sat-dog

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 $r$?

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?

If f is the function defined by , what is the value of ?

$d=16t$

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?

$f\left(x\right)=39$

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

The function $g$ is defined by $g\left(x\right)=6x$. For what value of $x$ is $g\left(x\right)=54$?

$4x+5=165$

What is the solution to the given equation?

A company that provides whale-watching tours takes groups of $21$ people at a time. The company’s revenue is $80$ dollars per adult and $60$ dollars per child. If the company’s revenue for one group consisting of adults and children was $\mathrm{1,440}$ dollars, how many people in the group were children?

In the xy-plane, the graph of the linear function $f$ contains the points $\left(0,3\right)$ and $\left(7,31\right)$. Which equation defines $f$, where $y=f\left(x\right)$?

The number $y$ is $84$ less than the number $x$. Which equation represents the relationship between $x$ and $y$?

The function $f$ is defined by the equation $f\left(x\right)=7x+2$. What is the value of $f\left(x\right)$ when $x=4$?

At how many points do the graphs of the equations $y=x+20$ and $y=8x$ intersect in the xy-plane?

Marisa needs to hire at least 10 staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid $640 per week, and senior directors, who will be paid $880 per week. Her budget for paying the staff members is no more than $9,700 per week. She must hire at least 3 junior directors and at least 1 senior director. Which of the following systems of inequalities represents the conditions described if x is the number of junior directors and y is the number of senior directors?

John paid a total of $\$165$ for a microscope by making a down payment of $\$37$ plus $p$ monthly payments of $\$16$ each. Which of the following equations represents this situation?

$y=3x$

$2x+y=12$

The solution to the given system of equations is $\left(x,y\right)$. What is the value of $5x$?

Valentina bought two containers of beads. In the first container 30% of the beads are red, and in the second container 70% of the beads are red. Together, the containers have at least 400 red beads. Which inequality shows this relationship, where x is the total number of beads in the first container and y is the total number of beads in the second container?

$y=x+4$

Which table gives three values of $x$ and their corresponding values of $y$ for the given equation?

The total cost, in dollars, to rent a surfboard consists of a $\$25$ service fee and a $\$10$ per hour rental fee. A person rents a surfboard for $t$ hours and intends to spend a maximum of $\$75$ to rent the surfboard. Which inequality represents this situation?

A model predicts that a certain animal weighed $241$ pounds when it was born and that the animal gained $3$ pounds per day in its first year of life. This model is defined by an equation in the form $f\left(x\right)=a+bx$, where $f\left(x\right)$ is the predicted weight, in pounds, of the animal $x$ days after it was born, and $a$ and $b$ are constants. What is the value of $a$?

A shipping company charged a customer $25 to ship some small boxes and some large boxes. The equation above represents the relationship between a, the number of small boxes, and b, the number of large boxes, the customer had shipped. If the customer had 3 small boxes shipped, how many large boxes were shipped?

What is the equation of the line that passes through the point $\left(0,5\right)$ and is parallel to the graph of $y=7x+4$ in the xy-plane?

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?

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?

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 ?

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?