Alternate interior angles theorem.
<u>Step-by-step explanation:</u>
By using the definition of Alternate Interior Angles theorem, we can say that If a transversal cuts any two parallel lines, then those pairs of alternate interior angles are seems to be congruent.
So in the given triangle,
∠4 ≅ ∠2
∠5 ≅ ∠3
Sum of all the angles in a triangle = 180°
∠1 + ∠2 + ∠3 = 180°
Since from the above congruence, we can write that
∠1 + ∠4 + ∠5 = 180°
Hence proved.
Answer:
Ginny made a mistake in step 1 when she identified b = 31. It should be b=-31
Step-by-step explanation:
Ginny factored 
as shown:
ac = –180 and
b = 31
36(–5) = –180 and 36 + (–5) = 31
+ 36x – 5x – 30
6x(x + 6) – 5(x + 6)
(x + 6)(6x – 5)
b is the coefficient of x and from the trinomial , b=-31.
Therefore Ginny made a mistake in step 1 when she identified b = 31. It should be b = –31.
The correct steps are: :
ac = –180 and
b = -31
36(–5) = –180 and -36+5 = -31
Answer: 92
Step-by-step explanation:
A.) Integers are positive and negative counting numbers. So, in order to find the integer coefficients, round off the coefficients in the equation to the nearest whole number. The function for g(x) is:
g(x) = 3x²+3x
B.) Substitute x=4 to the two functions.
f(x) = 2.912345x²<span>+3.131579x-0.099999
</span>f(4) = 2.912345(4)²+3.131579(4)-0.099999
f(4) = 59.023837
g(x) = 3x²+3x
g(4) = 3(4)²+3(4)
g(4) = 60
C.) The percentage error is equal to:
Percentage error = |g(4) - f(4)|/f(4) * 100
Percentage error = |60 - 59.023837|/59.023837 * 100
Percentage error = 1.65%
D.) If x is a large number, for example x=10 or x=20, then g(x) would be an overestimate. This is because the value of x is raised to the power of 2. So, as the x increases, the corresponding function would increase exponentially. Even at x=4, g(x) is already an overestimate. What more for larger values of x? That means that the gap from the true answer f(x) would increase.
I think it’s gonna be all real numbers except 13
