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The equation $40x+20y=160$ represents the number of sweaters, $x$, and number of shirts, $y$, that Yesenia purchased for $160. If Yesenia purchased 2 sweaters, how many shirts did she purchase?
Math
Algebra
Cathy has $n$ CDs. Gerry has 3 more than twice the number of CDs that Cathy has. In terms of $n$, how many CDs does Gerry have?
Math
Algebra
An artist paints and sells square tiles. The selling price $P$, in dollars, of a painted tile is a linear function of the side length of the tile $s$, in inches, as shown in the table below.
Side length, $s$ (inches)
Price, $P$ (dollars)
3
8.00
6
18.00
9
28.00
Which of the following could define the relationship between $s$ and $P$?
Math
Algebra
If $5(x+4)=4(x+4)+29$, what is the value of $x+4$
Math
Algebra
The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. If a triangle has side lengths of $\mathbf{6}$ and $12$, which inequality represents the possible lengths, $x$, of the third side of the triangle?
Math
Algebra
In the $xy$-plane, a line has a slope of 6 and passes through the point $(0,8)$. Which of the following is an equation of this line?
Math
Algebra
For the function $f$, the graph of $y=f(x)$ in the $xy$-plane has a slope of $3$ and passes through the point $(0,-8)$. Which equation defines $f$?
Math
Algebra
One gallon of paint will cover 220 square feet of a surface. A room has a total wall area of $w$ square feet. Which equation represents the total amount of paint $P$, in gallons, needed to paint the walls of the room twice?
Math
Algebra
A gardener buys two kinds of fertilizer. Fertilizer A contains 60% filler materials by weight and Fertilizer B contains 40% filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240 pounds of filler materials. Which equation models this relationship, where $x$ is the number of pounds of Fertilizer A and $y$ is the number of pounds of Fertilizer B?
Math
Algebra
In the $xy$-plane, the points $(-2,3)$ and $(4,-5)$ lie on the graph of which of the following linear functions?
Math
Algebra
$x$
$f(x)$
$0$
$-2$
$2$
$4$
$6$
$16$
Some values of the linear function $f$ are shown in the table above. What is the value of $f(3)$?
Math
Algebra
Oil and gas production in a certain area dropped from 4 million barrels in 2000 to 1.9 million barrels in 2013. Assuming that the oil and gas production decreased at a constant rate, which of the following linear functions $f$ best models the production, in millions of barrels, $t$ years after the year 2000?
Math
Algebra
$y=4x-9$
$y=19$
What is the solution $(x,y)$ to the given system of equations?
Math
Algebra
$x$
$f(x)$
$1$
$-64$
$2$
$0$
$3$
$64$
For the linear function $f$, the table shows three values of $x$ and their corresponding values of $f(x)$. Function $f$ is defined by $f(x)=ax+b$, where $a$ and $b$ are constants. What is the value of $a-b$?
Math
Algebra
For a training program, Juan rides his bike at an average rate of 5.7 minutes per mile. Which function $m$ models the number of minutes it will take Juan to ride $x$ miles at this rate?
Math
Algebra
$10=2x+4$
How many solutions exist to the equation shown above?
Math
Algebra
$4x+3y=24$
Mario purchased 4 binders that cost $x$ dollars each and 3 notebooks that cost $y$ dollars each. If the given equation represents this situation, which of the following is the best interpretation of 24 in this context?
Math
Algebra
A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, $p$ people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of $p$ ?
Math
Algebra
The graph of $7x+2y=-31$ 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 $ \frac{b}{a} $?
Math
Algebra
$x$
$f(x)$
0
29
1
32
2
35
For the linear function $f$, the table shows three values of $x$ and their corresponding values of $f(x)$. Which equation defines $f(x)$?
Math
Algebra
$y=-4x+40$
Which table gives three values of $x$ and their corresponding values of $y$ for the given equation?
Math
Algebra
The function $h$ is defined by $h(x)=3x-7$. What is the value of $h(-2)$?
Math
Algebra
$H=120p+60$
The Karvonen formula above shows the relationship between Alice's target heart rate $H$, in beats per minute (bpm), and the intensity level $p$ of different activities. When $p=0$, Alice has a resting heart rate. When $p=1$, Alice has her maximum heart rate. It is recommended that $p$ be between 0.5 and 0.85 for Alice when she trains. Which of the following inequalities describes Alice's target training heart rate?
Math
Algebra
$\bm{4x+6=18}$
Which equation has the same solution as the given equation?
Math
Algebra
$a(3-x)-b=-1-2x$
In the equation above, $a$ and $b$ are constants. If the equation has infinitely many solutions, what are the values of $a$ and $b$?
Math
Algebra
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