You are given that all three sides are equal. You also know that all three angles are also equal. Therefore since all three angles are equal and every triangle has 180 degrees, each angle is 180/3 = 60
So
7x - 3 = 60 Add three to both sides
7x - 3 + 3 = 60 + 3 Combine
7x = 63 Divide by 7
7x/7 = 63/7
x = 9 And that's your answer.
Step-by-step explanation:
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Answer:
a. 12 feet b. 12 feet 0.5 inches c. 8.33 %
Step-by-step explanation:
a. How far out horizontally on the ground will it protrude from the building?
Since the rise to run ratio is 1:12 and the building is 12 inches off the ground, let x be the horizontal distance the ramp protrudes.
So, by ratios rise/run = 1/12 = 12/x
1/12 = 12/x
x = 12 × 12
x = 144 inches
Since 12 inches = 1 foot, 144 inches = 144 × 1 inch = 144 × 1 foot/12 inches = 12 feet
b. How long should the ramp be?
The length of the ramp, L is gotten from Pythagoras' theorem since the ramp is a right-angled triangle with sides 12 inches and 144 inches respectively.
So, L = √(12² + 144²)
= √[12² + (12² × 12²)]
= 12√(1 + 144)
= 12√145
= 12 × 12.042
= 144.5 inches
Since 12 inches = 1 foot, 144.5 inches = 144 × 1 inch + 0.5 inches = 144 × 1 foot/12 inches + 0.5 inches = 12 feet 0.5 inches
c. What percent grade is the ramp?
The percentage grade of the ramp = rise/run × 100 %
= 12 inches/144 inches × 100 %
= 1/12 × 100 %
= 0.0833 × 100 %
= 8.33 %
Simplify -5x + 12 - 7x to -12x + 12
-12x + 12 = -3(5x + 8)
Expand
-12x + 12 = -15x - 24
Add 15x to both sides
-12x + 12 + 15x = -24
Simplify 12x + 12 + 15x to 3x + 12
3x + 12 = -24
Subtract 12 from both sides
3x = -24 - 12
Simplify -24 - 12 to -36
3x = -36
Divide both sides by 3
x = -36/3
Simplify 36/3 to 12
<u>x = -12</u>
