4+1/3x=5/12x-6 solve for x

Mathematics

2 answers:

Charra [1.4K]2 years ago

7 0

Times both side by 12
48+4x=5x-72
120=x

Anuta_ua [19.1K]2 years ago

3 0

First you need to find the least common denominator which would be 12
4+4/12x=5/12x-6
then you need to multiply everything by 12
48+ 4x=5x -72
then subtract 4x
48=x-72
then add 72
120=x <---- that's your answer

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

Gekata [30.6K]

Answer:

$\triangle EDF$ is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are given 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.

Finding  $\angle DFE$ :

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

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

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