Geometry problems - get 10 points if you get 1 and 2 right.?

Question

X---------------T---------------Z


1.If XZ = 3x, XT = x + 3, and TZ = 13, find XZ.

2. Suppose that T is the midpoint of line XZ. If XT = 2x + 11 and XZ = 5x + 8, fined the value of X.

What does postulate means?

Answer 1

1. 3x= x + 3 + 13



2x= 16



x=8



XZ=3x



XZ=3(8)=24



2. (5x + 8)/2=2x + 11



5x + 8= 4x + 22



x=14

Answer 2

Draw a superb-angled triangle with the hypotenuse being 12*sqrt (3), and another perspective being 30°. (it particularly is not mandatory to put in the different perspective). Label the factor adjoining to the 30° as A, the factor opposite the 30° as O and the hypotenuse as H. you ought to use sine and cosine. sin theta=O/H all of us be attentive to that theta=30°, O and H we've labelled, and H=12 sqrt 3. so sin 30°=O/(12 sqrt 3) O=12 sqrt 3 *sin 30° =6 sqrt 3 considering the fact which you're making use of sq. roots, i mean you're able to be attentive to your good values table. for the different factor, A, cos theta=A/H cos 30°=A/(12 sqrt 3) A=cos 30° * 12 sqrt 3 =sqrt (3)/2 * 12 sqrt (3) =6*3 =18 by making use of the way, in case you prefer it, good values: sin 0=0 sin 30=a million/2 sin forty 5= sqrt(2)/2 sin 60=sqrt(3)/2 sin ninety=a million cos 0=a million cos 30=sqrt(3) /2 cos forty 5= sqrt(2)/2 cos 60=a million/2 cos ninety=0 tan 0=0 tan 30=sqrt(3)/3 tan forty 5=a million tan 60=sqrt(3) tan ninety=undefined

Answer 3

XZ=XT+TZ

3x=x+3+13

2x=16

x=8



postulate is any mathematical statement that serves as a starting point from which other statements are logically derived.:)

Answer 4

1. x+3+13=3x

x+16=3x

16=2x

8=x



XZ=3x

XZ=3*8

XZ=24





2. 2(2x+11)=5x+8

4x+22=5x+8

14=x





Postulate: An axiom.

Answer 5

XZ = 24