Question

find each measure. figures are not drawn to scale. use an equation and show all work.

1. jl
2. ef
3. sv

use the number line to find each measure.

1. jl
2. kp
3. jp
4. ln

find the value of x and bc if b is between c and d.
cb = 2x, bd = 4x, and cd = 12

1. cb = 4x - 9, bd = 3x + 5, and cd = 17

Explanation:

Step1: Find JL in the first - type figures

Since JL = JK + KL, and JK = 0.75 cm, KL = 0.35 cm, then JL=0.75 + 0.35=1.1 cm.

Step2: Find EF in the first - type figures

Since EF = EG+GF, and EG = 2.5 in, GF = 2.8 in, then EF=2.5 + 2.8 = 5.3 in.

Step3: Find SV in the first - type figures

Since ST=SV + VT, then SV=ST - VT. Given ST = 4.1 in, VT = 2.6 in, so SV=4.1−2.6 = 1.5 in.

Step4: Find JL using the number - line

The coordinate of J is - 7 and the coordinate of L is - 2. Then JL=| - 2-( - 7)|=| - 2 + 7| = 5.

Step5: Find KP using the number - line

The coordinate of K is - 4 and the coordinate of P is 5. Then KP=|5-( - 4)|=|5 + 4| = 9.

Step6: Find JP using the number - line

The coordinate of J is - 7 and the coordinate of P is 5. Then JP=|5-( - 7)|=|5 + 7| = 12.

Step7: Find LN using the number - line

The coordinate of L is - 2 and the coordinate of N is 3. Then LN=|3-( - 2)|=|3 + 2| = 5.

Step8: Solve for x and BC when CB = 2x, BD = 4x, and CD = 12

Since CD=CB + BD, then 12=2x + 4x. Combine like - terms: 12 = 6x. Solve for x: x = 2. And BC=CB = 2x=4.

Step9: Solve for x and BC when CB = 4x - 9, BD = 3x + 5, and CD = 17

Since CD=CB + BD, then 17=(4x - 9)+(3x + 5). Combine like - terms: 17=4x-9 + 3x + 5, 17=7x-4. Add 4 to both sides: 17 + 4=7x, 21 = 7x. Solve for x: x = 3. And BC=CB = 4x-9=4×3 - 9=3.

Answer:

1. JL = 1.1 cm
2. EF = 5.3 in
3. SV = 1.5 in
4. JL = 5
5. KP = 9
6. JP = 12
7. LN = 5
8. x = 2, BC = 4
9. x = 3, BC = 3