Answer:
x=20 degrees
Step-by-step explanation:
because this is a supplementary angle, you add everything and set it equal to 180 degrees. so it would be x + 100 + 3x = 180. combine like terms to get 100 + 4x = 180. subtract 100 from both sides to get 4x = 80. divide by 4 on both sides to isolate the x and your final answer is 20. hope this helped! good luck in school xoxo
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Answer:
<em>SOLUTION: Over the last three evenings, Heather received a total of 109 phone calls at the call center. The third evening, she received 4 times as many calls as the second evening</em>
1. <span><span>20,000 </span><span>+7,000 </span><span>+500 </span><span>+40 </span><span>+9 -----WORD FORM :</span></span>twenty-seven thousand,
five hundred forty-nine
2. <span>Expanded Numbers Form:
</span>
<span><span> 700,000 </span><span>+90,000 </span><span>+2,000 </span><span>+0 </span><span>+60 </span><span>+5 </span></span>
WORD FORM : seven hundred ninety-two thousand,
sixty-five
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 %
