Math 10th grade questions?

Question

1. If points B, D , and X are collinear, with D between X and B. Given: DX = 4x + 6, BX= 6x -18, and DB= x+15, solve for x.

2. XB lies on the interior of <WXZ, If M<WXB= 30 and m<ZXW = 40, what is the m<BXZ?

3. C is between A and B. If AC=4x, AB= 3x+12, and CB = 10, then AB=?

Answer 1

Given that B,D and X are collinear

And D between X and B. So, XB = XD + DB

 Given: DX = 4x + 6, BX= 6x -18, and DB= x+15,

6x - 18 = (4x + 6) + (x + 15)

6x - 18 = 5x + 21

Subtract 5x from each side.

x - 18 = 21

Add 18 to each side.

x = 18 + 21 = 39

Therefore x = 39.

Answer 2

3). C is between A and B.  So, AB = AC + CB.

If AC=4x, AB= 3x+12, and CB = 10, then AB=?

AB = AC + CB.

AB = 4x + 10

 

But given AB = 3x + 12

4x + 10 = 3x + 12.

Subtract 3x from each side.

x + 10 = 12

Subtract 10 from each side.

x = 2.

Comments

x = 2.

AB = 3x + 12

Substitute x = 2 in AB = 3x + 12.

AB = (3 * 2) + 12

= 6 + 12

= 18.

∴ AB = 18.

Answer 3

• (2).

From the given data draw the below figure.

From, the figure,

WXB = 30 and ZXW = 40.

BZ = ZXW - WXB

= 40 - 30 = 10

⇒ BZ = 10.

Consider that, X is the mid point of WB.

WX = XB = 15.

BXZ = BX + BZ

= 15 + 10 = 25

⇒ BXZ = 25.