Math Help! Need Answers and an explanation- Thanks!?

Question

Point B is the midpoint of Point AC

8. a. Find x if AB = 4x and BC = 2x + 10.

b. Use the answer for x to find the values of AB and BC.

9. a. Find x if AC = 3x - 1 and BC = 12 - x.

b. Use the answer for x to find the value of AB.

10. a. Is it possible for AB = 10, BC = 2x + 5 and AC = 5x, given that point B is the midpoint?

b. Why or why not

Answer 1

problem 8. if B is the midpoint of AC, it means that AB=BC.  so we have 4x= 2x+10

separate the numbers from the variable:

4x-2x = 10

2x=10

x = 10/2

x=5.

if AB = 4x, and x=5 than AB = 4*5 =20

problem 9.  AC=AB+BC and  AB=BC (since B is the midpoint of AC) , so AC=2BC

3x-1= 2(12-x)

3x-1= 24 - 2x

3x+2x = 24+1

5x=25

x = 25/5= 5

10. again, AC=AB+BC

5x = 10+2x+5

5x-2x= 10+5

3x=15

x = 5

and also, we have to remember that BC=AB (point B is the midpoint of AC)

so 10 = 2x+5 , where x =5

so 10= 2*5+5

10 = 10+5 which is false, so it is not posible for AB = 10, BC = 2x + 5 and AC = 5x, given that B is the midpoint.

Answer 2

Hi,

Point B is the midpoint of Point AC

8. a. Find x if AB = 4x and BC = 2x + 10.

AB = BC

4x = 2x + 10

2x = 10

x = 5

b. Use the answer for x to find the values of AB and BC.

Since x = 5, AB = 4x = 4(5) = 20

Since x = 5, BC = 2x + 10 = 2(5) + 10 = 20

9. a. Find x if AC = 3x - 1 and BC = 12 - x.

AC = 2BC

3x - 1 = 2(12 - x)

3x - 1 = 24 - 2x

5x = 25

x = 5

b. Use the answer for x to find the value of AB.

AB = BC = 12 - x, so AB = 12 - 5 = 7

10. a. Is it possible for AB = 10, BC = 2x + 5 and AC = 5x, given that point B is the midpoint?

No, that would not be possible because B would not be the midpoint.

b. Why or why not

AB + BC = AC

10 + 2x + 5 = 5x

2x + 15 = 5x

15 = 3x

x = 5

If x = 5, then BC = 2x + 5 = 2(5) + 5 = 15. AB is supposed to equal BC, because B is the midpoint. But, AB = 10 and BC = 15, so B is not the midpoint as the problem stated.

I hope that helps!! :-)

Answer 3

8. a. A__________B____________C

        

                            AB=BC

                            4x=2x+10

                           4x - 2x = 10

                           2x = 10

then divide both sides by 2

                    2x/2 = 10/2

                    x = 5

b. AB = 4x

                  AB = 4 times 5

                 AB = 20

                 BC = 2x + 10

                BC = 2 times 5 + 10

                BC = 20

9. I have no idea

10. It is not possible

                     AC = AB + BC

                    AB = BC that means

                   1O = 2x + 5

                   10 - 5 = 2x

                    5 = 2x then divide both side by 2

                   x = 5/2 then lets substitute into this  formula

                      AC = AB + BC which means

                5 times 5/2 = 10 + ( 2 times 5/2 + 5 )

               25/2 =  10 + 10

               25/2 = 20 so this is not possible



    

Answer 4

8.  If Point B is the midpt of Segment AC, then AB = BC

Since we're given that AB = 4x and BC = 2x + 10,

4x = 2x + 10

Subtract 2x from both sides

2x = 10

x = 5

So, AB = 4x = 4(5) = 20

BC = 2x + 10 = 2(5) + 10 = 10 + 10 = 20

9.  AC is twice the size of BC

AC = 2BC

Plug in the equations they gave us,

3x - 1 = 2(12 - x)

Distribute

3x - 1 = 24 - 2x

Add 2x to both sides

5x - 1 = 24

Add 1 to both sides

5x = 25

x = 5

AB = BC since B is the midpt of segment AC

AB = BC = 12 - x = 12 - 5 = 7

10. AB + BC = AC and AB = BC if B is the midpoint

If AB = BC, 10 = 2x + 5

Subtract 5 from both sides

5 = 2x

x = 2/5

Now, let's test if AB + BC = AC with x = 2/5

10 + 2x + 5 = 5x

Plug in x = 2/5

10 + 2(2/5) + 5 = 5(2/5)

Multiply

10 + 4/5 + 5 = 10/5

15 + 4/5 = 2

This is not true, so

Answer: It's NOT possible

Hope this helps you!  Please email anytime for further quesitons.

Answer 5

Point B is the midpoint of Point AC

8. a. Find x if AB = 4x and BC = 2x + 10.

4x = 2x + 10

2x = 10

x = 5

b. Use the answer for x to find the values of AB and BC.

AB = 4x

AB = 4*5

AB = 20

BC = 2x + 10

BC = 2*5 + 10

BC = 10 + 10

BC = 20

9. a. Find x if AC = 3x - 1 and BC = 12 - x.

3x - 1 = 2(12 - x)

3x - 1 = 24 - 2x

5x = 25

x = 5

b. Use the answer for x to find the value of AB.

3x - 1 - (12 - x) = AB

3x - 1 - 12 + x = AB

4x - 13 = AB

4*5 - 13 = AB

20 - 13 = AB

7 = AB

10. a. Is it possible for AB = 10, BC = 2x + 5 and AC = 5x, given that point B is the midpoint?

AB + BC should = AC and AB should = BC

10 = 2x + 5

5 = 2x

x = 5/2

AB = 10

BC = 2x + 5

BC = 2(5/2) + 5

BC = 5 + 5

BC = 10

AB + BC =

10 + 10 = 20

AC = 5x

AC = 5(5/2)

AC = 25/2

AC = 12.5

NO ← Answer

b. Why or why not

Because AB + BC does not equal AC in this case.