Answer:
From the graph attached, we know that 
by the corresponding angle theorem, this theorem is about all angles that derive form the intersection of one transversal line with a pair of parallels. Specifically, corresponding angles are those which are placed at the same side of the transversal, one interior to parallels, one exterior to parallels, like 
and 
.
We also know that, by definition of linear pair postulate, 
and are linear pair. Linear pair postulate is a math concept that defines two angles that are adjacent and for a straight angle, which is equal to 180°.
They are supplementary by the definition of supplementary angles. This definition states that angles which sum 180° are supplementary, and we found that and together are 180°, because they are on a straight angle. That is, 
If we substitute for , we have 
, which means that and are also supplementary by definition.
I got the same answer you did. I think it’s right hope this helps!
Answer:
The area of the triangle is 28 square units
Step-by-step explanation:
First we have to calculate the length of the base of the triangle and the length of the height
To calculate the base we have to subtract point (-1 , 2) from point (7 , 2)
(7 , 2) - (-1 , 2) = ((7 - (-1)) , (2 - 2)) = (8 , 0)
because it has no component in y this means that the length of the base is 8
b = 8
To calculate the height we have to subtract point (-1 , 2) from point (-1 , 9)
(-1 , 9) - (-1 , 2) = (((-1) - (-1)) , (9 - 2)) = (0 , 7)
because it has no component in x this means that the length of the base is 7
h = 7
To calculate the area of a triangle we have to multiply the base by the height and then divide it by 2
a = (b * h)/2
a = (8 * 7)/2
a = 56/2
a = 28
The area of the triangle is 28 square units
Answer:
1). Profit = 3x - 180
2) Profit of selling 1000 video games = $2820
Step-by-step explanation:
Expression for the revenue = 5x² + 2x - 80
Expression for the production cost of the video games = 5x² - x + 100
Since, profit is the difference between the revenue and the cost,
Expression for the profit will be,
Profit = Revenue - Cost
= (5x² + 2x - 80) - (5x² - x + 100)
= 5x² + 2x - 80 - 5x² + x - 100
= 3x - 180
Here, x = Number of video games sold
If number of video games sold = 1000
Profit = (3×1000) - 180
= 3000 - 180
= $2820
Answer:
180(.30)=54, 180-54=126, 126(0.075)=9.45+126=135.45
Step-by-step explanation:
The total is $135.45.
