Answer/Step-by-step explanation:
1. An isosceles ∆ has two equal sides. The base angles of an isosceles ∆ are also equal.
Therefore:
m<U = 54° (base angle of isosceles ∆)
m<T = 180 - (54 + 54) (sum of ∆)
m<T = 72°
2. ∆LMN is an isosceles ∆, therefore:
m<M = ½*(180 - 28) = 76°
m<N = m<M (base angle of isosceles)
m<N = 76°
3. ∆FEG is an isosceles ∆, because it has two equal base angles.
Therefore:
EF = FG
EF = 18 in
m<F = 180 - (23 + 23) = 134°
4. ∆PQR is an equilateral ∆. All sides and angles of an equilateral ∆ are equal.
Therefore:
m<P = 60°
m<Q = 60°
m<R = 60°
5. 4x + 23 = 10x - 1 (2 asides of an isosceles ∆ are equal)
Collect like terms
4x - 10x = -23 - 1
-6x = -24
Divide both sides by -6
x = 4
6. 2*(9x - 25) = 180 - 104 (base angles of isosceles ∆)
18x - 50 = 76
Add 50 to both sides
18x = 76 + 50
18x = 126
Divide both sides by 18
x = 7
7. 5x - 7 = 8x - 55 (base angles of an isosceles)
Collect like terms
5x - 8x = 7 - 55
-3x = -48
Divide both sides by -3
x = 16
8. 4x + 8 = 60° (angle of an equilateral ∆)
Subtract 8 from each side
4x = 60 - 8
4x = 52
Divide both sides by 4
x = 13
Answer:1) 18
2)78
Step-by-step explanation:
20% increase in the amount of people
Answer:
x = 6
Step-by-step explanation:
Given that PQ = 3x + 14, QR = 7x - 10, and Q is the midpoint of PR, it means Q is equidistant from both endpoints of P and Q. In order words, the distance from P to Q is the same as the distance from Q to R.
Therefore, PQ = QR. Which is:
Solve for x. Collect like terms
Divide both sides by -4x
Answer:
Step-by-step explanation:
The equation of a line
y = mx + c
y - intercept point y
m - slope of the line
x - intercept point x.
c - intercept of the line
Step 1: find the slope
m = y2 - y1 / x2 - x1
Given two points
( -7 , -7) ( -7 , 4)
x1 = -7
y1 = -7
x2 = -7
y2 = 4
Insert the values into the equation
m = 4 - (-7) / -7 -(-7)
m = 4 + 7 / -7 + 7
m = 11/ 0
Step 2: sub any of the two points given into the equation
y= mx + c
y = 11/0x + c
(-7 ,4 )
x = -7
y = 4
4 = 11/0(-7) + c
4 = -77/0 +c
-77/0 is math error which means that the points are not correct