Question

Number 8 pls help geometry

Answer 1

8) x = 6

Explanation:

find TU by subtracting 4 + x from 3x + 4

3x + 4 - (4 + x)

3x + 4 - 4 -x

TU = 2x

SU = 2x + 1 because ST = 1

SU = 13

2x + 1 = 13

2x = 12

x = 6

Answer 2

x = 6

Explanation:

Given:

• ST = 1
• SU = 13
• UV = 4+x
• TV = 3x+4

Since SV is a straight line and T and U are the points in SV.

We get:

`\sf SV = ST+TU+UV`

`\sf SV = ST + TV`

Since the sum of TU and UV equals TV.

Substituting value:

`\sf SV = 1 + 3x+4`

`\sf SV = 3x +5 .......[i]`

Similarly;

`\sf \sf SV = ST+TU+UV`

`\sf \sf SV = SU+UV`

Since the sum of ST and TU equals SU.

Substituting value:

`\sf \sf SV =13+4+x`

`\sf \sf SV =17+x ......[ii]`

Now,

Equating equations [i] and [ii], we get

`\sf 3x+5 = 17+x`

Subtracting both sides by x and 5.

`\sf 3x+5-x-5 = 17+x-x-5`

Simplify:

`\sf \sf 2x =12`

Divide both sides by 2.

`\sf (2x)/(2) =(12)/(2)`

`\sf x=6`

Therefore, the value of x is 6.