Answer: g(f(-1))=-22
Step-by-step explanation:
To find g(f(-1)), you want to first want to solve f(-1). Once you solved that, you plig the answer you get into g(x). Then, you will have your final answer.
f(-1)=-(-1)²+4(-1)-9 [exponent]
f(-1)=-1+4(-1)-9 [multiply]
f(-1)=-1-4-9 [subtract from left to right]
f(-1)=-14
We have found that f(-1)=-14. Now, we know in -14 into g(x) and solve.
g(-14)=(-14)-8 [subtract]
g(-14)=-22
Now, we know that g(f(-1))=-22.
It's an isosceles triangle so angles A and BCA are congruent.
Angle BCA is the supplement of BCD, so 180-109 = 71.
Angle A is congruent to that, so A=71 degrees.
Let's see if we can get that in the format they want, kind of as a proof.
1. ∠BCD=109° Reason: Given
2. AB ≅ BC Reason: Given
3. ∠BCA = 71° Reason: Linear pairs are supplementary
4. ΔABC is isosceles. Reason: Definition of isosceles
5. ∠A ≅ ∠BCA Reason: Isoceles triangle theorem
6. ∠A = 71° Reason: Def congruent
Answer: 71 degrees
<h3>
Answer: Choice D</h3>
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Explanation:
The inequality sign has an "or equal to", which means the boundary line will be solid. We can rule out choices B and C because they have dashed boundary lines.
A solid boundary line means that points on the boundary are part of the solution set.
Now let's see what happens when we plug in a point like (x,y) = (4,0). This will tell us how to shade the blue region.

This is false because -20 is not larger than -1. It's the other way around.
This tells us the point (4,0) is not in the blue shaded region, and it's not on the boundary line either. We can rule out choice A because of this.
The only thing left is choice D, which is the final answer. I recommend plugging a point from this region into the inequality to confirm we have a true statement.