1. Given: AB = 64; M lies on the line AB AM = 4x + 4 BM= 6x-10

Prove: M is a midpoint.

Statements: Reason:
1) M lies on AB 1) Given
AB= 64
2) AM+MB=AB 2) ?

3) 4x+4+6x-10=64 3) ?

4) 10x- 6 = 64 4) ?

5) 10x=70 5) ?

6) x = 7 M 6) ?

7) AM= 4(7) + 4 7) substitution
MB = 6(7) - 10

8) AM=32 and 8) simplify
Mb = 32.

9) M is a midpoint. 9) ?

Reasoning bank for #1

Addition Property of equality
Combine like terms
Definition of midpoint.
Division property of equality
Segment addition postulate

Step-by-step explanation:

Given the following lengths AB = 64, AM = 4x + 4 and BM= 6x-10, If M lies on the line AB  then AM+MB = AB (addition property)

Substituting the given parameters into the addition property above;

AM+MB = AB

4x + 4 + 6x - 10 = 64

combine like terms

4x+6x = 64+10-4

10x = 74-4

10x = 70

Divide both sides by 10

x = 70/10

x = 7

Note that for M to be the midpoint of AB then AM must be equal to BM i.e AM = BM

To get AM ;

Since AM = 4x+4

substitute x = 7 into the function

AM = 4(7)+4

AM = 28+4

AM = 32

Similarly, BM = 6x-10

BM = 6(7)-10

BM = 42-10

BM = 32

Since AM = BM = 32,. then M is the midpoint of AB

80x^8−68x^6+16^5−20x^4−4x^3+8x^2

hope i'm right lol