Write the equation in general form for the line passing through (-4,-3) and parallel to the line whose intercepts are (0,2) and
1 answer:
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Answer:
The answerscan be calculated by doing the following steps;
Step-by-step explanation:
Answers:
- Similar = Yes, they are similar
- How: AA similarity
- Similarity statement: triangle HGF ~ triangle HMN
The ~ mark means "similar"
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The red angle markings tell us which angles are congruent to one another. We have these two pairs of congruent angles
- angle H = angle H (both triangles unfortunately reuse H) by the single arc marking
- angle G = angle M, by the double arc markings
Because we have two pairs of congruent angles, we use the AA similarity theorem. AA stands for angle angle. We could use three pairs, but two pairs is the minimum needed for similarity statements.
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To figure out what goes in the third answer box, note how the order HGF is given to us. The order is important.
We have H first, G second, F third.
H being first, and it having a single arc, means that whatever has a single arc on the other triangle must be first. That would be H. Unfortunately they reuse angle H which makes things confusing a bit.
G is second in HGF, and G has the double arc marking. Note how M also has this double arc marking. Therefore we have M second in the answer. So far we have HM as part of the third answer.
The only thing left is N. Therefore, we have triangle HMN as the answer for the third box.
Put another way, we have these pairings:
- H (single arc mark) = H (single arc mark)
- G (double arc mark) = M (double arc mark)
- F (no marking) = N (no marking)
This is why the order is important. So we can see how the angles pair up in the order that they do.
This is why triangle HGF is similar to triangle HMN.
We can write that as triangle HGF ~ triangle HMN
The ~ mark means "similar"
We don't have enough information to prove that the triangles are congruent or not. So we cannot say . Your teacher made a typo when using the congruence symbol
Instead, it should be
Answer:
Number of calls received in 1st evening = 24
Number of calls received in 2nd evening = 33
Number of calls received in 3rd evening = 72
Step-by-step explanation:
Let
number of calls received in first evening be "x"
number of calls received in 2nd evening be "y"
number of calls received in 3rd evening be "z"
Total, in 3 evenings, we have 129 phone calls, so we can write:
x + y + z = 129
3rd evening, 3 times as first evening. We can write:
z = 3x
2nd evening, 9 MORE THAN FIRST. So we can write:
y = 9 + x
Now we replace 2nd and 3rd equation in 1st equation to get:
x + y + z = 129
x + 9 + x + 3x = 129
Now, first, we solve for x:
Solving for y:
y = 9 + x
y = 9 + 24
y = 33
Solving for z:
z = 3x
z = 3(24)
z = 72
Thus,
Number of calls received in 1st evening = 24
Number of calls received in 2nd evening = 33
Number of calls received in 3rd evening = 72