Answer:
y = 14
Step-by-step explanation:
Since AC = BC then the triangle is isosceles and the base angles are congruent, that is
∠A = ∠B = 50°, thus
∠C = 180 - (50 + 50) ← sum of angles in Δ = 180°
= 180 - 100 = 80°, hence
5y + 10 = 80 ( subtract 10 from both sides )
5y = 70 ( divide both sides by 5 )
y = 14
1.) 4(x+3)
Find the GCF, Greatest Common Factor, of 4x and 12.
4x=2*2*x
12=3*2*2
The greatest common factor is 4. Put this outside of the parentheses. (You would multiply the 2*2)
Then, put the rest of the factors as a sum. (Only the factors on the same line.)
Solution: 4(x+3)
To check, distribute to see if it works.
4x+12
2.) 2(4r+7)
Find the GCF of 8r and 14
8r=2*2*2*r
14= -1*7*2
The greatest common factor is 2. (There is only 1 two, so you would not multiply them.)
Then, put the rest of the factors as a sum. (Only the factors on the same line.)
Multiply the 2*2*r as one addend and the -1*7 as the other.
Solution: 2(4r-7)
To check, distribute to see if it works.
8r-14
Do you get it now?
3.) 5(x+7)
4.) 7(2x+1)
5.) Cannot be factored.
32x-15
Find the GCF of 32x and -15
32x: 2*2*2*2*2*x
-15: -1*5*3
Because there are no similar factors other than 1, it cannot be factored.
6.) 8(4x+3)
7.) 3(2x-3)
8.) 24(1x+2)
9.) 9(-2x+8)
10.) Cannot be factored
11.) 8(1x+3)
12.) 50(1x+5)
Step-by-step explanation:
well,
(y - 7)² = (y - 7)(y - 7)
remember how to multiply 2 expressions ?
you have to multiply every term of one expression with every term of the other expression and sum the results all up (incl. considering their individual signs, of course).
so, when we do the multiplication, we get
(y - 7)(y - 7) = y×y - 7×y - 7×y + (-7)×(-7) =
= y² - 14y + 49
and that is clearly different to y² - 49
FYI
y² - 49 is the result of
(y - 7)(y + 7)
because
y×y + 7×y - 7×y + (-7)(7) = y² - 49
