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i have 4 questions

1. Suppose point T is between points R and V on a line. If RT = 63 units and RV = 131 units, then what is TV? 131 194 68 80

2.Given point P is between M and N. If MN = 26, MP = x + 4, and PN = 2x + 1, what is the value of x? x = 3 x = 7 x = 12.5 x = 22

3.Given M is the midpoint of HJ, HM = 4x - 12, and MJ = 3x + 9. What is the value of x?

4.If D is the midpoint of CE, DE = 2x + 4, and CE = 6x + 2, then what is CD?

Respuesta :

MrRoyal

Answer:

1.   [tex]TV = 68[/tex]

2.  [tex]x = 7[/tex]

3.   [tex]x = 21[/tex]

4.    [tex]CD = 8[/tex]

Step-by-step explanation:

Solving (1):

Given

[tex]RT = 63[/tex]

[tex]RV = 131[/tex]

Required

Determine TV

To solve TV, we make use of the following formula;

[tex]RV = RT + TV[/tex]

Substitute values for RT and RV

[tex]131 = 63 + TV[/tex]

Make TV the subject of formula

[tex]TV = 131 - 63[/tex]

[tex]TV = 68[/tex]

Solving (2):

Given

[tex]MN = 26[/tex]

[tex]MP = x + 4[/tex]

[tex]PN = 2x + 1[/tex]

Required

FInd x

To solve x, we make use of the following formula;

[tex]MN = MP + PN[/tex]

Substitute values for MP, MN and NP

[tex]26 =x + 4 + 2x + 1[/tex]

Collect Like Terms

[tex]2x + x = 26 - 4 -1[/tex]

[tex]3x = 21[/tex]

Divide both sides by 3

[tex]x = 7[/tex]

Solving (3):

Given

[tex]HM = 4x - 12[/tex]

[tex]MJ = 3x + 9[/tex]

Required

Find x

Since M is the midpoint;

[tex]HM = MJ[/tex]

This gives

[tex]4x - 12 = 3x + 9[/tex]

Collect Like Terms

[tex]4x - 3x = 12 + 9[/tex]

[tex]x = 21[/tex]

Solving (4):

Given

[tex]CE = 6x + 2[/tex]

[tex]DE = 2x + 4[/tex]

Required

FInd CD

Since D is the midpoint;

[tex]CD= DE[/tex]

and

[tex]CE = CD + DE[/tex]

Substitute CD for DE

[tex]CE = DE + DE[/tex]

[tex]CE = 2DE[/tex]

Substitute values for CE and DE

[tex]6x + 2 = 2(2x + 4)[/tex]

Open Bracket

[tex]6x + 2 = 4x + 8[/tex]

Collect Like Terms

[tex]6x - 4x = 8 - 2[/tex]

[tex]2x = 6[/tex]

Divide both sides by 2

[tex]x = 3[/tex]

Recall that;

[tex]CD= DE[/tex]

So;

[tex]CD = 2x + 4[/tex]

Substitute 2 for x

[tex]CD = 2 * 2 + 4[/tex]

[tex]CD = 4 + 4[/tex]

[tex]CD = 8[/tex]

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