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valina [46]
3 years ago
14

If AB = 10, AD = 8, and AE = 12, what is the length of EC?

Mathematics
1 answer:
Karolina [17]3 years ago
6 0

Answer:

AB is 16 units.

Step-by-step explanation:

Given:

AE = EC

BF = FC

EF = 8 and DF = 10

To Find:

AB = ?

Solution:

Mid Point Theorem:

The Midpoint Theorem states that "the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side".

AE = EC .....Given

Therefore E is the Mid Point of AC.

BF = FC .....Given

Therefore F is the Mid Point of BC.

Therefore,

EF || AB            ........................Mid Point Theorem.

         ..............Mid Point Theorem.

Substituting the values we get

Therefore AB is 16 units.

Step-by-step explanation:

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Answer:

Step-by-step explanation:

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3 years ago
Express 112 as a product of prime numbers in index form?
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                                   112
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                                  2   56
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                                     2   28
                                          /  \
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So, the answer is 2 x 2 x 2 x 7 or 2^3 x 7
6 0
3 years ago
A 20­ft ladder is leaning against a house. The bottom of the ladder is 3 ft from the house. To the nearest tenth of a foot, abou
Tasya [4]

Answer:  19.8 ft

Step-by-step explanation:

Use the Pythagorean Theorem formula to solve for how high the top of the ladder reach.  

The formula says  a^2 + b^2 = c^2

Where a and b are the two legs and  C is the hypotenuse.

In this situation, the hypotenuse will be length of the ladder , and either  a or b will be the length of the ladder from the building or the length of how long the ladder.

a will be 3 ,  and c will be 20. Input in the values  into the formula and solve for b.

3^2 + b^2 = 20^2

9 + b^2 = 400

-9              -9

 b^2 = 391  

    b = \sqrt{391}

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8 0
2 years ago
A spinner numbered 1 through 12 is spun. Find the probability that
anastassius [24]

Answer:

\dfrac{1}{6}

Step-by-step explanation:

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<em>P(A)</em> be the probability of getting an odd number.

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Here, total numbers in the game are 12 i.e \{1,2,3,....,12\}.

Formula for probability of an <em>event E</em> can be observed as:

P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}

P(A) = \dfrac{6}{12}\\\Rightarrow \dfrac{1}{2}

Let <em>B</em> be the event of getting 11.

<em>P(B)</em> be the probability of getting 11.

Total number of possible cases is 1.

P(B) = \dfrac{1}{12}

P(A \cap B) is the probability that we get 11 and an odd number.

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<em>P(B/A)</em> is the probability that we get an 11 given that it is an odd number.

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Hence, P(B/A) = \dfrac{1}{6}

4 0
3 years ago
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UNO [17]
X< -2 means that x must be smaller than -2, so something like -3, -4, -5, etc

The only solution set that fits this is A.
6 0
3 years ago
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