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3 years ago

What are the solutions to the system of equations? y=x2−5x−6 y=2x−6

Mathematics

2 answers:

Leya [2.2K]3 years ago

4 0

Answer:

I graphed both equations to find the solutions.

Step-by-step explanation:

When x is 0, y is -6. When x is 7, y is 8.

x = 0 and 7

allsm [11]3 years ago

4 0

Answer: The solutions are

(0, - 6)

(7, 8)

Step-by-step explanation:

The given system of equations is expressed as

y = x² - 5x - 6- - - - - - - - - - - - 1

y = 2x - 6- - - - - - - - - - - 2

We would apply the method of substitution by substituting equation 2 into equation 1. It becomes

x² - 5x - 6 = 2x - 6

x² - 5x - 2x - 6 + 6 = 0

x² - 7x = 0

x(x - 7) = 0

x = 0 or x - 7 = 0

x = 7 or x = 0

Substituting x = 0 into equation 2, it becomes

y = 2 × 0 - 6

y = - 6

Substituting x = 7 into equation 2, it becomes

y = 2 × 7 - 6

y = 14 - 6

y = 8

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4 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

Mrac [35]

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

$A=b^{2}$

where b is the length side of the square

we have

$A=49\ units^2$

substitute

$49=b^{2}$

$b=7\ units$

therefore

$AB=BE=ED=AD=7\ units$

step 2

Find the area of ACIG

The area of rectangle ACIG is equal to

$A=(AC)(AG)$

substitute the given values

$A=(9)(10)=90\ units^2$

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 $A=(7)(2)=14\ units^2$

step 4

Find the area of shaded rectangle BCFE

The area of rectangle BCFE is equal to

$A=(EF)(CF)$

we have

$EF=AC-AB=10-7=3\ units$

$CF=BE=7\ units$

substitute

$A=(3)(7)=21\ units^2$

step 5

sum the shaded areas

$14+21=35\ units^2$

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

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

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3 years ago