Table of Contents
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
| x | y |
|---|---|
| 18 | 130 |
| 23 | 160 |
| 26 | 178 |
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
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
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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 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
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
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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
$5x=15$
$-4x+y=-2$
The solution to the given system of equations is $(x,y)$. What is the value of $x+y$?
Difficulty: Easy
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
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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
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
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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
If $f$ is the function defined by $f(x)=\frac{2x-1}{3}$, what is the value of $f(5)$?
Difficulty: Easy
$d=16t$
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
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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
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