True or false: The midpoint of a given line segment must lie on the given line segment?

Answers

Answer 1

Answer: Answer:
True

Explanation:
A midpoint of a line is defined as half the distance between these two points.
Therefore, to get this midpoint, we should first connect the endpoints of the line and then get the half the distance

This means that the midpoint must lie on the given line segment

Hope this helps :)

Answer 2

Answer: True. The midpoint of a given line segment must lie on the given line segment because it is the half way point of the line.

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When Frederick was born, his grandparents gave him a gift of 2000, which was invested at an interest rate of 5% per year, compounded yearly. How much money will Frederick have when he collects the money at the age of 18? Give your answer to the nearest hundredth of a dollar.

Answers

Answer:

Frederick collects the an amount of $4813.24 at the age of 18 out of which $2000 was the beginning amount.

Step-by-step explanation:

We are given the following information in the question:

Amount = 2000

Interest rate = 5%

The money is compounded annually or yearly.

Time = 18 years

Compound interest =

$A = P\bigg(1+\displaystyle(r)/(n)\bigg)^(nt)$

where P is the principal amount, r is the interest rate, t is the time in years and n is the number of compounding in a year.

Since, the money is compounded yearly we put n = 1.

Putting all the values, we get,

$A = P\bigg(1+\displaystyle(r)/(n)\bigg)^(nt)\n\nA = 2000\bigg(1+(5)/(100)\bigg)^(18)\n\nA = 4813.24\n\n\text{Interest, I} = \text{Amount - Principal} = A - P\n\nI = 4813.24 - 2000 = 2813.24$

Thus, Frederick collects the an amount of $4813.24 at the age of 18 out of which $2000 was the beginning amount.

Answer:

$4813.24

Step-by-step explanation:

Five percent growth corresponds to multiplication by 1+5%=1.05. So, the amount of money Frederick will have in 18 years is 2000(1+.05)^18= $4813.24

(?,3) is on the line y=2x+5 find the other coordinate

Answers

Think about this. What do the numbers in a coordinate stand for? They stand for X and Y. If you're trying to figure out what the X is, wouldn't you be solving for x? And didn't they just give you an equation? ;) First off, do you see how the "Y" value is given to you in the coordinate? All you have to do is substitute that 3 in for the "y" in the equation! 3=2x+5. Hey.... that looks like a simple equation! First, you need to subtract 5 from the other side of the equation. Now you're left with 2x=-2. Divide both sides by 2, and you get that x=-1. Now, just substitute that "x' value into the coordinate, and your answer should come out to be (-1, 3). :D

What is 8/16 in simplest form

Answers

1/2 is the simpliest form,divide everything by 2

Not really because 8 times something equals 16 so, 8x2=16
So your answer is two.

2(3−8y)=? Does anyone know what this is?

Answers

Answer:

i think it’s y = -3/4

Step-by-step explanation:

At a local fitness center, members pay an $8 membership fee and $4 for each aerobic class. Nonmembers pay $6 for each aerobic class. For what number of aerobics classes will the cost for members and nonmember be the same?

Answers

In the aerobics classes of 4 will the cost for members and nonmember be the same.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

At a local fitness center, members pay an $8 membership fee and $4 for each aerobic class.

And, Nonmembers pay $6 for each aerobic class.

Now,

We can formulate;

For members, the cost = $8 + 4x

Where, x is the aerobic class.

For nonmembers;

The cost = 6x

We can equate both the equation, we get;

6x = 8 + 4x

Solve for x as;

6x - 4x = 8

2x = 8

x = 4

Thus, In the aerobics classes of 4 will the cost for members and nonmember be the same.

Learn more about the mathematical expression visit:

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An aerobic lesson will be defined as 'a'
For every member lesson, they pay $4, so they will be represented as 4a
For every non member lesson, they pay $6, so they are 6a
Don't forget members have to pay $8 at the start, so they have to be 4a + 8
So
4a + 8 = 6a is our final equation
Move the 'a's to one side, by subtracting 4a from each side, giving you
8 = 2a
Divide by 2 to isolate a
4 = a
After 4 aerobics classes, the cost will be the same

Which of the following employees has the greatest total employee compensation?a.
Employee A: total job benefits $49,200 and total job expenses $300
b.
Employee B: total job benefits $49,500 and total job expenses $500
c.
Employee C: total job benefits $ 49,800 and total job expenses $700
d.
Employee D: total job benefits $50,100 and total job expenses $900

Answers

We have to choose the correct answer which of the employees has the greatest total employee compensation. We just have to subtract the job expenses from total job benefits for everyone of them. A: $49,200 - $300 = $38,900. B : $49,500 - $500 = $49,000. C : $49,800 - $700 = $41,100. D : $50,100 - $900 = $49,200. The largest sum is $49,200 ( employee D ) . Answer: The greatest total employee compensation has Employee D.

D: Employee D: Total employee benefits $3,000 Total job benefits $52,300

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Solve -5(3 n + 4) = 40.