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Reika [66]
3 years ago
6

Given: Quadrilateral DEFG is a parallelogram.

Mathematics
1 answer:
levacccp [35]3 years ago
8 0

Answer:

The correct option is A.

Step-by-step explanation:

It is given that  DEFG is a parallelogram.

Draw the diagonals DF and EG. Place point H where DF and EG intersect.

In triangle HGD and HEF

,

∠HGD ≅ ∠HEF                            (Alternate Interior angle)

∠HDG ≅ ∠HFE                      (Alternate Interior angle)

By the definition of a parallelogram, the opposite sides of a parallelogram are congruent.

DG ≅ EF                                      (Opposite sides of parallelogram)

According to ASA postulate, two triangles are congruent if any two angles and their included side are equal in both triangles.

So, by using ASA criterion for congruence we get,

ΔDGH ≅ ΔFEH

Since corresponding sides of congruent triangles are congruent, therefore

GH ≅ EH                      (CPCTC)

DH ≅ FH                     (CPCTC)

Option A is correct.

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Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with μ=10
Tanya [424]

Answer:

a) 0.7734

Step-by-step explanation:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 101, \sigma = 24

(a) what proportion of children aged 13 to 15 years old have scores on this test above 83 ?

This is 1 subtracted by the pvalue of Z when X = 83. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{83 - 101}{24}

Z = -0.75

Z = -0.75 has a pvalue of 0.2266

1 - 0.2266 = 0.7734

The answer is 0.7734

5 0
3 years ago
simplify the mathematical expressions to determine the product or quotient in scientific notation. Round so the firs factor goes
cupoosta [38]

Answer:

hol on im finna learn about it then answer

Step-by-step explanation:

...

7 0
3 years ago
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Which equation represents the relationship shown in the table?
Mila [183]
Y=4x because 20/5 equals 4
5 0
3 years ago
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The mean of seven numbers is 12.0. When one new number is added , the average of eight numbers becomes 12.5 . What is the new nu
Gnesinka [82]
(12 * 7 + n)8=12.5
(12 * 7 + n)= 100
N= 16. The new number will be 16. Hope this helps. :)
8 0
3 years ago
Read 2 more answers
I Need The Answer Plz!!! Geometry Is Hard!!
prohojiy [21]

Answer:

12√5

Step-by-step explanation:

According to the attached sketch, there are 2 triangles which we need to focus on, triangle A (in yellow) and triangle B (In red).

If you look at triangle A, we notice that X is the hypotenuse of triangle A. This means that X must be the largest length in triangle A, hence we can say that x must be greater than 24 (or 24 < x)

Now look at triangle B, in this case, they hypotenuse is 30 and x is the length of one of the sides. This means that x must be shorter than the hypotenuse (i.e x < 30)

from the 2 paragraphs above, we can see now that we can assemble an inequality in x

24 < x < 30

If we look at the choices, we can immediately ignore 33 because x must be less than 30,

working out the choices, we find that the only choice which falls into the range 24<x<30 is the 2nd choice 12√5  (= 26.83)  (which is the answer)

The last 2 choices give values smaller than 24 and are hence cannot be the answer

8 0
2 years ago
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