Answer:
a. A = -1 and B = 1
b. A = 7 and B = -5
Step-by-step explanation:
a.
To the equation be true, the "x-parts" and "nonx-parts" mist be the same, so:
Ax + Bx = 0
(A + B)x = 0
A + B = 0
A = -B
B - A = 2
B - (-B) = 2
2B = 2
B = 1 and A = -1
b.
To the equation be true, the "x-parts" and "nonx-parts" mist be the same, so:
Ax + Bx = 2x
(A + B)x = 2x
A + B = 2
A = 2 - B
2A + 3B = -1
2*(2-B) + 3B = -1
4 - 2B + 3B = -1
B = -5 and A = 2 - (-5) = 7
bearing in mind that parallel lines have the same exact slope, then any parallel line to the one above will have the same slope as that one.
66 degrees
Add 30, 57, and 27, then subtract from 180
Answer: (3x + 11y)^2
Demonstration:
The polynomial is a perfect square trinomial, because:
1) √ [9x^2] = 3x
2) √121y^2] = 11y
3) 66xy = 2 *(3x)(11y)
Then it is factored as a square binomial, being the factored expression:
[ 3x + 11y]^2
Now you can verify working backwar, i.e expanding the parenthesis.
Remember that the expansion of a square binomial is:
- square of the first term => (3x)^2 = 9x^2
- double product of first term times second term =>2 (3x)(11y) = 66xy
- square of the second term => (11y)^2 = 121y^2
=> [3x + 11y]^2 = 9x^2 + 66xy + 121y^2, which is the original polynomial.
