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3 years ago

Triangle ABC is similar to Triangle DEF. What is the measure of angle DEF? Refer to image, please show work :)

Mathematics

1 answer:

Ne4ueva [31]3 years ago

4 0

Remember, all the interior angles of a triangle equals 180.
So in triangle ABC, it already gives us two out of the three angles.

First, we add 52 and 36 and that gives us 88.

Now we subtract 88 from 180.

180 - 88 = 92

So that means that ∠ABC is 92°

Now we have to look at triangle DEF.
The equation says that triangle DEF is similar to triangle ABC.

Looking at the picture, triangle DEF is smaller and is flipped upside down.

So that means that ∠ABC ≈ ∠DEF

In similar triangles, the measurements of angles does NOT change. Just the side length.

So since ∠ABC = 92° that means that ∠DEF = 92°

You might be interested in

125 divided by 32 equals what

andreyandreev [35.5K]

32 × 2 = 68
32 × 3 = 96
32 × 4 = 128

So far we can conclude that the answer to your question lies somewhere between the numbers 3 and 4. To narrow down the answer some more, multiply 32 by 3.5 (a midway point between 3 and 4).

32 × 3.5 = 112
The number 112 tells us that the decimal we are looking for is higher than 3.5. (Because we need to get to 125, not 112.) Let's try some decimals between 3.5 and 4.

32 × 3.7 = 118.4
32 × 3.8 = 121.6
32 × 3.9 = 124.8
32 × 4 = 128

As we narrow down our answer, we can see that the number we are looking for lies between 3.9 and 4 on the number line. Now we need to start testing some decimals between 3.9 and 4.

32 × 3.905 = 124.96
Again, use the number five as a "midway" point to decide if you should use numbers that are higher or lower than 3.905. In this case, we need to use numbers higher than 3.905.

32 × 3.906 = 124.992
32 × 3.907 = 125.024

We are getting even closer to our number now that we know the decimal is somewhere between 3.906 and 3.907.

32 × 3.9065 = 125.008
With our midway point we can see that our number lies between 3.906 and 3.9065. Let's try a quarter point to see where our number lies from there.

32 × 3.90625 = 125
And BINGO! We have found the answer to the question. To be rephrased, our answer can be put like this:

$\frac{125}{32}$ = 3.90625

6 0

3 years ago

- 9 (K - 17 ) = 54 please solve

kirza4 [7]

Answer: k=11

Step-by-step explanation:

7 0

2 years ago

Given that lines b and c are parallel, select all that apply.

dangina [55]

Answer:

Angles 7, 2, and 6

Step-by-step explanation:

Angle 7 is congruent by corresponding angles to angle 3.

Angle 2 is congruent by vertical angles to angle 3.

Angle 6 is congruent by vertical angles to angle 7, which is congruent to angle 3, so angle 3 and angle 6 must also be congruent.

4 0

2 years ago

Paul and his neighbors decided to build a fence along his farm. After three hours, they have 15 meters of fencing complete. They

Goshia [24]

Let the be the time in hours, and meters of fencing completed.

We know that After three hours, they have 15 meters of fencing complete, our graph will go from the point (0,0) to the point (3,15). We also know that they decide to take a 2-hour break for lunch and then resume building the fence, so our graph will go from the point (3,15) to the the point (5,15). Finally, After four more hours, they have a fence that is a total of 55 meters long, so the final part of our graph will go from the point (5,15) to the point (9,55)

We can conclude that the graph of t vs y is:

8 0

3 years ago

A certain medical test is known to detect 73% of the people who are afflicted with the disease Y. If 10 people with the disease

Setler [38]

The probability of an event is the measurement of the chance of that event's occurrence. The probabilities of considered events are:

P(At least 8 have the disease) ≈ 0.4378
P(At most 4 have the disease) ≈ 0.0342

<h3 /><h3>How to find that a given condition can be modeled by binomial distribution?</h3>

Binomial distributions consist of n independent Bernoulli trials. Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

X = B(n,p)

The probability that out of n trials, there'd be x successes is given by

P(X=x) = $^nC_xp^x(1-p)^{n-x}$

Since 10 people can be either diseased or not and they be so independent of each other (assuming them to be selected randomly) , thus, we can take them being diseased or not as outputs of 10 independent Bernoulli trials.

Let we say

Success= Probability of a diseased person tagged as diseased by the clinic

Failure = Probability of a diseased person tagged as not diseased by the clinic.

Then,

P(Success) = p = 72% = 0.72 (of a single person)

P(Failure) = q = 1-p = 0.28

Let X be the number of people diagnosed diseased by the clinic out of 10 diseased people. Then we have: X ≈ B(n+10,P=0.73)

Calculating the needed probabilities, we get:

a) P(At leased 8 have disease) = P(X≥8) =P(X=8) + P(X=9) + P(X=10)

P(X≥8) = $^{10}C_8(0.73)^8(0.28)^2+^{10}C_9(0.73)^9(0.27)^1+^{10}C_{10}(0.73)^{10}(0.27)^0$

P(X≥8) ≈ 0.2548 + 0.1456 + 0.0374 ≈ 0.4378

b) P(At most 4 have the disease) = P(X≤4) = P(X=0) + P(X=1)+P(X=2)+P(X=3)+P(X=4)

P (X ≤ 4) =

$^{10}C_0(0.73)^0(0.27)^{10}+^{10}{C_1(0.73)^1(0.27)^9+^{10}{C_2(0.73)^2(0.27)^8+^{10}C_3(0.73)&^3(0.27)^7 \\$

$+^{10}C_4(0.73)^4(0.27)^6$

P (X ≤ 4) = 0.000003 + 0.000076+0.00088+0.00604+0.02719

P (X ≤ 4) = 0.0342

Thus,

The probabilities of considered events are:

P(At leased 8 have disease) = 0.4378 approx
P(At most 4 have the disease) = 0.0342 approx

Learn more about binomial distribution here:

brainly.com/question/13609688

#SPJ1

4 0

2 years ago