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rosijanka [135]
3 years ago
15

Rewrite without absolute value for the given conditions:

Mathematics
1 answer:
malfutka [58]3 years ago
4 0
If x = 3, then y = |3-3| + |3+2| - |3-5|

Thus, after adding and subtracting within the absolute quantity groupings, you have

y = |0| + |5| - |-2|

Absolute value can be defined as distance from zero on the number line. Thus,

y = 0 + 5 - 2

Complete the equation bu adding/subtracting.

y = -3
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Prove that the triangle EDF is isosceles. Give reasons for your answer.
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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)

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<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

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