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Lady bird [3.3K]
2 years ago
5

6.

Mathematics
1 answer:
Katarina [22]2 years ago
7 0

Answer:

Step-by-step explanation:

Comparing the triangles in the given questions, the following can be deduced:

5. The scale factor = \frac{15}{10} = \frac{12}{8} ≠ \frac{9}{7}

So that;

QR is similar to UT, PR is similar to US, but PQ is NOT similar to TS.

Thus, the triangles are NOT similar.

6. Scale factor = \frac{15}{10} = \frac{12}{8} = \frac{9}{6}

                         = 1.5

So that;

QR is similar to UT, PR is similar to US, but PQ is similar to TS.

Thus, the triangles are similar by Side-Side-Side (SSS).

7. Here, an exact scale factor can not be determined. Thus, the triangles are NOT similar.

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40%

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Two buses leave towns 304 miles apart at the same time and travel toward each other. One bus travels 14 mih slower than the othe
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Answer:

The faster bus moves at 83mi/h and the slower one moves at 69mi/h.

Step-by-step explanation:

Let's define:

R₁ = rate of bus 1, this is the faster one.

R₂ = rate of bus 2, this is the slower one.

We know that one bus travels 14mi/h slower, then:

R₂ = R₁ - 14mi/h.

Now we know that:

Distance = Speed*Time.

If we add the distances that both busses travel in 2 hours, it should be equal to the initial distance between the buses, then:

R₁*2h + R₂*2h = 304 mi

Then we have the two equations:

R₂ = R₁ - 14mi/h

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The first step is to replace the first equation in the second one, to get:

R₁*2h + (R₁ - 14mi/h)*2h = 304 mi

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R₁*2h + R₁*2h - 14mi/h*2h = 304 mi

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The function f(t) = t2 + 6t − 20 represents a parabola.
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Answer:

Step-by-step explanation:

Part A:

To complete the square, we will do the first few steps all at once, since they are necessary but not complicated to follow all at once.  Set the function equal to 0 first, then move the constant over to the other side:

t^2+6t=20

The most important rule for completing the square is that the leading coefficient (the number on the t-squared term) is a positive 1.  Ours is, but if it wasn't it would need to be factored out.

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Part B:

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f(t)=(t-h)^2+k

our vertex can be rewritten as (t - (-3)).  Therefore, our axis of symmetry is

x = -3

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