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2 years ago

LM is a perpendicular bisector of NP The length of LN is 12w +7, and the length of LP is 15w 5. What is the length of LN?

Mathematics

1 answer:

Mazyrski [523]2 years ago

8 0

Answer:

$LN = 55$

Step-by-step explanation:

Given

$LN = 12w + 7$

$LP = 15w - 5$

Required

Determine LN

Since LM is a bisector, then we have:

$LP = LN$ (See attachment for illustration)

$15w - 5 = 12w + 7$

Collect Like Terms

$15w - 12w = 5 +7$

$3w = 12$

Solve for w

$w = 12/3$

$w = 4$

LN is calculated as thus:

$LN = 12w + 7$

Substitute 4 for w

$LN = 12 * 4 + 7$

$LN = 48 + 7$

$LN = 55$

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2 years ago

An express train travels 80km/h from Ironton to Wildwood. A local train, traveling at 48km/h, takes 2 hours longer for the same

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Answer:

They are 240 kilometers apart.

Step-by-step explanation:

This question can be solved using the following relation:

$v = \frac{d}{t}$

In which v is the velocity, d is the distance and t is the time.

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Here we have $v = 80, t = x$ . So

$v = \frac{d}{t}$

$80 = \frac{d}{x}$

$d = 80x$

A local train, traveling at 48km/h, takes 2 hours longer for the same trip.

This means that when $v = 48, t = x + 2[tex]. So[tex]v = \frac{d}{t}$

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$48 = \frac{80x}{x+2}$

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2 years ago

Solve the system of equations - 8x + 3y = -17 and 3x - y = 7 by combining the<br> equlations.

NeTakaya

Given :

Two equations :

-8x + 3y = -17 ....1)

3x - y = 7 ....2)

To Find :

The solution of the system.

Solution :

Multiplying equation 2) by 3 and adding with equation 1), we get :

(-8x + 3y) + 3(3x - y) = -17 + 21

x = 4

Putting above value of x equation 2) we get :

12 - y = 7

y = 5

Therefore, solution of system is ( 4,5 ).

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