There are 4 pairs of overlapping triangles that I can see that are congruent. Two pairs share vertically opposite angles.
One more pair have right angles at the bottom of the rectangle.
One other pair have right angles at the top of the rectangle.
Answer:
A. (x,y) → (-x,y)
Step-by-step explanation:
A: (-5,-1)
A': (5,1)
B: (-3, -3)
B': (3, -3)
C: (-5, -5)
C': (5, -5)
D: (-7, -3)
D': (7,-3)
The x values change sign but the y values don't.
Answer:
Wonka bars=3 and Everlasting Gobstoppers=24
Step-by-step explanation:
let the wonka bars be X
and everlasting gobstoppers be Y
the objective is to
maximize 1.3x+3.2y=P
subject to constraints
natural sugar
4x+2y=60------1
sucrose
x+3y=75---------2
x>0, y>0
solving 1 and 2 simultaneously we have
4x+2y=60----1
x+3y=75------2
multiply equation 2 by 4 and equation 1 by 1 to eliminate x we have
4x+2y=60
4x+12y=300
-0-10y=-240
10y=240
y=240/10
y=24
put y=24 in equation 2 we have'
x+3y=75
x+3(24)=75
x+72=75
x=75-72
x=3
put x=3 and y=24 in the objective function we have
maximize 1.3x+3.2y=P
1.3(3)+3.2(24)=P
3.9+76.8=P
80.7=P
P=$80.9
"Better to have loved a short man than never to have loved a tall".
Answer:
12 a. 4605 feet 12 b. 1,459,063 square feet
Step-by-step explanation:
For the perimeter, we simply add the lengths of each of the 5 sides together (or multiply 5 times one side length).
P = 5(921)
P = 4605 feet
For the area, we will use composition...add the area of the triangle to the area of the trapezoid.
For the area of the triangle, the formula is
.
Filling in our values gives us
and
A = 403,045 square feet.
Now for the trapezoid. The formula for a trapezoid is

where the b's represent the bases and the h represents the height. Filling in our values gives us

Work inside the parenthesis first:
and
A = 1,056,018
Now we add those together to get that area of the Pentagon is 1,459,063 square feet