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3 years ago

What is one of the solutions to the following systems of equations? Y squared plus X squared equals 65 and Y plus X equals seven

Mathematics

1 answer:

alukav5142 [94]3 years ago

7 0

Answer:

Step-by-step explanation:

y^2 + x^2 = 65

y + x = 7......x = 7 - y

y^2 + (7 - y)^2 = 65

y^2 + (7 - y)(7 - y) = 65

y^2 + 49 - 7y - 7y + y^2 = 65

2y^2 - 14y + 49 = 65

2y^2 - 14y + 49 - 65 = 0

2y^2 - 14y - 16 = 0

2(y^2 - 7y - 8) = 0

2(y + 1)(y - 8) = 0

y + 1 = 0 y - 8 = 0

y = -1 y = 8

solution :

y = -1...........y + x = 7.....-1 + x = 7......x = 7 + 1......x = 8........(8,-1)

y = 8........y + x = 7.....8 + x = 7......x = 7 - 8........x = -1........(-1,8)

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3 years ago

The area of ABED is 49 square units. Given AGequals9 units and ACequals10 units, what fraction of the area of ACIG is represent

stiks02 [169]

Answer:

The fraction of the area of ACIG represented by the shaped region is 7/18

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the square ABED find the length side of the square

we know that

AB=BE=ED=AD

The area of s square is

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where b is the length side of the square

we have

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substitute

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therefore

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step 2

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The area of rectangle ACIG is equal to

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substitute the given values

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step 3

Find the area of shaded rectangle DEHG

The area of rectangle DEHG is equal to

$A=(DE)(DG)$

we have

$DE=7\ units$

$DG=AG-AD=9-7=2\ units$

substitute

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step 4

Find the area of shaded rectangle BCFE

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we have

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substitute

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step 5

sum the shaded areas

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step 6

Divide the area of of the shaded region by the area of ACIG

$\frac{35}{90}$

Simplify

Divide by 5 both numerator and denominator

$\frac{7}{18}$

therefore

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