Question

The Question Is In The Picture.

Answer 1

part I: XZ+ZY=XY

We can divide the line in two parts and sum of both paths must be equal to the whole line

Given XZ=3(n+5)

ZY=4n

let statement be true:

3n+15+4n=71

7n=71-15

n=8

now XZ=3(8+5)

XZ=39

ZY=4*8=32

So XZ+ZY=71 =XY

ii)Since Part i is true so Calculating part ii is right

Given XZ=3(n+5)

ZY=4n

let statement be true:

3n+15+4n=71

7n=71-15

n=8

now XZ=3(8+5)

XZ=39

ZY=4*8=32

So XZ+ZY=71 =XY

Hence proved

Answer 2

a) Definition of Segment Addition

b) Substitution Property of Equality

c) Distributive Property

d) Combine like terms

e) Subtraction Property of Equality

f) Division Property of Equality

Step-by-step explanation:

Reason a)

The Segment Addition Postulate states that if a line segment has two endpoints, X and Y, and a third point Z lies somewhere on the line segment XY, the distance from X to Z plus the distance from Z to Y is equal to the distance from X to Y:

• XZ + ZY = XY

Reason b)

The values of XZ and ZY are substituted into the equation in place of XZ and ZY, respectively. This is allowed by the Substitution Property of Equality, which states that if two quantities are equal, you can replace one with the other in an equation.

Reason c)

The distributive property is used to distribute the factor 3 to both terms inside the parentheses, resulting in 3n + 15.

Reason d)

Combining like terms involves simplifying an algebraic expression by adding or subtracting terms that have the same variable and exponent. So in this case, we combine like terms 3n and 4n to get 7n.

Reason e)

The Subtraction Property of Equality states that subtracting the same quantity from both sides of an equation maintains the equality relationship between the two expressions. So, this property is used to subtract 15 from both sides of the equation.

Reason f)

The Division Property of Equality states that dividing both sides of an equation by the same non-zero number preserves the equality between the two expressions. So, this property is used to divide both sides by 7 to solve for n.