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Gelneren [198K]
3 years ago
12

Prove that the triangle EDF is isosceles. Give reasons for your answer.

Mathematics
1 answer:
Gekata [30.6K]3 years ago
8 0

Answer:

\triangle EDF is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are <u>given</u> the following things:

\angle EDF = y

\text{External }\angle DFG = 90 +\dfrac{y}{2}

Let us try to find out \angle E and \angle DFE. After that we will compare them.

<u>Finding </u>\angle DFE<u>:</u>

Side EG is a straight line so \angle GFE = 180

\angle GFE is sum of internal \angle DFE and external \angle DFG

\angle GFE = 180 = \angle DFE  + \angle DFG\\\Rightarrow 180 = \angle DFE + (90+\dfrac{y}{2})\\\Rightarrow \angle DFE = 180 - 90 - \dfrac{y}{2}\\\Rightarrow \angle DFE = 90 - \dfrac{y}{2} ....... (1)

<u>Finding </u>\angle E<u>:</u>

<u>Property of external angle:</u> External angle in a triangle is equal to the sum of two opposite internal angles of a triangle.

i.e. external \angle DFG = \angle E + \angle EDF

\Rightarrow 90+\dfrac{y}{2} = \angle E + y\\\Rightarrow \angle E = 90+\dfrac{y}{2}  -y\\\Rightarrow \angle E = 90-\dfrac{y}{2} ....... (2)

Comparing equations (1) and (2):

It can be clearly seen that:

\angle DFE = \angle E =90-\dfrac{y}{2}

The two angles of \triangle EDF are equal hence \triangle EDF is isosceles.

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Leann is 3 cm taller than Fred. If Fred's height is f cm, then Leann's height is cm?
jek_recluse [69]
F + 3 = leann's height
6 0
3 years ago
A certain plant runs three shifts per day. Of all the items produced by the plant, 50% of them are produced on the first shift,
Snezhnost [94]

Answer:

0.2941 = 29.41% probability that it was manufactured during the first shift.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Defective

Event B: Manufactured during the first shift.

Probability of a defective item:

1% of 50%(first shift)

2% of 30%(second shift)

3% of 20%(third shift).

So

P(A) = 0.01*0.5 + 0.02*0.3 + 0.03*0.2 = 0.017

Probability of a defective item being produced on the first shift:

1% of 50%. So

P(A \cap B) = 0.01*0.5 = 0.005

What is the probability that it was manufactured during the first shift?

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.005}{0.017} = 0.2941

0.2941 = 29.41% probability that it was manufactured during the first shift.

6 0
3 years ago
A survey was given to 339 people asking whether people like dogs and/or cats.
lina2011 [118]

Answer:

80

Step-by-step explanation:

Think of it as a Venn diagram.  One circle is the people who like dogs, and one circle is the people who like cats.  The overlap is people who like both dogs and cats.

190 people in the survey said they like dogs.  That includes the people who like both dogs and cats.

141 people in the survey said they like cats.  That includes the people who like both dogs and cats.

If we simply add the two numbers together, we'll be counting the overlap twice.  So to find the total number of people who like dogs or cats, we have to subtract one overlap.

dogs or cats = 190 + 141 − x

Therefore:

190 + 141 − x + 88 = 339

419 − x = 339

x = 80

80 people said they liked both cats and dogs.

5 0
3 years ago
DOES ANYONE KNOW HOW TO DO THIS????????
Harrizon [31]

1. r closest to 1: Figure 4

2. Least signs of linear relationship: Figure 1

3. r equal to -1: Figure 3

Step-by-step explanation:

Correlation is the link between two things or variables.

The scatter plots can be used to determine the correlation values for given sets of data.

If both values are increasing, then the correlation is positive

If one value is increasing and the other is decreasing then the correlation is negative

So,

In the given pictures

Figure 4 has the correlation coefficient closest to 1 as both values are increasing but the data points are not in a straight line so r will be close to 1.

Figure 3 has the correlation coefficient equal to one as one value is increasing and the other is decreasing. And the points are in a straight line so r will be equal to one.

As the data points in Figure 1 are more scattered so there will be no relationship between two quantities.

So, the answers are as follows

1. r closest to 1: Figure 4

2. Least signs of linear relationship: Figure 1

3. r equal to -1: Figure 3

Keywords: Correlation, Data set

Learn more about correlation at:

  • brainly.com/question/12884373
  • brainly.com/question/12896802

#LearnwithBrainly

4 0
3 years ago
Dont tell me the Answer but walk me through the steps plz
sveticcg [70]

Answer:

Find the multiplies of 2

7 0
3 years ago
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