I am having trouble with my Geometry Homework. We haven't gone over it in class, so we have to learn it by ourselves. I have finished some of it, but not for sure if it's accurate or correct. Medal will be rewarded if answer is correct and accurate and you helped me some. Attachments will be in comment box below

- Firejay5

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- mathstudent55

The first one is correct.

- Firejay5

positive with the reasons

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## More answers

- mathstudent55

Wait. The first one is an example in your book?

- Firejay5

Yea, I took it, so you knew what we had to do

- mathstudent55

I see. I see that it's called Example 1.

- Firejay5

Yea

- mathstudent55

Ok. Now I am at Try These a.
1. Given is correct.

- Firejay5

what about the other 6

- mathstudent55

2. What is the 10 doing on both sides of the equation? What operation is the 10 involved with?

- Firejay5

multiplying the 2 and the 5

- mathstudent55

If it's multiplying both sides, what property is it?

- Firejay5

multiplication property

- mathstudent55

It's not multiplying the 2 and the 5. It's multiplying the fraction of the left side and the fraction on the right side. Yes, "Multiplication property of equality" is the reason for 2.

- Firejay5

#3 is Division Property of Equality

- mathstudent55

For 3. You are simply dividing the 10 by 2 on the left and the 10 by 5 on the right. This is not a property. It's simply reducing each fraction.

- mathstudent55

Step 4. The distributive property is applied on each side, so 4. is Distributive property.

- Firejay5

5. Subtraction property of equality
6. Division Property
7. Reflexive Property

- mathstudent55

In step 5 you go from
5x - 15 = 12 + 2x
to
3x - 15 = 12
The 2x was subtracted from both sides, so 5. Subtraction property of equality.

- mathstudent55

For 6. You go from
3x - 15 = 12
to
3x = 27
15 was added to both sides to get
3x = 27, so 6. is Addition property of addition.

- mathstudent55

Finally, in step 7. you go from
3x = 27 to
x = 9
by dividing both sides by 3, so
7. Division property of equality

- Firejay5

okay thank you and I don't get the 3rd link

- mathstudent55

In the third link, you need to solve the equation to find out what you are trying to prove.

- Firejay5

like how

- mathstudent55

Then you can go back to the solution, and justify every step with a reason, and fill in the Prove statement at the top.

- mathstudent55

We'll solve the equation together first.

- mathstudent55

We can solve the equation with each step accompanied by a reason. This way the proof part will be done. Then we find out what the solution to the equation is, ans we'll fill out the Prove part of the proof on top.
Statements Reasons
1. \(4x + 9 = 18 = \dfrac{1}{2}x \) 1. Given

- Firejay5

Wait am I doing the same thing like the previous page

- mathstudent55

- Firejay5

so basically do the same thing we did before correct

- mathstudent55

Yes.

- Firejay5

that's what it's asking us to do

- mathstudent55

Yes, you need a two column proof.

- Firejay5

it did the first statement for us

- mathstudent55

Here are the first statement and reason again. I had an extra equal sign above by mistake.
Statements Reasons
1. \(4x+9=18 - \dfrac{1}{ 2} x\) 1. Given

- mathstudent55

Now we need to add \( \dfrac{1}{2}x \) to both sides.
2. \(\dfrac{9}{2}x + 9 = 18 \) 2. Addition property of equality

- mathstudent55

Now we subtract 9 from both sides.
3. \( \dfrac{9}{2}x = 9 \) 3. Subtraction property of equality

- Firejay5

Could you leave it as 4.5

- mathstudent55

Now we multiply both sodes by 2/9
4. \( x = 2 \) 4. Multiplication property of equality

- Firejay5

Wait

- Firejay5

4. Division Property of Equality, because I divided 9 by 4.5 to get 2

- mathstudent55

Now that we know the solution is x = 2, we can fill out the line above of what to prove:
Prove: x = 2

- mathstudent55

Yes. If you used 4.5x = 9, then you divide both sides by 4.5 to get x = 2, so for you, Division property is correct.

- Firejay5

so we worked both differently for the last one

- mathstudent55

That's fine. We are both correct.

- Firejay5

Example 2: Was I correct?

- mathstudent55

Which link is that?

- Firejay5

4th link

- mathstudent55

Ok, I'll look.

- Firejay5

My homework goes in order of the links except the first link

- mathstudent55

For the 4th lionk:
All your answers are correct exept for the last one.

- Firejay5

what's c

- mathstudent55

x + 7 = 10
What do you do to x + 7 to end up with x?

- Firejay5

subtraction

- mathstudent55

Right, so the answer is: Subtraction property of equality?

- Firejay5

But it asked for: State the property of equality that justifies the conclusion of the statement

- mathstudent55

That is it.

- Firejay5

I took it like substituting 3 for x

- Firejay5

Was I wrong

- mathstudent55

That is not substitution.
This is substitution:
Given: x = 2
y + x = 10
Prove: y = 8
1. x = 2 1. Given
2. y + x = 10 2. Given
3. y + 2 = 10 3. Substitution
4. y = 8 4. Subtraction property of equality.
What happened from step 2 to step 3? Notice that in step 3, x was substituted by what x is equal to, 2. That is what substitution is.

- mathstudent55

Yes, you were wrong because there was no substitution done in your problem in Link #4.

- Firejay5

Is link 5 right? and I need a little help with link 6

- mathstudent55

Substitution is a property of equality. It's just not the one that used in that probelm.

- Firejay5

Is link 5 right, and I need help with link 6

- mathstudent55

5a and 5b are correct.
In 5c, you switched the hypothesis and the conclusion.

- Firejay5

so switch x^2 = 16 and x = 4

- mathstudent55

Yes.
In link 6, the hypothesis and conclusion are easy to do like you did in link 4.

- mathstudent55

a, The part after "if" is the hypothesis.
b. The part after "then" is the conclusion.
c. Think of any two odd numbers and add them together. Is the sum odd or even?

- Firejay5

A. 2 #'s are odd
B. sum is odd
C. 25 + 99 = 124, so two numbers that are odd, the sum should be even

- Firejay5

is my answer correct

- mathstudent55

For a and b you are correct.
For c you are on the right track.
You need to show one example where the conclusioin is false.
You did it by choosing 25 and 99 and showing the sum is 124, an even number. Therfeore, you have shown a counterexample.
All you need to do is state, "odd numbers 25 and 99 have a sum of 124, an even number, proving the if-then statement flase."

- Firejay5

Thank you for your help @mathstudent55

- mathstudent55

You're welcome.

- Firejay5

@mathstudent55 Somethings you were wrong though

- Firejay5

You were wrong on 4th link on C, it was substitution property

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