Matthew borrowed $24,000 dollars to buy a new truck. After 5 years, he paid $7,500 in simple interest. What was the interest rat
1 answer:
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Let the unknown number be .
Then the opposite of this unknown number will be .
It is given to us in the question that when this unknown number, is increased by 9, or in other words when 9 is added to this unknown number,
, then this becomes 5 times it's opposite, which is
.
Thus, from the given condition in the question, the equation we get is as:
We will solve this by isolating as:
Thus the required number is -1.5
Answer:
41°
Step-by-step explanation:
This problem involving the Law of Cosines has been mostly worked for you. The value of the cosine is the solution to the remaining one-step linear equation. The inverse cosine function (cos⁻¹ or arccos) is used to find the angle from the value of the cosine.
-1125 = -1500·cos(A)
cos(A) = -1125/-1500 = 3/4 . . . . . divide by -1500 (this is the one step)
A = arccos(3/4) ≈ 41.4096°
The angle formed by the lines to the lampposts is about 41°.
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<em>Additional comment</em>
If you find the angle using the ACOS( ) function of a spreadsheet, you will always get the result in radians. Most calculators offer the choice of units for angles, so be sure you set the mode appropriately.
In the calculator screenshot, there is a decimal point in the fraction to force the angle result to be displayed as a numerical value. Otherwise, this calculator shows cos⁻¹(3/4), which isn't terribly helpful.
