Thank you for posting your question here, to solve the compound inequality of 5x + 11 ≥ –9 and 10x – 3 ≤ 27 the answer is A which is " x ≥ –4 and x ≤ 3". Below is the solution:
5x + 11 ≥ -9 and 10x - 3
≤ 27<span>
5x ≥ -9 - 11 and 10x ≤ 27 + 3
5x ≥ -20 and 10x ≤ 30
x ≥ -20/5 and x ≤ 30/10
<span>x ≥ -4 and x ≤ 3</span></span>
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 %
Yes
slope = (26 - 13) / (16-8) = 13/8
y = mx + b passing (8,13)
13 = 13/8(8) + b
13 = 13 + b
so b = 13-13 = 0
equation y = 13/8x