I cannot figure this out for the life of me! Can someone help me out? Ignore the stuff written down.

Explanation:

Focus on the slanted side of the parallelogram, which is 26 units long. The opposite side to this is also 26 units long since opposite sides of any parallelogram are always congruent.

Now turn your attention to the triangle formed by that dashed line. Specifically this is a right triangle. It has a legs of x and 10, where x is the unknown height (also the height of the parallelogram). The hypotenuse of this right triangle is 26 units as mentioned in the previous paragraph.

Use the pythagorean theorem to find x

a^2+b^2 = c^2

10^2+x^2 = 26^2

100+x^2 = 676

x^2 = 676-100

x^2 = 576

x = sqrt(576)

x = 24

This is a 10,24,26 right triangle, which is based on the 5,12,13 right triangle (divide every part by 2)

Now that we know the height of the parallelogram, the area is simply base times height

area of parallelogram = base*height = 32*24 = 768

Then we subtract off the area of the shaded gray rectangle, so we subtract off 7*16 = 112 to get 768 - 112 = 656 and this is the area of the unshaded region inside the parallelogram.

Side note: The hypotenuse of 10*sqrt(2) you wrote down would only be correct if that dashed height line was 10 units.

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: