Answer: (1) 12 (2) 36 or 22 (3) 40
<u>Step-by-step explanation:</u>
NOTES about diagonals of a rectangle:
- diagonals are congruent (equal lengths)
- diagonals intersect at the midpoint
(1) Given: MR = 4x - 60 and AK = 30 - x
Per rule 1 → MR = AK
4x - 60 = 30 - x
5x - 60 = 30
5x = 90
x = 18
MR = 4(18) - 60
= 72 - 60
= 12
(2) Given: MP = x² + 2 and AP = x + 14
Per rule 1 → MP = AP
x² + 2 = x + 14
x² - x - 12 = 0
(x - 4)(x + 3) = 0
x - 4 = 0 or x + 3 = 0
x = 4 or x = -3
AP(4) = (4) + 14 = 18
AP(-3) = (-3) + 14 = 11
Per rule 2 → AK = 2AP
AK(4) = 2(18) = 36
AK(-3) = 2(11) = 22
(3) Given: MR = 4x - 60 and MP = x + 5
Per rule 2 → MR = 2MP
4x - 60 = 2(x + 5)
4x - 60 = 2x + 10
2x - 60 = 10
2x = 70
x = 35
MP = (35) + 5
= 40
Per rule 1 → PR = MP
PR = 40
Step-by-step explanation:
Given
mZEFH = (5x + 1)'
mZHFG = 62°
mZEFG = (18x + 11)',
The addition property of the angle is true
mZEFG = mZEFH + mZHFG
(18x + 11) = (5x + 1)'+ 62
18x+11 = 5x + 63
collect like terms
18x - 5x = 63-11
13x = 52
divide both sides by 13
13x/13 = 52/13
x = 4
Since angle mZEFH = (5x + 1)' and x = 4, we will substitute x = 4 into the function;
mZEFH = 5(4) + 1
mZEFH = 20 + 1
mZEFH = 21°
Similarly for mZEFG = (18x + 11)'
mZEFG = 18(4) + 11
mZEFG =72+11
mZEFG = 83°
Answer:
16 feet
Step-by-step explanation:
just cuz that's what it is
BC is 40% Im a hundred percent sure about it
Answer:
36
Step-by-step explanation:
(2*10)+(2*8)=36