 2, 3, 5$ and complete the function table with the values of $g(x)$ .

A pond starts with 300 liters and fills at 29 liters/min. Write $W$ in terms of $T$ and find $W$ after 17 minutes.

Solve for $x$ in the equation: $-10.1 = x + 5.3$ .

Given $f(x)=5x+8$ and $g(x)=x^{2}$ , find the composite functions and their domains: (a) $f \circ g$ (b) $g \circ f$ (c) $f \circ f$ (d) $g \circ g$ Find and simplify each expression and state the domain.

Find values of $g(x)=3x+2$ for $x=-1, 0, 2, 3, 5$ . Complete the function table.

Find values of $f(x)=4x+4$ for $x=-1, 0, 1, 2, 5$ .

Find the composite functions for $f(x)=8x+4$ and $g(x)=x^{2}$ : (a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ . Also, state the domain for each function.

Find $f(-6)$ for $f(x)=2x+2$ and $g(-3)$ for $g(x)=-2x^{3}-5$ . Simplify your answers.

Solve the equations: $-2x + 3y = 8$ and $5x - 2y = -9$ . Choose the correct solution from the options provided.

Find the composite functions for $f(x)=4x+7$ and $g(x)=x^{2}$ , and state their domains: (a) $f \circ g$ (b) $g \circ f$ (c) $f \circ f$ (d) $g \circ g$

Solve the equations: $-3x + 4y = 13$ and $5x - 3y = -18$ . Choose the correct solution from the options provided.

For $f(x)=8x+3$ and $g(x)=x^{2}$ , find the composite functions: (a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ and their domains.

Find the composite functions for $f(x)=8x+3$ and $g(x)=x^{2}$ , and state their domains:
(a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ .

Find composite functions for $f(x)=\sqrt{x}$ and $g(x)=8x+1$ : (a) $f \circ g$ , (b) $g \circ f$ , (c) $f \circ f$ , (d) $g \circ g$ .

Calculate moles of $\mathrm{CH}_{3} \mathrm{OH}$ in $150.0 \mathrm{~mL}$ of $0.210 \mathrm{M} \mathrm{CH}_{3} \mathrm{OH}$ .

A rectangle's length is $5 \mathrm{ft}$ more than twice the width, with an area of $42 \mathrm{ft}^{2}$ . Find its dimensions.

Find the functions: a. $(f \circ g)(x)$ ; b. $(g \circ f)(x)$ ; c. $(f \circ g)(2)$ ; d. $(g \circ f)(2)$ for $f(x)=6-x$ and $g(x)=2x^2+x+9$ .

Select the graph of $f(x)=-2$ and compare it with its parent function $f(x)=0$ .

A pond's water amount $W$ (liters) is given by $W=35T+600$ for time $T$ (minutes) in [0, 90]. Find domain and range sets.

A publishing company has $C=25N+700$ for costs. Find the domain and range values for $N$ (0 to 300) and $C$ .

Calculate $f+g$ , $f-g$ , $fg$ , and $\frac{f}{g}$ for $f(x)=4x-9$ , $g(x)=x-2$ . Find their domains.

An airplane's fuel tank holds 300 gallons. If $W=7F+4000$ , describe the domain and range values. Choose the best sets.

Find the secant line for $f(x)=\frac{5}{x}$ between $x=4$ and $x=5$ , and the tangent line at $x=4$ .

Let $x$ be the weight bench-pressed by other competitors. Write the inequality: $x \leq 400 - 23$ .

Solve for $y$ : $3(4y - 1) = 2\left(5y + \frac{1}{2}\right)$ . What is $y$ ?

Rewrite the cost of the software product as an inequality: $235 < x < 370$ .

How many years does light take to travel $3.65 \times 10^{8}$ miles if a light year is $5.87 \times 10^{12}$ miles?

A weight-lifting winner bench-pressed 400 lbs; others pressed at least 23 lbs less.
a. Write the inequality for others' weights: $x \leq 377$ . b. Can someone bench-press 379 lbs? No, 379 lbs is not a solution.

Find the height from which a marble falls in 3 seconds using the formula $s=16 t^{2}$ . What is the height $s$ ?

A forest area of $2700 \mathrm{~km}^{2}$ decreases by $3.75\%$ yearly. Find the area after 13 years, rounded to the nearest km.