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Mathematics

1 answer:

Gwar [14]4 years ago

3 0

In similar figures, the angle measures are the same but the side lengths are different. So in #4, x = 42. Since all the angles of a quadrilateral added up equal 360, then y is 360-90-90-42=138. For number 5, make sure you match up the sides correctly in your ratio: $\frac{2}{x}= \frac{4}{8}$ . You could cross multiply to get 4x=16, and x = 4, or you could just realize that reducing 4/8 will give you 2/4 and x = 4. Going back to the idea that in similar shapes corresponding angles are the same measure, x in #6 is 63

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Point O is a centroid of the triangle LMN. If OM=38 cm, what is MP?

Yuri [45]

9514 1404 393

Answer:

c.) 57 cm

Step-by-step explanation:

The centroid divides the median into parts with a 2:1 ratio.

OM : OP = 2 : 1

OM : MP = 2 : (2+1) = 2 : 3

As a fraction with MP on top, this is ...

MP/OM = 3/2

MP = (3/2)OM = 3/2×(38 cm)

MP = 57 cm

<em>Comment on the answer choices</em>

Often, you can eliminate a number of the choices in a multiple-choice question just by testing whether they are reasonable. Here, the longer part of a line segment has length 38, so the whole segment will not be shorter than that. The choices 19 and 25.5 make no sense.

The remaining choices are 114 cm and 57 cm. The former is 3 times the length of the given segment, which the drawing tells us is unreasonable.

The only reasonable choice offered is 57 cm.

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tekilochka [14]

5x + 2y = 8
2y = -5x + 8
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