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Question

I need to check my answers and I'm not sure I got them right. If you could please explain...?

QUESTION 1:
Solve the equation. Check your solution. (sqrt)r + 5 = 11
a) 126
b) 6
c) 17
d) 116


QUESTION 2:
If the password to get into a garage is four numbers long, and you can only use the numbers one through nine, how many different passwords would there be?
a) 3024
b) 6561
c) 36
d) 4


QUESTION 3:
Suppose the area of a square is x^2 - 6x + 9. What is the perimeter of the square?
a) x-3
b) 2x-6
c) 4x-12
d) x+3


QUESTION 4:
Simplify the expression. 4(sqrt)7 + 8(sqrt)63
a) 76(srt)7
b) 12(sqrt)63
c) 28(sqrt)7
d) 28(sqrt)63

QUESTION 5:
How many real roots are there for the equation: x^2 + 4x - 1 = 0
a) 0
b) 1
c) 2
d) 4

Answer 1

1)
sqrt(r+5)=11
r+5=121
r=116 (d)

2)
9 * 9 * 9 * 9 = 6561 (b)

3) Find the square root of the area to find the length of a side and then multiply that by 4:
p = 4sqrt(x^2 - 6x + 9)
= 4sqrt((x-3)^2)
= 4(x-3)
= 4x - 12 (c)

4)
4sqrt(7) + 8sqrt(63)
= 4sqrt(7) + 8sqrt(9*7)
= 4sqrt(7) + 8sqrt(9) * sqrt(7)
= 4sqrt(7) + 8*3 * sqrt(7)
= 4sqrt(7) + 24sqrt(7)
= 28sqrt(7) (c)

5) use quadratic formula (there may be another way):

(-b +/- sqrt(b^2 - 4ac))/2a
= (-4 +/- sqrt(16 - 4(1)(-1))/(2(1))
= (-4 +/- sqrt(16 + 4))/2
= (-4 +/- sqrt(20))/2
= (-4 +/- sqrt(4*5))/2
= (-4 +/- sqrt(4)*sqrt(5))/2
= (-4 +/- 2*sqrt(5))/2
= (2(-2 +/- sqrt(5)))/2
= -2 +/- sqrt(5)
= -2 + sqrt(5) and -2 - sqrt(5)
both are real (c)

Answer 2

1. sqrt(r + 5) = 11
then r + 5 = 11^2
r + 5 = 121
r = 121 -5
r = 116

2. pass

3. x - 3

4. 4sqrt7 + 8sqrt63
4 sqrt7 + 8 sqrt(9 x 7)
4 sqrt7 + 8 sqrt (3 x 3 x 7 )
4 sqrt7 + 8 x 3 sqrt7
4 sqrt7 + 24sqrt7
28sqrt7 - c

5. Using the determinant b^2 - 4ac >0

then 4^2 - 4(1)(1) =
16 - 4 = 12 >0
therefore has two real roots

Answer 3

1) d
2) b
3) c
4) c
5) c