Question

Finding Median of a trapezoid Please Help: Question in comments!
I know the answer is 4 but I dont know how to solve these equations.

Answer 1

The length of the median is the average of the lengths of the 2 bases.
In other words, to find the length of the median, add the lengths of the 2 bases and divide by 2.

Answer 2

I understand that part. I am having problems with the substitution where you have to add the 2 equations together

Answer 3

Think of the expressions for the 2 bases as numbers.
Let's call them A and B.
If you need to find the average of A and B, you simply do this:

\(\dfrac{A + B}{2} = ~average\)

You know the average is 23.
Also, for you, A = 8x + 3, and
B = 3x - 1.

Substitute those values for A, B, and "average" in the expression above.

Then solve for x.

Answer 4

I understand that part. I'm having problems with substitution. Do you think you could help me with that?

Answer 5

Ok, let's set up the equation with x.

Add the bases: (8x + 3) + (3x - 1)

Ok so far?

Answer 6

Or I guess adding the 2 equations together I should say...

Answer 7

Ok I have my paper ready that looks good so far

Answer 8

Since we are finding the average of the lengths of the bases, after we add them, we divide them by 2.

\(\dfrac{(8x + 3)+(3x - 1)}{2} \)

Ok, so far?

Answer 9

yes

Answer 10

The figure shows us that the median has a length of 23.
Our expression is the length of the median, so our expression must be equal to 23.

\(\dfrac{(8x + 3)+(3x - 1)}{2} = 23\)

This is the equation that has to be solved to x.

Answer 11

how do you add the 2 equations together is what Im wondering

Answer 12

First, remove the parentheses because in this case, they're unnecessary.

\(\dfrac{8x + 3+3x - 1}{2} = 23\)

Now you add like terms.
Like terms are terms that have the same variable part.
The variables are the letters. In our case our variable is x.

You add 8x to 3x, and you subtract 3 - 1.
That goes in the numerator.

Answer 13

ok so now I have 5x + 2 =23 And I subtract the 2 from 23?

Answer 14

11x*

Answer 15

BTW, they are not equations. An equation is a statement that "equates" two things. An equation is a statement with an equal sign. These are simply expressions.

Answer 16

Wait. Don't forget the denominator.

Answer 17

ok thanks for clarifying Not that I have enough to worry about :) haha

Answer 18

This is what you have now.

\(\dfrac{11x + 2}{2} = 23\)

Answer 19

Yes that is what i have

Answer 20

Now we multiply both sides by 2 to get rid of the denominator of 2 on the left side.

\(\dfrac{11x + 2}{2} \times 2= 23 \times 2\)

\(11x + 2 = 46\)

Answer 21

Now you subtract 2 from both sides.

Answer 22

Oh I see. OK let me solve that hld on

Answer 23

I will give you the steps and you tell me if their right?

Answer 24

\[11x + 2 =46 \]

Answer 25

11x = 44 x =4

Answer 26

Thank you so much! I really appreciate it!

Answer 27

is there a way I can rate you?

Answer 28

This is how it should look:

11x + 2 = 46
11x = 44 (subtracting 2 from both sides)
x = 4 (dividing both sides by 4)

Answer 29

You can click on "Best Response" to give me a medal if you'd like to.

Answer 30

May I ask if you are in college or what school you attend?

Answer 31

What college did you attend if you dont mind me asking?

Answer 32

Lovely, Im only a sophomore in HS but I plan on attending Embry Riddle in Daytona Beach. Im sure you have heard of that school.

Answer 33

I live right near Boca Raton acually lol

Answer 34

yes

Answer 35

Great. Keep studying and asking questions. That's how you learn. Also, in math, solving tons of practice problems helps a lot.

Answer 36

Thanks for the help, I would love to give you a medal how do i do that?

Answer 37

Click on "Best Response" in one of my answers.