Question

Use the image below to answer problems A-C. Show all work.


A. Calculate the value of x.


B. Calculate the value of the line segment of MN.


C. Calculate the value of the line segment of NP.


ANSWER ALL PARTS AND SHOW YOUR WORK!!

Answer 1

QUESTION A

From the diagram, line segment ON is the bisector of angle MOP.

This implies that;

|MN|=|NP|

In terms of x, we have;

$7x + 3 = 10x - 9$

Group like terms to obtain,

$3 + 9 = 10x - 7x$

This implies that,

$12 = 3x$

Divide through by 3 to get,

$4 = x$

Or

$x = 4$

QUESTION B

The line segment MN has the expression
$7x + 3$

But x=4.

This implies that,

$MN = 7(4) + 3$

$MN = 28 + 3$

$MN = 31 \: units$

QUESTION C.

The line segment MP has the length expressed in terms of x as,

$MP=10x-9$

We substitute x=4 to obtain;


$MP=10(4)-9$

$MP=40-9$

$MP = 31 \: units$