Smaller Angle: 49 degrees
Bigger Angle: 131 degrees
Note that supplementary angles add up to be 180 degrees. Knowing this and the information provided in the question, we can use the following system of equations:
x + y = 180 (showing they both add up to 180)
x + 82 = y (to show one angle is 82 more than the other)
We can use the substitution method to solve. Since the second equation ends in "= y" we can substitute the value of it into y for the first equation.
x + y = 180; x + 82 = y ==> x + (x + 82) = 180
And now, solve for x:
x + (x + 82) = 180
x + x + 82 = 180 > combine like terms
2x + 82 = 180
2x = 98
x = 49
So now we have the value for one of the angles! Remembering that the other angle is 82 degrees bigger, dd 49 + 82, which equals 131.
So, our two angle values are 131 and 49! This is correct since both angle measures add up to be 180, which also makes them supplementary!
Answer:
25
Step-by-step explanation:
5+5=10 10+5=15 15+5=20 20+5=25
This equation in word form would be 7x -6 = -20, and the solution to that equation is x = -2
Answer:
- (x + 3)(x - 3)(x² - 2x + 5)
Step-by-step explanation:
<u>One of the zeros given:</u>
<u>Since it is a complex number, its conjugate is also a zero:</u>
<u>The product of two factors are:</u>
- (x - (1 + 2i))(x - (1 - 2i)) =
- x² - x(1 + 2i + 1 - 2i) + (1 - 4i²) =
- x² - 2x + 5
<u>We need two more zeros. Let them be m and n, then we have:</u>
- (x - m)(x - n) = x² - (m +n)x + mn
<u>The product of all factors:</u>
- (x² - 2x + 5)(x² - (m+n)x + mn) = x⁴ - 2x³ - 4x² + 18x - 45
- x⁴- (m+n+2)x³ + (mn+5)x² - (2mn+5m+5n)x + 5mn = x⁴- 2x³- 4x²+ 18x- 45
<u>Compare left and right sides and solve for m and n:</u>
- m + n + 2 = 2 ⇒ m + n = 0
- mn + 5 = -4 ⇒ mn = -9
- 2mn + 5(m + n) = -18 ⇒ mn = -9
<u>From the above equations we get:</u>
- m = -n
- -n² = -9
- n = 3
- m = -3
The other zero's are 3 and -3
<u>All of the factors:</u>
- (x + 3)(x - 3)(x² - 2x + 5)
