14 less than 8 times a number is 3 more than 4 times the number. What is the number?
1 answer:
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Answer:
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- <u>She should aim 6 feet down the wall</u>
Explanation:
The diagram attached sketches the situtation.
Since the angle with which the ball hits the wall is the same with which it bounces, angle β is the same for the two shown triangles.
Then, since both are right triangles, then all the angles are congruent and the triangles are similar. Hence, you can equal the ratios of the sides, to make an equation:
- x/4 = y/2 ⇒ x = 2y
You have other equation:
- x+ y = 18
Substitute
- 2y + y = 18
- 3y = 18
- y = 18/3
- y = 6 ← this is the distance down the wall where the ball should hit
- x = 2(6) = 12
Then, she should aim 6 feet down the wall.
