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gtnhenbr [62]
3 years ago
8

Given that ABC~LMN What is the length of AC?

Mathematics
1 answer:
sleet_krkn [62]3 years ago
6 0

Answer:

B. 12

Step-by-step explanation:

✔️Find the value of x

The side lengths of two similar triangles are always proportional.

Given that ∆ABC ~ ∆LMN, therefore:

\frac{AB}{LM} = \frac{AC}{LN}

AB = 5

LM = 10

AC = x + 5

LN = 3x + 3

Plug in the values

\frac{5}{10} = \frac{x + 5}{3x + 3}

Cross multiply

5(3x + 3) = 10(x + 5)

15x + 15 = 10x + 50 (distributive property)

Collect like terms

15x - 10x = -15 + 50

5x = 35

Divide both sides by 5

x = 7

✔️Find AC

AC = x + 5

Plug in the value of x

AC = 7 + 5

AC = 12

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Step-by-step explanation:

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We plug these values into the given vertex form equation of a parabola:

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Subbing these values into y - k = a(x - h)^2, we obtain:

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3 years ago
Find the volume of a pyramid with a square base where the area of the base is 8.3 m 2 and the height of the pyramid is 9.8 m
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3 years ago
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kodGreya [7K]
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3 years ago
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Picture related to the question is attached below

Answer:

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Step-by-step explanation:

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