Multiple Choice
What is the y-intercept of the equation y=4x+5?
a. (5/4, 0)
b. (4, 0)
c. (0, 4/5)
d. (0, 5)
d. (0, 5)
WORK
y=4x+5
y = 4(0) + 5
y = 5
Solve for x:
5 = 5x - 23 + 2x
x = 4
WORK
5 = 5x - 23 + 2x
5 = 5x + 2x - 23
5 = 7x - 23
5 + 23 = 7x - 23 + 23
28 = 7x
28/7 = 7x/7
4 = x
Write the equation of the line in slope-intercept form.
Point: (0, 3)
Slope: -2
y = -2x + 3
WORK
y - 3 = -2(x - 0)
y - 3 = -2x
y = -2x + 3
Which of the following is perpendicular to y=-3x + 12?
a. y= 1/3x + 18
b. y= -1/3x - 5
c. y= 3x + 2
d. y= -3x - 7
a. y= 1/3x + 18
WORK
Check the slopes:
m1 * m2 = -1
-3 * -1/3 = -1
Solve for x:
8x + 12 = 48 - 3(x + 1)
x = 3
WORK
8x + 12 = 48 -3x - 3
11x = 33
x = 3
Write the equation of the line in slope-intercept form.
Point: (5, 2)
Slope: 3
y = 3x - 13
WORK
y - 2 = 3 (x - 5)
y - 2 = 3x - 15
y = 3x - 13
Solve:
A 36-inch stick is broken into two pieces. If one piece is 8 inches longer than the other, how long is each piece?
14 in., 22 in.
WORK
x = length of first piece
x+8 = length of second piece
x + x+8 = 36
2x + 8 = 36
2x = 28
x = 14 in.
plug x in to the length of second piece
(14) + 8 = 22 in.
Which of the following lists the correct order of operations?
a. exponents, parenthesis, multiplication, addition, division, subtraction
b. parenthesis, exponents, multiplication, division, addition, subtraction
c. parenthesis, multiplication, addition, division, subtraction, exponents
d. exponents, parenthesis, multiplication, addition, subtraction, division
b. parenthesis, exponents, multiplication, division, addition, subtraction
PEMDAS
Solve for x:
1/3x + 1/4 = 5/6x - 1
x = 5/2
WORK
Get rid of fractions by multiplying each term by the LCD.
12 * (1/3x + 1/4) = (5/6x - 1) * 12
4x + 3 = 10x - 12
4x - 10x = -12 -3
-6x = -15
x = 5/2
Write the equation of the line in slope-intercept form.
Point: (3, -2)
Point: (-3, 0)
y = -1/3x - 1
WORK
m = (0 + 2)/ (-3 - 3) = 2/-6 = -1/3
Use point-slope formula:
y - 0 = -1/3 (x + 3)
y = -1/3x - 1
Solve:
One number is 40% more than another number. If the sum of the two numbers is 84, find the numbers.
The two numbers are 35 and 49
WORK
x + x +.4x = 84
2.4x = 84
x = 35
plug x in to the other number = 35 + .4(35) = 49
Which of the following fractions is in the lowest terms?
a. 3/6
b. 3/12
c. 5/12
d. 5/30
c. 5/12
Solve for x:
3.5 - 0.02x = 1.24
x = 113
WORK
3.5 - 0.02x = 1.24
100*(3.5 - 0.02x) = 1.24*100
350 - 2x = 124 [Distributive Property]
350 - 350 - 2x = 124 - 350
-2x/(-2) = -226/(-2)
x = 113
Find the equation of the line that passes through the given point and is parallel to the given line.
Point: (2, 0)
Parallel to: y = -1/2x + 1/5
y = -1/2x + 1
WORK
m = -1/2
Use point-slope formula:
y - 0 = -1/2 (x - 2)
y = -1/2x + 1
Express the problem algebraically. Don't Solve.
The rotational inertia I of a solid sphere is two fifths of the product of the sphere's mass m and its radius squared r2.
I = (2/5)mr2
Which of the following states that if any quantity is added to (or subtracted from) both sides of an equation, the equation remains true?
a. addition property of equality
b. inverse properties
c. multiplication property of equality
d. identity properties
a. addition property of equality
Solve for x:
5|2x+6| - 13 = -3
[remember that absolute values have two solutions]
-4, -2
WORK
5|2x+6| -13 = -3
5|2x+6|=10
|2x+6| = 2 -> 2x+6 = 2 or 2x+6 = -2
x= -2 x = -4
Graph each line, using the given information.
x - 3y = -6
There are many ways:
1. Change the equation to Slope-Intercept Form then graph.
x - 3y = -6
-3y = -x - 6
y = 1/3x + 2
2. Create a table then plot the points.
x | y
0 | 2
-6 | 0
6 | 4
Solve
Glenda wants to earn $2,000 in simple interest through a bank account earning 5% annually. How much principal would she need to invest in the account to meet her interest goal in 4 years? (Hint: i=prt)
$10,000
WORK
i=prt -> p = i/rt
2,000/(0,05)(4) = 2,000/.2 = $10,000