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Which of the following statements is true only if triangles EFI and GFH are similar?

igomit [66]

Answer: Choice B

FH/FI = HG/IE

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Explanation:

We're told that triangles EFI and GFH are similar. The order of the lettering is important because it tells us how the angles pair up.

E and G pair up because they are the first letters of EFI and GFH
F and F pair up as they are the second letters
I and H pair up because they are the third letters

This means

E = G
F = F
I = H

Furthermore, it means

EF corresponds to FG
FI corresponds to FH
IE corresponds to GH

Focus on the last two items of the list above. We can then form the proportion

FI/FH = IE/GH

which is the same as

FH/FI = GH/IE

when we apply the reciprocal to both sides. Since HG is the same as GH, we can then say

FH/FI = HG/IE

So basically the corresponding sides create equal ratios to form this proportion. There are many other proportions that can be formed.

4 0

2 years ago

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Segment YB is x+3 units long and segment BW is 2x-9 units long. The diagonal YW is ___ units long.

Gnom [1K]

Answer:

3x - 6

Step-by-step explanation:

Segment YB = x + 3

Segment BW = 2x - 9

Add the two segments.

x + 3 + 2x - 9

3x - 6

The diagonal YW is 3x - 6 units long.

6 0

2 years ago

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A farmer kept 96 kilograms of animal feed in his barn.

lesya692 [45]

Answer:

The amount of animal feed left was 86.4 kilograms.

Step-by-step explanation:

Initial amount of animal feed in the barn was 96 kilograms.

The barn leaked and $\frac{1}{10}$ of the feed was wasted.

So, the amount of feed wasted $=\frac{1}{10}(96)=9.6$ kilograms.

Now, for finding the amount of feed that was left, we need to subtract the amount of wasted feed from the initial amount of feed.

So, the amount of animal feed left $=(96-9.6)\ kilograms=86.4\ kilograms$

4 0

2 years ago

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ALL THE POINTS!! (01.01 LC) What is the rational number equivalent to 3 point 12 with a bar over 12? (1 point) 3 and 4 over 33 3

saul85 [17]

Answer:

A is the answer

Step-by-step explanation:

6 0

2 years ago

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A waterbed filled with water has the dimensions 8ft by 7 ft by .75 ft taking the density of water to be 1.00/gm cubed how many k

monitta

By definition, the density is given by:

$D = \frac{m}{V}$

Where,

m: mass

V: volume

Clearing the mass we have:

$m = DV$

The volume is given by:

$V = (8) * (7) * (0.75)$

$V = 42ft ^ 3$

Then, we have the following conversion:

$1foot = 0.3048m$

Applying the conversion we have:

$V = 42 * (0.3048) ^ 3$

$V = 1.19m ^ 3$

On the other hand we have the following conversions:

$1m = 100cm$

$1Kg = 1000g$

Applying the conversions for the density we have:

$D = (1\frac{g}{cm^3})((\frac{100}{1})^3\frac{cm^3}{1m^3})(\frac{1}{1000}\frac{Kg}{g})=1000\frac{Kg}{m^3}$

Then, the mass of the water is:

$m = (1000) * (1.19)$

$m = 1190$

Answer:

1190 kilgrams of water are required to fill the waterbed

7 0

2 years ago