Algebra

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Algebra

CE

Chief Editor

Mar 28, 2024

Table of Contents

Practice Quiz Mode

Take all 16 MCQs in interactive quiz mode with timer and progress tracking

The function $h$ is defined by $h(x)=4x+28$. The graph of $y=h(x)$ in the $xy$-plane has an $x$-intercept at $(a,0)$ and a $y$-intercept at $(0,b)$, where $a$ and $b$ are constants. What is the value of $a+b$?

Difficulty: Medium

A:

21

B:

28

C:

32

D:

35

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x y 181302316026178 For line $h$, the table shows three values of $x$ and their corresponding values of $y$. Line $k$ is the result of translating line $h$ down 5 units in the $xy$-plane. What is the $x$-intercept of line $k$?

Difficulty: Hard

A:

(-\frac{26}{3},0)

B:

(-\frac{9}{2},0)

C:

(-\frac{11}{3},0)

D:

(-\frac{17}{6},0)

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An economist modeled the demand $Q$ for a certain product as a linear function of the selling price $P$. The demand was 20,000 units when the selling price was $\$40$ per unit, and the demand was 15,000 units when the selling price was $\$60$ per unit. Based on the model, what is the demand, in units, when the selling price is $\$55$ per unit?

Difficulty: Hard

A:

16,250

B:

16,500

C:

16,750

D:

17,500

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Hiro and Sofia purchased shirts and pants from a store. The price of each shirt purchased was the same and the price of each pair of pants purchased was the same. Hiro purchased 4 shirts and 2 pairs of pants for $\$86$, and Sofia purchased 3 shirts and 5 pairs of pants for $\$166$. Which of the following systems of linear equations represents the situation, if $x$ represents the price, in dollars, of each shirt and $y$ represents the price, in dollars, of each pair of pants?

Difficulty: Easy

A:

4x+2y=86 \\$$3x+5y=166

B:

4x+3y=86 \\ 2x+5y=166

C:

4x+2y=166 \\ 3x+5y=86

D:

4x+3y=166 \\ 2x+5y=86

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A store sells two different-sized containers of a certain Greek yogurt. The store's sales of this Greek yogurt totaled $1,277.94$ dollars last month. The equation $5.48x+7.30y=1,277.94$ represents this situation, where $x$ is the number of smaller containers sold and $y$ is the number of larger containers sold. According to the equation, which of the following represents the price, in dollars, of each smaller container?

Difficulty: Easy

A:

$5.48$

B:

$7.30y$

C:

$7.30$

D:

$5.48x$

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Line $k$ is defined by $y=3x+15$. Line $j$ is perpendicular to line $k$ in the $xy$-plane. What is the slope of line $j$?

Difficulty: Easy

A:

-\frac{1}{3}

B:

-\frac{1}{12}

C:

-\frac{1}{18}

D:

-\frac{1}{45}

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The point $(8,2)$ in the xy-plane is a solution to which of the following systems of inequalities?

Difficulty: Easy

A:

x>0 \\ y>0

B:

x>0 \\ y<0

C:

x<0 \\ y>0

D:

x<0 \\ y<0

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$5x=15$ $-4x+y=-2$ The solution to the given system of equations is $(x,y)$. What is the value of $x+y$?

Difficulty: Easy

A:

x>0 \\ y<0

B:

x<0 \\ y>0

C:

x<0 \\ y<0

D:

$17$

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The cost of renting a backhoe for up to $10$ days is $\$270$ for the first day and $\$135$ for each additional day. Which of the following equations gives the cost $y$, in dollars, of renting the backhoe for $x$ days, where $x$ is a positive integer and $x\leq 10$?

Difficulty: Hard

A:

$y=270x-135$

B:

$y=270x+135$

C:

$y=135x+270$

D:

$y=135x+135$

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What value of $p$ satisfies the equation $5p+180=250$?

Difficulty: Easy

A:

14

B:

65

C:

86

D:

250

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The front of a roller-coaster car is at the bottom of a hill and is 15 feet above the ground. If the front of the roller-coaster car rises at a constant rate of 8 feet per second, which of the following equations gives the height $h$ in feet, of the front of the roller-coaster car $s$ seconds after it starts up the hill?

Difficulty: Easy

A:

$h=8s+15$

B:

h=15s+\frac{335}{8}

C:

h=8s+\frac{335}{15}

D:

$h=15s+8$

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Line $p$ is defined by $2y+18x=9$. Line $r$ is perpendicular to line $p$ in the $xy$-plane. What is the slope of line $r$?

Difficulty: Medium

A:

$-9$

B:

-\frac{1}{9}

C:

\frac{1}{9}

D:

$9$

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Adam's school is a 20-minute walk or a 5-minute bus ride away from his house. The bus runs once every 30 minutes, and the number of minutes, $w$, that Adam waits for the bus varies between 0 and 30. Which of the following inequalities gives the values of $w$ for which it would be faster for Adam to walk to school?

Difficulty: Hard

A:

$w-5<20$

B:

$w-5>20$

C:

\(w+5<20\)

D:

$w+5>20$

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If $f$ is the function defined by $f(x)=\frac{2x-1}{3}$, what is the value of $f(5)$?

Difficulty: Easy

A:

\frac{4}{3}

B:

\frac{7}{3}

C:

$3$

D:

$9$

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$d=16t$ The given equation represents the distance $d$, in inches, where $t$ represents the number of seconds since an object started moving. Which of the following is the best interpretation of 16 in this context?

Difficulty: Easy

A:

The object moved a total of 16 inches.

B:

The object moved a total of 16$t$ inches.

C:

The object is moving at a rate of 16 inches per second.

D:

The object is moving at a rate of $\frac{1}{16}$ inches per second.

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$f(x)=39$ For the given linear function $f$, which table gives three values of $x$ and their corresponding values of $f(x)$?

Difficulty: Medium

A:

x f(x) 001020

B:

x f(x) 039139239

C:

x f(x) 00139278

D:

x f(x) 03910 2 -39

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