Which does NOT represent the interior angle measures of a triangle?
2 answers:
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Answer:
We want to find a solution of the system:
x^2 + y^2 > 49
y ≤ –x^2 – 4
Here we do not have any options, so let's try to find a general solution.
First, we can remember that the equation of a circle centered in the point (a, b) and of radius R is:
(x - a)^2 + (y - b)^2 = R^2
If we look at our first inequality, we can write it as:
x^2 + y^2 > 7^2
So the solutions of the first inequality are all the points that are outside (because the symbol used is >) of the circle of radius R = 7 centered in the origin.
From the other equation, we would get:
y ≤ –x^2 – 4
This is parabola, anything that is in the graph of the parabola or below will be a solution for this inequality.
Then the solutions of the system, are the ones that are in the region of solutions for both inequalities.
You can see the graph below, where both regions are graphed. The intersection of these regions is the region of the solutions for the system of inequalities:
by looking at the graph, we can see a lot of points that are solutions, like:
(0, -10)
(0, -15)
(2, -10)
etc.
Answer:
See Below.
Step-by-step explanation:
Paragraph Proof:
We are given that ∠1 ≅ ∠4. ∠1 and ∠4 are alternate exterior angles. Since they are congruent, by the Alternate Exterior Angles Converse, the two lines being cut by the transversal must be parallel. Then by the Alternate Interior Angles Theorem, ∠3 ≅ ∠2.
2-Column Proof
Statements Reasons:
1) Given
2) Alternate Exterior Angles Converse
3) Alternate Interior Angles Theorem
I would write a flowchart as well, but unfortunately, I never learned it that way.