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REY [17]
3 years ago
9

Find the value of m that makes ABC~DEF when AB= 3, BC= 4, DE= 2m, EF= m+5, and ∠B≅∠E.

Mathematics
1 answer:
Yuki888 [10]3 years ago
8 0

Answer:

m = 3

Step-by-step explanation:

It is given that there are two triangles \triangleABC and

\triangleABC ~

Also, the sides are:

AB= 3

BC= 4

DE= 2m

EF= m+5 and

∠B≅∠E

Please have a look at the attached figure for \triangleABC and

The triangles are similar so as per the property of similar triangles, the ratio of corresponding sides will be same.

i.e.

\dfrac{AB}{DE} = \dfrac{BC}{EF}\\\Rightarrow \dfrac{3}{2m} = \dfrac{4}{m+5}\\\Rightarrow 3 \times (m+5) = 4 \times 2m\\\Rightarrow 3m +15= 8m \\\Rightarrow 5m=15\\\Rightarrow m = 3

So, <em>value of m = 3.</em>

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Given a point A(-2,5), find the coordinates of a point B so that the line segment AB has each slope.
Kaylis [27]

Step-by-step explanation:

I understand this that we need to find a point B for each of a) to f).

remember, the slope is the (y coordinate difference / x coordinate difference) when going from one point on the line to the other.

a)

the slope 2/3 means that when going to B x has to increase by 3, and y has to increase by 2.

so, B = (-2 + 3, 5 + 2) = (1, 7)

b)

-2/3 means that either x or y have to decrease and the other to increase.

e.g. x increases by 3, y decreases by 2.

so, B = (-2 + 3, 5 - 2) = (1, 3)

c)

4 stands for 4/1.

so, x increases by 1, y increases by 4.

B = (-2 + 1, 5 + 4) = (-1, 9)

d)

similar to c) -3 stands for -3/1.

and similar to b) either x or y has to decrease and the other to increase.

e.g. x increases by 1, y decreases by 3.

B = (-2 + 1, 5 - 3) = (-1, 2)

e)

that means the y difference is 0. B has the same y coordinate.

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x can be any value.

the line is a horizontal line going through y = 5 or (0, 5) on the y-axis.

f)

that means the x difference is 0. B has the same x coordinate.

e.g. B = (-2, 9)

y can be any value.

the line is a vertical line going through x = -2 or (-2, 0) on the x-axis.

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10 months ago
Plz helppp thank uuuu :)
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