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Math
Algebra
$$F(x)=\frac{9}{5}(x-273.15)+32$$
The function $F$ gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of $x$ kelvins. If a temperature increased by $9.10$ kelvins, by how much did the temperature increase, in degrees Fahrenheit?
Math
Algebra
An employee at a restaurant prepares sandwiches and salads. It takes the employee 1.5 minutes to prepare a sandwich and 1.9 minutes to prepare a salad. The employee spends a total of 46.1 minutes preparing $\bm{x}$ sandwiches and $\bm{y}$ salads. Which equation represents this situation?
Math
Algebra
$y=2x+10$
$y=2x-1$
At how many points do the graphs of the given equations intersect in the $xy$-plane?
Math
Algebra
A team of workers has been moving cargo off of a ship. The equation below models the approximate number of tons of cargo, $y$, that remains to be moved $x$ hours after the team started working.
$y=120-25x$
The graph of this equation in the $xy$-plane is a line. What is the best interpretation of the $x$-intercept in this context?
Math
Algebra
$y\leq x+7$
$y\geq-2x-1$
Which point $x,y$ is a solution to the given system of inequalities in the $xy$-plane?
Math
Algebra
$x+y=18$
$5y=x$
What is the solution $(x,y)$ to the given system of equations?
Math
Algebra
How many solutions does the equation $10(15x-9)=-15(6-10x)$ have?
Math
Algebra
A bakery sells trays of cookies. Each tray contains at least 50 cookies but no more than 60. Which of the following could be the total number of cookies on 4 trays of cookies?
Math
Algebra
The equation $y=0.1x$ models the relationship between the number of different pieces of music a certain pianist practices, $y$, during an $x$-minute practice session. How many pieces did the pianist practice if the session lasted 30 minutes?
Math
Algebra
On a car trip, Rhett and Jessica each drove for part of the trip, and the total distance they drove was under 220 miles. Rhett drove at an average speed of 35 miles per hour (mph), and Jessica drove at an average speed of 40 mph. Which of the following inequalities represents this situation, where $r$ is the number of hours Rhett drove and $j$ is the number of hours Jessica drove?
Math
Algebra
A total of 364 paper straws of equal length were used to construct two types of polygons: triangles and rectangles. The triangles and rectangles were constructed so that no two polygons had a common side. The equation $3x+4y=364$ represents this situation, where $x$ is the number of triangles constructed and $y$ is the number of rectangles constructed. What is the best interpretation of $(x,y)=(24,73)$ in this context?
Math
Algebra
$(b-2)x=8$
In the given equation, $b$ is a constant. If the equation has no solution, what is the value of $b$ ?
Math
Algebra
A machine makes large boxes or small boxes, one at a time, for a total of 700 minutes each day. It takes the machine 10 minutes to make a large box or 5 minutes to make a small box. Which equation represents the possible number of large boxes, $x$, and small boxes, $y$, the machine can make each day?
Math
Algebra
$2n+6=14$
A tree had a height of 6 feet when it was planted. The equation above can be used to find how many years $n$ it took the tree to reach a height of 14 feet. Which of the following is the best interpretation of the number 2 in this context?
Math
Algebra
Line $t$ in the $xy$-plane has a slope of $-\frac{1}{3}$ and passes through the point $(9,10)$. Which equation defines line $t$?
Math
Algebra
$y\leq X$
$y\leq-X$
Which of the following ordered pairs $X\,,y$ is a solution to the system of inequalities above?
Math
Algebra
The function $g$ is defined by $g(\chi)=-\chi+8$. What is the value of $g(0)$?
Math
Algebra
A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let \(d\) represent the number of containers of detergent, and let \(s\) represent the number of containers of fabric softener, where \(d\) and \(s\) are nonnegative integers. Which of the following systems of inequalities best represents this situation?
\($7.35d+6.2s\leq 300\)
\(d\geq 2s\)
\($7.35d+6.2s\leq 300\)
\(2d\geq s\)
\($14.7d+6.2s\leq 300\)
\(d\geq 2s\)
\($14.7d+6.2s\leq 300\)
\(2d\geq s\)
Math
Algebra
Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, which equation can Alan use to determine how many fewer average miles, $m$, he should drive each week?
$$\begin{array}{ll}&\frac{25}{4}\,m=95\\ &\\ &\frac{25}{4}\,m=5\\ &\\ &\frac{4}{25}\,m=95\\ &\\ &\frac{4}{25}\,m=5\\ \end{array}$$
Math
Algebra
$3(2x-6)-11=4(x-3)+6$
If $x$ is the solution to the equation above, what is the value of $x=3$?
$23$
$2$
$17$
$15$
Math
Algebra
The equation above relates the number of minutes, $x$, Maria spends running each day and the number of minutes, $y$, she spends biking each day. In the equation, what does the number 75 represent?
Math
Algebra
In North America, the standard width of a parking space is at least 7.5 feet and no more than 9.0 feet. A restaurant owner recently resurfaced the restaurant's parking lot and wants to determine the number of parking spaces, $n$, in the parking lot that could be placed perpendicular to a curb that is 135 feet long, based on the standard width of a parking space. Which of the following describes all the possible values of $n$ ?
### $18\leq n\leq 135$
### $7.5\leq n\leq 9$
### $15\leq n\leq 135$
Math
Algebra
A petting zoo sells two types of tickets. The standard ticket, for admission only, costs $5. The premium ticket, which includes admission and food to give to the animals, costs $12. One Saturday, the petting zoo sold a total of 250 tickets and collected a total of $2,300 from ticket sales. Which of the following systems of equations can be used to find the number of standard tickets, s, and premium tickets, $p$, sold on that Saturday?
$$\begin{array}{c}s+p=250\\
Math
Algebra
A group of 202 people went on an overnight camping trip, taking 60 tents with them. Some of the tents held 2 people each, and the rest held 4 people each. Assuming all the tents were filled to capacity and every person got to sleep in a tent, exactly how many of the tents were 2-person tents?
Math
Algebra
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