sat-dog

One of the two equations in a linear system is . The system has no solution. Which of the following could be the other equation in the system?

The point with coordinates $(d,4)$ lies on the line shown. What is the value of $d$?

$66x=66x$

How many solutions does the given equation have?

The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food. If the 180 food calories in a granola bar come entirely from p grams of protein, f grams of fat, and c grams of carbohydrate, which of the following expresses f in terms of p and c ?

Which of the following systems of equations has the same solution as the system of equations graphed above?

A moving truck can tow a trailer if the combined weight of the trailer and the boxes it contains is no more than $\mathrm{4,600}$ pounds. What is the maximum number of boxes this truck can tow in a trailer with a weight of $500$ pounds if each box weighs $120$ pounds?

An object hangs from a spring. The formula relates the length , in centimeters, of the spring to the weight w, in newtons, of the object. Which of the following describes the meaning of the 2 in this context?

The equation , where a and b are constants, has no solutions. Which of the following must be true?

I.

II.

III.

If is the solution to the given system of equations, what is the value of y ?

In the equation above, F represents the total amount of money, in dollars, a food truck charges for x drinks and y salads. The price, in dollars, of each drink is the same, and the price, in dollars, of each salad is the same. Which of the following is the best interpretation for the number 7.00 in this context?

For the function f, if for all values of x, what is the value of ?

A proposal for a new library was included on an election ballot. A radio show stated that $3$ times as many people voted in favor of the proposal as people who voted against it. A social media post reported that $\mathrm{15,000}$ more people voted in favor of the proposal than voted against it. Based on these data, how many people voted against the proposal?

A rocket contained $\mathrm{467,000}$ kilograms (kg) of propellant before launch. Exactly $21$ seconds after launch, $\mathrm{362,105}$ kg of this propellant remained. On average, approximately how much propellant, in kg, did the rocket burn each second after launch?

$2x+3y=7$
$10x+15y=35$

For each real number $r$, which of the following points lies on the graph of each equation in the xy-plane for the given system?

In the xy-plane, line k is defined by . Line j is perpendicular to line k, and the y-intercept of line j is . Which of the following is an equation of line j ?

The average annual energy cost for a certain home is $4,334. The homeowner plans to spend $25,000 to install a geothermal heating system. The homeowner estimates that the average annual energy cost will then be $2,712. Which of the following inequalities can be solved to find t, the number of years after installation at which the total amount of energy cost savings will exceed the installation cost?

Henry receives a $\$60.00$ gift card to pay for movies online. He uses his gift card to buy $3$ movies for $\$7.50$ each. If he spends the rest of his gift card balance on renting movies for $\$1.50$ each, how many movies can Henry rent?

The table shows three values of $x$ and their corresponding values of $y$, where $n$ is a constant, for the linear relationship between $x$ and $y$. What is the slope of the line that represents this relationship in the xy-plane?

The minimum value of $x$ is $12$ less than $6$ times another number $n$. Which inequality shows the possible values of $x$?

The width of a rectangular dance floor is w feet. The length of the floor is 6 feet longer than its width. Which of the following expresses the perimeter, in feet, of the dance floor in terms of w ?

A neighborhood consists of a $2$-hectare park and a $35$-hectare residential area. The total number of trees in the neighborhood is $\mathrm{3,934}$. The equation $2x+35y=\mathrm{3,934}$ represents this situation. Which of the following is the best interpretation of x in this context?

Jay walks at a speed of $3$ miles per hour and runs at a speed of $5$ miles per hour. He walks for $w$ hours and runs for $r$ hours for a combined total of $14$ miles. Which equation represents this situation?

Scientists collected fallen acorns that each housed a colony of the ant species P. ohioensis and analyzed each colony's structure. For any of these colonies, if the colony has $x$ worker ants, the equation $y=0.67x+2.6$, where $20\le x\le 110$, gives the predicted number of larvae, $y$, in the colony. If one of these colonies has $58$ worker ants, which of the following is closest to the predicted number of larvae in the colony?

A librarian has 43 books to distribute to a group of children. If he gives each child 2 books, he will have 7 books left over. How many children are in the group?

The graph of the function f is a line in the xy-plane. If the line has slope and , which of the following defines f?