math help!? (mulitple choice q's)?

Question

If |2r-2| =8 and |3r+2| =17, then what is the value of r?

[a] -5
[b] -19/6
[c] -3
[d] 5
[e] 15

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if 3(2c^2 +3c +4) and b= -c +4 what is a in terms of b?
[a] 6c^2 -48b +96
[b] 6c^2 -57b +132
[c] 6c^2 -57b +144
[d] 6c^2 -9b -132
[e] 6c^2 -9b +144

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which of the following expressions must be negative of x<0?
[a] x^4 +x^2 +4
[b] x^5 -1
[c] x^6 -1
[d] x^6 +x^2 +1
[e] x^2 +10

I need it throughtly explained, because I ALREADY tried figuring out the questions but I DIDN'T get any of the following answers.

Answer 1

Please do your own HW

Answer 2

d
e
b

First one |2r-2|=8. 2|r-1|=8. |r-1|=4. (r-1) = ±4 r= 5 or -3
|3r+2|=17 (3r+2)=±17. r = 5 or -19/3
r=5 satisfies both equations

2nd one. b=-c+4. c = 4-b. Subsitute.
6(4-b)² + 9(4-b) + 12
6(16-8b+b²) + 9(4-b) + 12
96-48b+6b² + 36-9b+12
6b² - 57b + 144

Third one. x^(even) = positive for all real x. x^(odd) = same sign as x. so, if x is negative, x^(5) will be negative; x^5-1 will still be negative.

Answer 3

2r - 2 = +/- 8; solve both ways
2r = 10; r = 5 OR 2r = -6; r = -3
Plug both possibilities into the second equation:
I 3(5) + 2 I = 17; this checks out
I 3(-3) + 2 I = 17; this is not true; the answer is r = 5

The second question is written incorrectly because there is no "a" term in either expression.

For the third question: all of these equations have positive real solutions; I don't understand what you're asking.

Answer 4

For the first one simply insert each number into the equation and see if both sides are true. -5 looks right at first but 3 times -5 = -15 and if you add 2 you get -13. The correct answer is 5.

For the second one you have to factor out the equation first in order to find b. Try it if you still have a problem I'll help

Third one you need to also factor to see what the value of x is going to be. x4+x2+4 factors out to be what? it will look something like this (x + ) (x+ ) or could be (x - )(x - )

Answer 5

2r-2=8 | 2r=10 | r=5 answer [d]
3r+2=17 | 3r =15 | r=5


b= -c +4 --> c=4-b

3(2c^2 +3c +4)=6c^2 +9c+12=6(4-b)^2 +9*4-9b+12=

72-48b+6b^2+48-9b+12=6b^2-57b+132

answer [b]


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x^5-1
answer [b]

Answer 6

1) The lines indicate taking the positive value between them.
Answer is d
2)where's a?
3)b, because the others have even powers which will produce a positive number

Answer 7

First answer is D

Answer 8

all i know is the answer to the 1st one is d.