NEED SOME ALGEBRA HELP.....please please please?

Question

Please help me with all you can for these. And if you do, please let me know how sure you are of your answers (0%-100%). Thanks.


19: Find the solution set for x:
2x - 4 (x + 1) ≤ -8
a. the set of all numbers greater than 2
b. the set of all numbers greater than or equal to 2
c. the set of all real numbers
d. the set of all real numbers less than or equal to 2

20. Simplify:
(1 + √3)^2
a. 3√5 + 10√3
b. 4 + 2√3
c. 2 + √3
d. 18

33: What is the distance between the origin and the point (-4, -5)?
a. √52
b. 4√2
c. √41
d. 2√2

35: Simplify:
25x^2 + 10x + 1/12x – 18 x(times) 10x – 15/25x^2 - 1

a. (5x^2 + x – 1) / 3
b. [5(5x + 1)] / [6(5x - 1)]
c. (25 - 2x) / [3(x - 3)]
d. (5x^2 + x + 1) / 3

Answer 1

19. 2x - 4 (x + 1) ≤ -8
2x - 4x - 4 ≤ -8
-2x ≤ -4
x >= 2 (multiplying by a negative number, -1/2, flips the inequality).
That's answer (b). 100% sure.

20.
(1 + √3)^2
1^2 + 2*1*√3 + (√3)^2
1 + 2√3 + 3
4 + 2√3
That's answer (b). 100% sure.

33. The formula for distance between two points is:
d = sqrt((x1-x2)^2 + (y1-y2)^2)
Given one point, and that the origin is (0,0):
d = sqrt((0 - -4)^2 + (0 - -5)^2)
d = sqrt(16 + 25)
d = sqrt(41) = √41
That's answer (c). 100% sure.

35.
25x^2 + 10x + 1/12x – 18 x(times) 10x – 15/25x^2 - 1
You need to place some parentheses in that so it is clear what is going on. And you can use "*" for "times" so there aren't any extraneous x's.

I'm assuming you mean:

(25x^2 + 10x + 1)/(12x - 18) * (10x - 15)/(25x^2 - 1)

Factored:

(5x + 1)(5x + 1)/6(2x - 3) * 5(2x - 3)/(5x + 1)(5x - 1)

With the numerators and denominators combined into a single fraction:

5(5x + 1)(5x + 1)(2x - 3)/6(5x + 1)(5x - 1)(2x - 3)

One 5x+1 and 2x-3 cancel from the numerator and denominator, leaving:

5(5x+1)/6(5x-1)

... which is your answer (b). I'd say maybe 75% correct. If I'm right about where the parentheses go, it's 100%, but you'd have to compare that to the original problem.

Answer 2

(19) 2x - 4(x + 1) <= -8
2x - 4x - 4 <= -8
-2x - 4 <= -8
-2x <= -4
x >= 2

Answer (B) -> 100% sure

(20) (1 + sqrt(3))^2
(1 + sqrt(3))(1 + sqrt(3))
1 + 2sqrt(3) + 3
4 + 2sqrt(3)

Answer (B) -> 100% sure

(33) sqrt((-4 - 0)^2 + (-5 - 0)^2)
sqrt(16 + 25)
sqrt(41)

Answer (C) -> 100% sure

(35) (25x^2 + 10x +1/12x - 18) * (10x - 15/25x^2 - 1)
If this is how the problem is stated, there must be an x^4 term in the answer. There are no answer choices given that have an x^4 term. Please re-state the question.

Answer 3

19. 2x - 4 (x + 1) ≤ -8
2x - 4x - 4 ≤ -8
-2x ≤ -8 + 4
x >= -4/-2
x >= 2 (B 100%)

20. (1 + √3)^2
= (1 + √3)(1 + √3)
= 1 + √3 + √3 + (√3)(√3)
= 1 + 2√3 + 3
= 4 + 2√3 (B 100%)

33.
length on x-axis = 4
length on y-axis = 5
distance = √(4^2 + 5^2)
= √(16 + 25)
= √41 (C 100%)

35.
question is not clear

Answer 4

2x - 4 (x + 1) ≤ -8
2x-4x-4≤ -8
-2x ≤ -4
x = or > 2 [100%]

(1 + √3)^2
= 1+ 2√3 +3
= 4+2√3 [100%]

sqrt((-4)^2 +(-5)^2)
sqrt(16+25) = √41 [100%]

25x^2 + 10x + 1/12x – 18 x(times) 10x – 15/25x^2 - 1
= (5x+1)^2/[6(2x-3)] * 5(2x-3)/[(5x-1)(5x+1)]
= 5(5x+1)/[6(5x-1)] {100%}