Inequalities and Equations
Simplify:
4-5(-4n+3)
20n-11
What is the domain and range of the following set of ordered pairs:
{(2,4), (-8,3), (4,6), (-3,4), (2,7)}
Range: {3,4,6,7}
What would be the value of c so that the points (-5,10) and (3,c) lie on a line with a slope of -3/8?
c=7
Write an equation in slope-intercept form of a line having an undefined slope that passes through the point (5,-3)?
x=5
A boy has 7 more nickels than quarters. The total value of the coins is $4.90. Write a system that could be used to find how many nickels and quarters he has. Use n for nickels and q for quarters.
n - q = 7
0.05n+0.25q=4.90
Simplify:
3-8(7-5n)+2(n+4)
42n-45
A plane can carry a maximum cargo weight of 160,000 pounds. A company uses one of these planes to ship 2,000-pound containers. The total cargo weight is a function of the number of containers in the plane. What is the greatest value in the domain for this situation?
80
Find the x and y intercept and the slope for the following linear functions:
x y
-3 | -6
0 | -4
3 | -2
6 | 0
x-int: 6
y-int: -4
slope: 2/3
Write the following equation in standard form:
y=-2/3x+8
2x+3y=24
Determine the number of solutions for the following system:
y=2x
y=1/2x-3
One solution
Solve for b:
a = 4br2
b = a/4r2
A rocket takes off from Earth and ascends at a rate of 1,500 feet per minute (domain is at 0). What is a reasonable domain if the rocket starts at the ground, y=0, and continuously ascends straight up into space for an infinite time? (You don’t have to take inconsideration of the earth rotation).
0≤x<infinity
(continous)
Write an equation in slope-intercept form. Identify the slope and y-intercept of each.
-2x+3y=-21
y=2/3x-7
slope: 2/3
y-int: (0,-7)
If the 5th term of an arithmetic sequence is equal to 23 and the 6th term is equal to 27. What is the first term of the sequence and what is the common difference?
First term: 7
Common difference: 4
Find the solution to the system of equations using substitution:
x+y=3
-4x-4y=12
No solution
Solve the inequality:
-8x+2x-16<-5x+7x
x>-2
Let g(x) = -7x+4. Find the what g(x) is when x is equal to 3/2?
g(x) = -13/2
Write the equation in slope intercept form for the two points below.
(6,7) and (9,7)
y=7
Use the Arithmetic Explicit Form to solve.
1,6,11,16, ...; Find a8
36
Find the solution to the system of equations using elimination:
2x+7y=2
5x-2y=83
(-13,4)
How many solutions does the following inequality have?
3(10+x)≤3x+36
All real solutions
If f(x) = (x-3)2 +4 and g(x) = x3+2, which statement is true:
F: f(-2) = g(-3)
G: f(0) = g(-1)
H: f(8) = g(3)
J: f(2) = g(1)
H
How does the graph of y=8x+1 compare to the graph y=3x=1?
The slope of y=8x+1 is steeper
Stephen is walking from his house to his friend Sharon's house. When he is 12 blocks away, he looks at his watch. he looks again when he is 8 blocks away and finds that 6 minutes have passed. Write a linear equation in slope intercept form for the two points (0,12) and (6,8) and find what is the total amount of time it takes Stephen to reach Sharon's house.
y=-2/3x+12
18 minutes
A farmer plants corn and wheat on a 180-acre farm. The farmer wants to plant 3 times as many acres of corn as wheat. Write a system of linear equations that represents this situation. How many acres of each crop should the farmer plant?
Equations:
x+y=180
x=3y
The farmer should plants 135 acres of corn and 45 acres of wheat.