Question

Can someone help me with both of the or may be one

I’m stuck on both of the question if someone could help me I would highly appreciate:)

Answer 1

6.) QS = 16

7.) QS = 8

Explanation:

The midpoint splits the segment into 2 equal segments. Therefore, set both expressions equal to each other and solve for x.

6.)

`QR=RS\\\\x+6=4x\\\\x+6-x=4x-x\\\\6=3x\\\\(6)/(3)=(3x)/(3)\\\\2=x\\\\\\QR+RS=QS\\\\(2)+6+4(2)=QS\\\\16=QS`

7.)

`QR=RS\\\\3x-2=2x\\\\3x-2-3x=2x-3x\\\\-2=-x\\\\(-2)/(-1)=(-x)/(-1)\\\\2=x\\\\\\QR+RS=QS\\\\3(2)-2+2(2)=QS\\\\8=QS`

Answer 2

Question 6

Given:

QR = RS

QR = x + 6

RS = 4x

To find:

Length of line segment QS

Steps:

We know QR = RS, so substituting we get,

x + 6 = 4x

6 = 4x - x

6 = 3x

6/3 = x

2 = x

x = 2

Now,

QS = QR + RS

QS = x + 6 + 4x

QS = 2 + 6 + 4(2)

QS = 2 + 6 + 8

QS = 8 + 8

QS = 16 units

Therefore, the length of QS is 16 units

Question 7

Given:

QR = RS

QR = 2x - 2

RS = 2x

To find:

Length of line segment QS

Steps:

We know that QR = RS, so substituting the values we get,

QR = RS

3x - 2 = 2x

3x - 2 - 2x = 0

3x - 2x = 2

x =2

Now,

QS = QR + RS

QS = 3x - 2 + 2x

QS = 3(2) - 2 + 2(2)

QS = 6 - 2 + 2(2)

QS = 6 - 2 + 4

QS = 4 + 4

QS = 8 units

Therefore, the length of QS is 8 units

Happy to help :)

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