In △abc,a=13 △ a b c , a = 13 , b=14 b = 14 , and c=18 c = 18 . find m∠a m ∠ a .

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ladybugys

26.04.2023

Mathematics

$\dfrac{1}{4}x+\dfrac{5}{3}x-4=2-\dfrac{1}{12}x--------------x=3$

3.2b-4.7=3b-3.3---------------b=7

4.6y-y+4=y-1.2--------------y=-2

7.5c-2.5c+8=-7--------------c=-3

Step-by-step explanation:

We are asked to solve the pair of equations:

$\dfrac{1}{4}x+\dfrac{5}{3}x-4=2-\dfrac{1}{12}x$

On solving the equation:

$\dfrac{3x+20x}{12}-4=2-\dfrac{1}{12}x\\\\i.e.\\\\\dfrac{23x}{12}-4=2-\dfrac{1}{12x}\\\\\\i.e.\\\\\dfrac{23x}{12}+\dfrac{x}{12}=2+4\\\\i.e.\\\\\dfrac{24x}{12}=6\\\\i.e.\\\\2x=6\\\\i.e.\\\\x=3$

$3.2b-4.7=3b-3.3\\\\i.e.\\\\3.2b-3b=4.7-3.3$

Since we combined the like terms.

Now on further simplifying we get:

$0.2b=1.4\\\\i.e.\\\\b=7$

4.6y-y+4=y-1.2

Now, on combining the like terms we get:

$4.6y-y-y=-1.2-4\\\\i.e.\\\\4.6y-2y=-5.2\\\\i.e.\\\\2.6y=-5.2\\\\i.e.\\\\y=-2$

$7.5c-2.5c+8=-7\\\\i.e.\\\\5c=-7-8\\\\i.e.\\\\5c=-15\\\\i.e.\\\\c=-3$

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