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Olegator [25]
3 years ago
10

Can someone please help me on this ASAP

Mathematics
2 answers:
OLEGan [10]3 years ago
8 0
<span>(a) Triangles ABC and PQR are similar triangles since they both share 2 congruent angles and therefore their 3rd angle is also congruent. So the triangles are similar due to the AAA similarity theorem. (b) The area of triangle PQR is 1 million times larger than the area of triangle ABC. This can be shown since the area of a triangle is 1/2 base times height. You can show that the base of triangle PQR is 1000 times larger than the base of triangle ABC. And since all the sides are in proportion to each other, the height of triangle PQR is also 1000 times larger than the height of triangle ABC. And since 1000 times 1000 equals 1,000,000 or 1 million, the area of triangle PQR is 1 million times larger than triangle ABC.</span>
Damm [24]3 years ago
7 0

Answer:

(a) Yes, Δ ABC and ΔPQR are similar triangles.

(b) Ratio of the areas of ΔPQR and ΔABC will be k².

Step-by-step explanation:

In the figure attached two triangles, Δ ABC and Δ PQR have been given.

(a).In these triangle ∠ABC ≈ ∠PQR, ∠ACB ≈ ∠PRQ (Given)

Since it is given that two angles of the given triangles are equal so third angle will also be equal.

So by the theorem AAA both the triangles will be similar.

(b). Since in two similar triangles corresponding sides are in the same ratio (By theorem of similar triangles)

Therefore, sides of Δ PQR and Δ ABC will be in the same ratio = k where k > 1

Now area of Δ ABC A= \frac{1}{2}(AB)(Height)=\frac{1}{2}(AB)(h)

Similarly area of Δ PQR = A"=\frac{1}{2}(PQ)(Height)=\frac{1}{2}(PQ)(H")

Now ratio of area of Δ PQR and Δ ABC

\frac{A"}{A}=\frac{(\frac{1}{2})(PQ)(H")}{\frac{1}{2}(AB)(h) }

\frac{A"}{A}=\frac{(PQ)(H")}{(AB)(h)}

\frac{A"}{A}=\frac{(4k)(kh)}{(4)(h)}

\frac{A"}{A}=k^{2}

So ratio of area of Δ PQR and Δ ABC will be k².

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Mr.Lopez owns a home that sits on 7/8 of an acre. He has decided to plow up 1/4 of the property to create a garden. What fractio
vodomira [7]

In math, "of" almost always means "times".

"The property" is 7/8 acre.

So "1/4 of the property" means "1/4 times 7/8 acre".

1/4 x 7/8 = (1 x 7) / (4 x 8)

That's 7/32 .

Mr. Lopez hasn't plowed up anything yet, but his plan is to plow up 7/32  acre for his garden.


3 0
2 years ago
Then, answer Part B. A number cube that has sides numbered 1 through 6 is rolled 180 times. Part A How many times would you expe
Nitella [24]

Using the binomial distribution, it is found that the expected values are given by:

a) 120.

b) 150.

<h3>What is the binomial probability distribution?</h3>

It is the probability of <u>exactly x successes on n repeated trials, with p probability</u> of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

In this problem, for both items, we consider that the number cube is rolled 180 times, hence n = 180.

Item a:

4 of the 6 possible values are greater than 2, hence p = 4/6 = 2/3.

The expected value is given by:
E(X) = 180 x 2/3 = 120.

Item b:

5 of the 6 values are less than 6, hence p = 5/6.

The expected value is given by:
E(X) = 180 x 5/6 = 150.

More can be learned about the binomial distribution at brainly.com/question/24863377

4 0
2 years ago
What is the value of sin 2900 + cos 2900 ?<br><br>​
Rzqust [24]

Answer:

-1.25737973739

Step-by-step explanation:

plz make it brillent ans

7 0
2 years ago
What is one tenth of 0.04
Lyrx [107]
One tenth is equal to .1 or 1/10

and .04 is nothing but 4/100

So just multiply them together:

1/10 x 4/100 = 4/1000

And since there are 3 0's we need to move the decimal spot 3 places the the left:

.004

So our final answer is \sf{\boxed{.004}}
7 0
2 years ago
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