Answer:
- s + m + L = 78
- 0.45s +0.60m +0.75L = 46.95
- s - m + L = 4
Step-by-step explanation:
The problem statement asks for the number of each size cup sold. You are told there are three sizes, so it is convenient to use one variable to represent the number of cups of a given size that were sold—three variables total.The problem statements tell you the relationships between the numbers:
- the total number of cups sold
- the total value of cups sold
- the relationship between numbers of one size versus other sizes
It is appropriate to write an equation for each of these relationships, for a total of three equations. (Here, the last of these equations is put into standard form to make it easier to translate this to a matrix equation for solving by calculator.)
___
The solution is: 20 small, 37 medium, and 21 large.
Answers:
- Part A) There is one pair of parallel sides
- Part B) (-3, -5/2) and (-1/2, 5/2)
====================================================
Explanation:
Part A
By definition, a trapezoid has exactly one pair of parallel sides. The other opposite sides aren't parallel. In this case, we'd need to prove that PQ is parallel to RS by seeing if the slopes are the same or not. Parallel lines have equal slopes.
------------------------
Part B
The midsegment has both endpoints as the midpoints of the non-parallel sides.
The midpoint of segment PS is found by adding the corresponding coordinates and dividing by 2.
x coord = (x1+x2)/2 = (-4+(-2))/2 = -6/2 = -3
y coord = (y1+y2)/2 = (-1+(-4))/2 = -5/2
The midpoint of segment PS is (-3, -5/2)
Repeat those steps to find the midpoint of QR
x coord = (x1+x2)/2 = (-2+1)/2 = -1/2
y coord = (x1+x2)/2 = (3+2)/2 = 5/2
The midpoint of QR is (-1/2, 5/2)
Join these midpoints up to form the midsegment. The midsegment is parallel to PQ and RS.
-5=-5
-12+7 = x+3
-5 = x+3
-5-3 =x
x = -8
-12+7 = -8 +3
-5 = -5
Remember that the y-intercept is where the function has a value of 
and the x-intercept is where the function has a value of 
. Thus, to find the x-intercept and y-intercept, we can substitute these values into the equation and solve for the other variable.
<u>x-intercept</u>
Since the x-intecept has a y-value of 0, we can substitute this into the function and solve for 
.
The x-value of the x-intercept is 
and the y-value is 0, meaning that the x-intercept has coordinates 
.
<u>y-intercept</u>
Since the y-intercept has a x-value of 0, we can substitute this into the equation and solve for 
:
The y-value of the y-intercept is -3, meaning that the y-intercept of the function is 
.
