Answer:
The answer is 5x^2+32x-21
Step-by-step explanation:
To find the area of a rectangle, you have to multiply the length by the width. Then, you will get the equation of (5x-3)(x+7). Then, multiply these two together, therefore getting 5x^2+32x-21.
-5.8 - (-8.4)
When we multiply two negatives they become a positive. In this situation, where there is no other number, you can assume there's basically a 1 in that place.
-5.8 - 1(-8.4) would be just as correct. (If this helps visually clarify anything.)
So we take that -1 and multiply it by that -8.4. Multiplying 1 against anything leaves it the same, so we just need to change the sign. Two negatives make a positive.
-5.8 + 8.4
Now we add these together.
This gives us our final answer of 2.6
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 %
