Let's make variables for two angles first. One angle will be x, and the other will be y.
Since they're supplementary, we know x + y = 180
We also know x = y - 32, since it's 32 degrees less than it's supplement.
Input the value of x into the first equation and...
y - 32 + y = 180
2y - 32 = 180
Add 32 to both sides:
2y = 212
Divide both sides by 2:
y = 106
We can solve for x in two ways.
One, we can subtract 32 from 106 since x is 32 degrees less.
Or, we could also just subtract 106 from 180 since we know the angles are supplementary.
x = 74
74 degrees and 106 degrees. The equation is y - 32 + y = 180, or x + y = 180
Answer:
It is the second option B
Step-by-step explanation:
right
Answer:
The amount of sales in order to meet her goal must be greater than or equal to $20,000
Step-by-step explanation:
Let
x----> represent the amount of sales Liz will need
we know that
The amount of sales for the month multiplied by the commission rate as a decimal plus the fixed amount must be greater than or equal to $2,800 each month
so
The inequality that represent this situation is
solve for x
subtract 2,200 both sides
divide by 0.03 both sides
The amount of sales in order to meet her goal must be greater than or equal to $20,000
We could find the slope with this formula
m = (y₂ - y₁)/(x₂ - x₁)
with (x₁,y₁) and (x₂,y₂) are the points that is located on the line.
NUMBER 20
Given:
(x₁,y₁) = (-2,3)
(x₂,y₂) = (7,-4)
Solution:
Input the points to the formula
m = (y₂ - y₁) / (x₂ - x₁)
m = (-4 - 3) / (7 - (-2))
m = -7 / (7+2)
m = -7/9
The slope of the line is -7/9
NUMBER 21
Given:
(x₁,y₁) = (-6,-1)
(x₂,y₂) = (4,1)
Solution:
Input the points to the formula
m = (y₂ - y₁) / (x₂ - x₁)
m = (1-(-1)) / (4 -(-6))
m = (1+1) / (4+6)
m = 2/10
m = 1/5
The slope of the line is 1/5
NUMBER 22
Given:
(x₁,y₁) = (-9,3)
(x₂,y₂) = (2,1)
Solution:
Input the points to the formula
m = (y₂ - y₁) / (x₂ - x₁)
m = (1 - 3) / (2 - (-9))
m = -2 / (2 + 9)
m = -2/11
The slope of the line is -2/11
Step-by-step explanation:
Let alpha be the unknown angle. We can set up our sine law as follows:
or
Solving for alpha,
