Answer:
$70
Step-by-step explanation:
1 - ⅙ - ¼ = (12 - 2 - 3)/12 = 7/12
7/12 × 480 = 280
280/4 = 70
Observation one
From the markings on the diagram <1 = 60o The left triangle is at least isosceles. Therefore equal sides produce equal angles opposite them.
Now we have accounted for 2 angles that are equal (each is 60 degrees) and add up to 120 degrees. The third angle (angle 2) is found from this equation.
<1 + 60 + <2 = 180 degrees. All triangles have 180 degrees.
60 + 60 + <2 = 180
Observation 2
<2 = 60 degrees.
120 + <2 = 180
m<2 = 180 - 120
m<2 = 60 degrees.
Observation 3
m<3 = 120
<2 and <3 are supplementary.
Any 2 angles on the same straight line are supplementary
60 + <3 = 180
<3 = 180 - 60
<3 = 120
Observation 4
m<4 = 40 degrees.
All triangles have 180 degrees. No exceptions.
m<4 + 20 +m<3 = 180
m<4 + 20 + 120 = 180
m<4 + 140 = 180
m<4 = 180 - 140
m<4 = 40
<span>Because the four numbers are consecutive, we can call the first one x, and the other three are x+1, x+2, and x+3, respectively.
x * (x+1) = (x+2) * (x+3) - 38
x^2 + x = x^2 + 5x +6-38
x^2 + x = x^2 + 5x - 32
-4x = -32
x=8
The four numbers are 8, 9, 10, and 11
check solution: 8*9=10*11-38
72=110-38
72=72</span>
Answer:
70%
Step-by-step explanation:
Percentage is out of 100
35/50 change denominator
multiply both numerator and denominator by 2
70/100= 70%
HG^2 = FG * (FG + EF)
Fill in the values:
(x+3)^2 = x * (7+x)
Simplify the right side:
(x+3)^2 = 7x +x^2
Rewrite the left side using the FOIL method
x^2 + 6x + 9 = 7x +x^2
Subtract x^2 from both sides:
6x +9 = 7x
Subtract 6x from both sides:
x = 9
Now you have x solve for HG
HG = x +3 = 9+3 = 12
The answer is A.
