<u><em>Answer:</em></u>
θ = 76°
<u><em>Explanation:</em></u>
<u>The given equation is:</u>
8 cotθ + 3 = 5
8 cotθ = 5-3
8 cotθ = 2
cot θ = 
<u>Now, we find θ</u>
We know that the cot function is the inverse of the tan function.
The tan of an angle is positive in the first and third quadrants, therefore, the cot will be <u>positive</u> in the <u>first and third quadrants</u> as well
<u>Now, we are given the condition:</u>
0° ≤ x ≤ 90°
<u>Therefore, we know for sure that our angle is in the first quadrant</u>
θ = cot⁻¹(
) = 75.96° = 76° to the nearest degree
Hope this helps :)
Answer: 1.25 square feet
This converts to the improper fraction 5/4
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Explanation:
The area of the triangle on the left is base*height/2 = 0.5*2/2 = 0.5 square feet. Note that 1/2 = 0.5
The area of the triangle on the right side is base*height/2 = 0.2*3/2 = 0.75 square feet. This converts to the fraction 3/4
Add up the two results: 0.5+0.75 = 1.25 square feet
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If you need the answer as an improper fraction, then,
1.25 = 1 + 0.25
1.25 = 1 + 1/4
1.25 = 4/4 + 1/4
1.25 = (4+1)/4
1.25 = 5/4
The GCF (Greatest Common Factor) is 6a.
24000 + 3000x = 30000 + 2400x
3000x - 2400x = 30,000 - 24,000
600x = 6000
x = 6000/600
x = 10 years
