Chapter 1
What is the verbal expression for 19a?
The product of 19 and a number.
What is the proportion of 2/7 = x/42?
x = 12
Determine whether the following equation is linear.
y = 4 - 3x
Add 3x to each side and simplify it. The equation is now in standard form where A = 3, B = 1, and C = 4. The equation is linear.
Write the slope-intercept form for the slope of 3/4 and the y-intercept of -2.
y = 3/4x + (-2)
What is the inequality for x - 7 > 3?
{x|x > 10}
What property is used in n + 0 = 7?
Additive Identity Property
t = 2 1/2
0 = 1/3x - 2
Add 2 to each side: 0 + 2 = 1/3x - 2 + 2
Multiply each side by 3: 3(2) = 3(1/3x)
Solve: 6 = x
Write 3x + 2y = 6 in slope-intercept form.
Subtract 3x from each side: 3x + 2y - 3x = 6 - 3x
Simplify: 2y = 6 - 3x
Switch: 2y = -3x + 6
Divide each side by 2: 2y/2 = -3x + 6/2
The slope-intercept form is y = -3/2x + 3
What inequality has the solution set of {x|x > 3 or x < -3}?
|2x| > 6
What property is used in 12(100) + 12(13)?
Distributive Property
$4.20
Number of Games: x = 2, 4, 6
Total Cost: y = 78, 156, 234
rate of change = change in y/change in x
= change in cost/change in number of games
= 156-78/4-2
= 78/2 or 39/1
The rate of change is 39/1 which means each game costs 39 dollars.
Write an equation of the passing line.
(3,1) and (2,4)
m = y2-y1/x2-x1
=4-1/2-3
=3/-1 or -3
If x < 0, which integer does not satisfy the inequality x + 2 < 1?
-1
What is the solution to x+4=7 if the replacement set is {1,2,3,4,5}?
x = 3
What is the percent of change from 10 to 12?
20%
Find the slope of these two pairs of points.
(-2,0) and (1,5)
m = y2-y1/x2-x1
5-0/1-(-2)
=5/3
Write an equation for the line that passes through (-3,5) and is parallel to the graph of y = 2x - 4.
Point-slope form: y - y1 = m(x-x1)
Replace m with 2 and (x1, y1) with (-3,5): y - 5 = 2[x-(-3)]
Simplify: y - 5 = 2(x+3)
Distributive Property: y - 5 = 2x + 6
Add 5 to each side: y - 5 + 5 = 2x + 6 = 5
Write in slope-intercept form: y = 2x + 11
What is the best method for solving this equation?
5x - 2y = 4
2x + 2 = 8
Elimination using addition.
What is the domain of (1,3), (-1,1), (3,0), and (0,-2)?
(-1, 0, 1, 3)
How do you translate the following equation into a sentence?
The number x plus five is two times the sum of seven and x.
x + 5 = 2(7 + x)
Which is considered an arithmetic sequence?
5,2,6,3,7
3,5,7,9,11
2,1,9,8,11,10
3,5,7,9,11
Distributive Property: y + 3 = 3/2x + 3/2
Subtract 3 from each side: y = 3/2x - 3/2
The slope-intercept form is y = 3/2x - 3/2.
If A = [2 -1, 3 0] and B = [1 0, 4 1], what is A+B?
[3 -1, 7 1]