Solving linear equations and inequalities
If x - 9 = 1, what is the value of x?
Stephanie is twice as old as her sister Rosa. If Stephanie is 18 years old, how old is Rosa?
Rosa is 9 years old.
The y-intercept of the graph of y=-7x+140 is located at (0, c). What is the value of c?
140 is the value of c.
5x - y = 3
-5x + 2y = 4
Which ordered pair (x, y) satisfies the given system of equations?
a. (2/5 , -1)
b. (4/5 , 1)
c. (1 , 2)
d. (2 , 7)
Freddie's goal is to walk at least 25 kilometers a week. If he has already walked 13.6 kilometers this week, what is the minimum distance, in kilometers, he still needs to walk this week to meet his goal?
11.4
If p - 18 = 3, what is the value of p?
21
Video games create a sense of motion by displaying still images, called frames, in rapid succession. A popular video game displays 60 frames per second. Which of the following equations shows the total number of frames, f, that the video game will display in s seconds?
a. f = s +60
b. f = s/60
c. f = 60/s
d. f = 60s
f= 60s
The system of inequalities y>= x\] and y<= 1/2 x is graphed in the xy-plane. Which of the following is a solution to the system?
a. (-5 , -3)
b. (-3 , -4)
c. (0 , 1)
d. (3 , 2)
(-5 , -3)
Jordan and Kamron are playing an arcade basketball game. At the end of the game, Kamron scored \[8\] fewer points than Jordan did, and Jordan scored \[1.2\] times as many points as Kamron did. Which of the following systems of equations could be used to find \[j\], the number of points Jordan scored, and \[k\], the number of points Kamron scored?
a. j = 1.2k
j - 8 = k
b. j = 1.2k
k - 8 = j
c. k = 1.2j
j - 8 = k
d. k = 1.2j
k - 8 = j
a. j = 1.2k
j - 8 = k
3x + 2y >= 24
Erica's goal is to score at least \[24\] points in her next playground basketball game. The given inequality represents this goal, where \[x\] is the number of \[3\]-point field goals she scores and \[y\] is the number of \[2\]-point field goals she scores. If she scores 5 3-point field goals, what is the minimum number of \[2\]-point field goals she must score to meet her scoring goal?
5
If -18=6-12x , what is the value of 1-2x ?
-3
Last month, Margo bought a tree that grows 2.5 cm each day. It was 5 cm tall when she bought it and now it is 65 cm tall. How many days has Margo owned the plant?
24 days
The equation -x-2y=0 is graphed in the \[xy\]‑plane. Which of the following is a true statement about the graph?
a. The graph goes through the point \[(-1,2)\].
b. The graph has a slope of \[2\].
c. The graph goes through the point \[(0,0)\].
d. The graph has a slope of 1/2.
c
y= 4.5x + 3
y= C(x + 2)
In the system of equations, \[C\] is a constant. For which values of \[C\] does the system have no solution?
a. 1.5
b. 4.5
c. all real numbers
d. No real numbers
b. 4.5
Trevon is going to buy a coat and a hat. The coat costs \[3\] times as much as the hat. He must spend less than \[\$94\]. If the cost of the hat is \[x\] dollars, which inequality best models this situation?
a. 3x < 94
b. 3x > 94
c. 4x < 94
d. 4x > 94
c. 4x < 94
During her last road trip, Sophia drove 402 miles on 12 gallons of gas. Sophia's car averages 37 miles per gallon (mpg) on highways and 25 mpg in cities. Which of the following best approximates the number of city miles she drove in her car on this trip?
a. 3.5
b. 8.5
c. 87.5
d. 314.5
c. 87.5
The number of problems assigned as homework by a savvy math professor is a function of the length of the class on a particular day, which is either 45 minutes, 90 minutes, or 135 minutes. He first multiplies the number of minutes by 4 and then divides that number by 9. Finally, he subtracts 12 from that amount. Which of the following functions best represents the number of math problems the professor assigns depending on the length of the class, t in minutes?
f(t) = 4/9t - 12
f(t) = 4/9(t - 12)
f(t) = 12 - 4/9t
f(t) = 12 +4/9t
f(t) = 4/9t - 12
Which of the following is the equation of the line A graphed in the xy-plane that passes through the point (-2,2) and is parallel to the line B whose equation is y-3=0?
y+2=0
x+2=0
y-2=0
x-2=0
y - 2 = 0
11e-9f+1 = 5(f-3e)
2f+4e = 3
Consider the system of equations. Which of the following statements is true?
There is only one solution (e,f) and e times f is positive.
There is only one solution (e,f) and e times f is negative.
There are infinitely many solutions.
There are no solutions.
There is only one solution (e,f) and e times f is positive
If the system of inequalities y≤ ⅔ x - 1 and y≤ -2x + 7 is graphed in the xy-plane, which quadrant contains no solutions to the system?
Quadrant I
Quadrant II
Quadrant III
Quadrant IIII
Quadrant 4