Pretty please help me with my geometry work, thank you :)

9. MP = 49

10. VT = 62

Step-by-step explanation:

#9

∵ In the rhombus, all the sides are equal in length

∵ MNOP is a rhombus

∵ MN = NO = OP = PM

∵ MN = 9x - 77

∵ OP = 3x + 7

→ Equate them to find x

∴ 9x - 77 = 3x + 7

→ Add 77 to both sides

∴ 9x = 3x + 84

→ Subtract 3x from both sides

∴ 6x = 84

→ Divide both sides by 6

∴ x = 14

→ Substitute the value of x in the expression of OP to find its length

∵ OP = 3(14) + 7 = 42 + 7

∴ OP = 49

∵ All the sides are equal in length

∴ MP = 49

#10

∵ The diagonals of the square bisect each other

∵ STUV is a square

∵ SU and TV are its diagonals

∴ W is the mid-point of SU and TV

∴ SW = WU

∵ SW = 2x + 13

∵ WU = 8x - 41

→ Equate them to find x

∴ 8x - 41 = 2x + 13

→ Add 41 to both sides

∴ 8x = 2x + 54

→ Subtract 2x from both sides

∴ 6x = 54

→ Divide both sides by 6

∴ x = 9

→ Substitute x in the expression of SW to find it

∵ SW = 2(9) + 13 = 18 + 13

∴ SW = 31

∵ SU = SW + WU

∵ SW = WU

∴ SU = 31 + 31 = 62

∵ Diagonals of the square are equal in length

∴ SU = VT

∴ VT = 62

75%

step-by-step explanation: