Question

Help and show work plz

Answer 1

NQ=15, NP=20

Explanation:

9/(2x+1)=12/(3x-1)

cross product

12(2x+1)=9(3x-1)

24x+12=27x-9

12=27x-24x-9

12=3x-9

3x=12+9

3x=21

x=21/3

x=7

NQ=2x+1=2(7)+1=15

NP=3x-1=3(7)-1=21-1=20

Answer 2

x = 7

Explanation:

Since the triangles are similar the ratio of the sides must be the same

AB AK

------- = --------------

QN NP

9 12

---------- = ------------

2x+1 3x-1

Using cross products

9(3x-1) = 12(2x+1)

Distribute

27x -9 = 24x +12

Subtract 24x from each side

3x-9 = 12

Add 9 to each side

3x = 21

Divide by 3

x = 7