sat-dog

$3x+21=3x+k$

In the given equation, $k$ is a constant. The equation has infinitely many solutions. What is the value of $k$?

If x is the solution to the equation above, what is the value of ?

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?

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?

The function g is defined by . What is the value of ?

Which of the following ordered pairs is a solution to the system of inequalities above?

Line $t$ in the xy-plane has a slope of $-\frac{1}{3}$ and passes through the point $\left(9,10\right)$. Which equation defines line $t$?

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?

$2x+16=a\left(x+8\right)$

In the given equation, $a$ is a constant. If the equation has infinitely many solutions, what is the value of $a$?

If $\frac{x}{8}=5$, what is the value of $\frac{8}{x}$?

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?

The perimeter of an isosceles triangle is $83$ inches. Each of the two congruent sides of the triangle has a length of $24$ inches. What is the length, in inches, of the third side?

In the given equation, b is a constant. If the equation has no solution, what is the value of b ?

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 $\left(x,y\right)=\left(24,73\right)$ in this context?

The function $f$ is defined by $f\left(x\right)=4x$. For what value of $x$ does $f\left(x\right)=8$?

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 $35 \text{miles} \text{per} \text{hour} \left(\text{mph}\right)$, and Jessica drove at an average speed of $40 \text{mph}$. 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?

A local transit company sells a monthly pass for $95 that allows an unlimited number of trips of any length. Tickets for individual trips cost $1.50, $2.50, or $3.50, depending on the length of the trip. What is the minimum number of trips per month for which a monthly pass could cost less than purchasing individual tickets for trips?

The equation 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?

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?

How many solutions does the equation $10\left(15x-9\right)=-15\left(6-10x\right)$ have?

$x+y=18$

$5y=x$

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

According to the graph, what is the cost for each additional mile traveled, in dollars, of a cab ride?

In the xy-plane, line k intersects the y-axis at the point and passes through the point . If the point lies on line k, what is the value of w ?

$y\le x+7$

$y\ge -2x-1$

Which point $\left(x,y\right)$ is a solution to the given system of inequalities in the xy-plane?

The graph of this equation in the xy-plane is a line. What is the best interpretation of the x-intercept in this context?