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lianna [129]
3 years ago
7

Can someone please help me Find EF

Mathematics
1 answer:
Nimfa-mama [501]3 years ago
6 0

Answer:

Step-by-step explanation:

Remark

The relationship that solves this is

The outside segment * the whole length of the secant = the outside segment of the other secant * the whole length of the second secant.

Put in symbolic (and hence easier language)

GF * EG = HG * SG

Givens

GF = 4

EG = 2x + 4

GH = 5

SG = x + 5

           

Equation

4*(2x + 4) = 5*(x + 5)               Remove the brackets

8x + 16 = 5x + 25                    Subtract 5x from both sides

8x - 5x + 16 = 25                    Combine

3x + 16 = 25                            Subtract 16 from both sides

3x = 25 - 16                        

3x = 9                                     Divide by 3

3x/3 = 9/3

x = 3

EF = 2 * 3

EF  = 6

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Answer:

Step-by-step explanation:

In this particular case we have the following system of equations:

y

=

−

3

x

+

4

[

E

q

.

1

]

x

+

4

y

=

−

6

[

E

q

.

2

]

Substituting

[

E

q

.

1

]

in

[

E

q

.

2

]

:

x

+

4

(

−

3

x

+

4

)

=

−

6

Applying the distributive property on the left side:

x

−

12

x

+

16

=

−

6

Simplifying

:

−

11

x

=

−

22

Solving for

y

:

x

=

−

22

−

11

=

2

Substituting

x

=

2

in

[

E

q

.

1

]

:

y

=

−

3

(

2

)

+

4

=

−

2

Therefore

, the solutions are

x

=

2

and

y

=

−

2

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