SOLUTION: I need help with this three problems i've tried them every way possible but i don't get the answer. I have the answers but i don't know how to get to them. so i can understand the

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Question 70971: I need help with this three problems i've tried them every way possible but i don't get the answer. I have the answers but i don't know how to get to them.
so i can understand them and do my own homework. please help.
Problem# 30 for chapter 9.5
Solve each of the equaitons . Be sute to show how to check the solutions.
inside of the square root it has : 2y+7 then space +4 = y


Problem # 16 from chapter 9.6
Geometry. For the home described in exercise 15, if the roof is 7m from peak to eave and the attic space is 3m high at the peak, how long does each of the pieces of insultaion need to be? round to the nearest tenth.



Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
#30. Solve:
sqrt%282y%2B7%29%2B4+=+y Subtract 4 from both sides of the equation.
sqrt%282y%2B7%29+=+y-4 Now square both sides.
2y%2B7+=+%28y-4%29%5E2 Simplify the right side.
2y%2B7+=+y%5E2-8y%2B16 Subtract (2y+7) from both sides.
y%5E2-10y%2B9+=+0 Factor the quadratic equation.
%28y-1%29%28y-9%29+=+0 Apply the zero product principle.
y-1+=+0 and/or y-9+=+0
y+=+1 and y+=+9
Check:
y = 1
sqrt%282%281%29%2B7%29+%2B+4+=+1
sqrt%289%29%2B4+=+1 Note that sqrt%289%29+=+-3 or +3
-3%2B4+=+1 The extraneous root of (+3) was introduced when squaring sqrt%282y%2B7%29
y= 9
sqrt%282%289%29%2B7%29+%2B+4+=+9
sqrt%2825%29+%2B+4+=9 Note that sqrt%2825%29+=+5 or -5
5%2B4+=+9 The extaneous root of (-5) was introduced when squaring sqrt%282y%2B7%29
#16
The geometry of the problem describes a right triangle in which the height is 3 m. and the length of the hypotenuse is 7 m.
Use the Pythagorean theorem c%5E2+=+a%5E2%2Bb%5E2 to calculate the third side of this triangle. The hypotenuse is 7 m. so c = 7 and the height is 3 m. so a = 3
7%5E2+=+3%5E2+%2B+b%5E2 Solve for b which is the required length of the insulation.
49+=+9+%2B+b%5E2 Subtract 9 from both sides.
40+=+b%5E2 Take the square root of both sides.
sqrt%2840%29+=+b
b+=+6.3m To the nearest tenth.