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2 years ago

Find X and Y please explain

Mathematics

1 answer:

Alex777 [14]2 years ago

5 0

In this diagram we see that 80 and 3x+4y are both vertical angles and vertical angles are congruent or always equal so we can set those two equations equal to each other then we can see that a line splits two angles making them supplementary (they equal 180 degrees) So we can have another equation, the two equations are:

3x+4y=80 and 3x+4y+7x-8y=180 (add like terms to simplify and get 10x-4y=180

Then use elimination to get rid of the y variables

10x-4y=180 (plus)

+3x+4y=80 (the negative 4 and positive 4 cancels each other out so you are left with:)

13x=160 (divide by x)

x=12.30769 which can be rounded to x=12.31

Then we have to plug in x into the first equation:

3(12.31) + 4y = 80

36.93 + 4y = 80 (subtract 36.93 from 80)

4y = 43.07 (divide)

y=10.7675 or rounded to 10.77

so x=12.31 and y=10.77

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3 years ago

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2 years ago

There is a L-shaped sidewalk that is 158 meters long. By cutting across the lawn, the

NikAS [45]

Answer:

Each side of the L-shaped sidewalk is 126 m and 32m respectively.

Step-by-step explanation:

Given:

Total length of the sidewalk = 158 meters

Cutting across the lawn the distance = 130 meters

The L-shaped lawn will be treated as a right angled triangle.

So the 130 m distance is the hypotenuse here.

Let one side of the L-shaped lawn be 'x' meter so the another side will be (158-x) meters.

Applying Pythagoras formula.

$(Hypotenuse)^2=(height)^2+(base)^2$

So,

⇒ $(130)^2=x^2 +(158-x)^2$

⇒ $(130)^2=x^2+(158-x)(158-x)$

⇒ $16900=x^2+24964-158x-158x+x^2$

⇒ $16900 =2x^2-316x+24964$

⇒ $2x^2+316x+24964-16900=0$

⇒ $2x^2-316x+8064=0$

⇒ $x^2-158x+4032=0$

Applying quadratic formula;

Quadratic formula : $\frac{\pm b \sqrt{b^2-4ac} }{2a}$ where a=1 and b=-158 and c=4032

So the value of x= 126 and 32.

The length of each side of the sidewalk is 'x'= 126 m and '(158-x)'='(158-126)'=32 m

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3 years ago

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