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2 years ago

Points L, M, and N are collinear.

Mathematics

1 answer:

Natali5045456 [20]2 years ago

6 0

<h3>Answer:</h3>

<h3>Step-by-step explanation:</h3>

Vocabulary

Before going into an explanation, let's go over some important vocabulary.

Collinear - Collinear describes points that are on the same line. This means that there is 1 line with the 3 points L, M, and N.
Segment addition postulate - The segment addition postulate states that if there are 2 collinear points (A and C) with another point in between them (B), then the statement AB + BC = AC must be true.

Solving for MN

Using the postulate above we can make a new equation. First, let's set up an equation that mirrors the postulate.

LM + LN = MN

Now, let's plug in the values we know.

13 + 20 = MN

Then, solve.

33 = MN

This proves that a possible value of MN is 33.

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Write an equation for a circle with<br> a center at (9 -2) and has a<br> radius of 7.

fenix001 [56]

The equation of a circle is given as:

(x-a)^2 + (y- b)^2 = r^2 where (a, b) is the center.

(x-9)^2 = x^2 -18x + 81 - ----(i)
(y+2)^2 =y^2 + 4y +4 ------ (ii)
r^2 = 49 ------ (iii)

Adding equation (i) and (iii)
x^2 + y^2 - 18x + 4y + 85 -----(iv)

Equating equation (iv) and (iii)

<span>x^2 + y^2 - 18x + 4y + 85 = 49

Arrange the equation:

</span> <span>x^2 + y^2 - 18x + 4y + 36 = 0
</span><span>
I hope this helps

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8 0

3 years ago

For an annual membership fee of $500,Mr.Bailey can join a country club that would allow him to play a round of golf for $35. Wit

IRISSAK [1]

Answer:

25 rounds

Step-by-step explanation:

Let

x -----> the number of rounds of golf

y ---> total charges to play

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

<em>Membership</em>

$y=35x+500$ ----> equation A

The slope is m=$35 per round

The y-intercept b=$500 (annual membership fee)

<em>Non-Membership</em>

$y=55x$ ----> equation B

The slope is m=$55 per round

The y-intercept b=$0

Equate equation A and equation B

$55x=35x+500$

solve for x

$55x-35x=500$

$20x=500$

$x=25\ rounds$

For x=25 rounds the cost to be the same with and without a membership

8 0

3 years ago

Read 2 more answers

Isabelle is using a square piece of cardboard to make a box without a lid. She cuts 2-inch squares from each corner and folds up

katrin2010 [14]

<em>The dimensions of the cardboard to make a box without a lid is 11 inches by 11 inches.</em>

<h2>Explanation:</h2>

In this problem, we have that Isabelle is using a square piece of cardboard to make a box without a lid. She cuts 2-inch squares from each corner and folds up the edges. The figure below shows this statement. The finished box has a volume (V) of 98 cubic inches, in other words:

$V=98in^3$