Find the value of x to the nearest tenth.

Question

1. A= 17.1 B= 25.2 C= 18.6 D= 15.2
2. Find the value of x to the nearest tenth.
3. A. 12.1 B. 14.3 C. 16.1 D.13.1
4. Find the value of x to the nearest tenth.
5. a. 0.4 B. 4 C. 3.5 D. 3.8

Answer 1

Hey David,

These types of problems are pretty easy if you know the appropriate theorems. I don't have them memorized so I had to look them up, but here is how they work.

1) For a situation which involves the intersection of two secant lines (like this example) have the relationship that the ratio between the length of the entire line to its external segment equals the same ratio of the other line. IE:

(Total Length of A) x (Length of external part of A) = (Total Length of B) x (Length of external part of B)

In problem 1 this means that:

(19+9) 9 = (10 + x) 10

(28)9 = 100 + 10x

252 - 100 = 10x

152 = 10x

x = 15.2

2) For this problem we need the relationship of an intersecting tangent line and secant line. It says that the length of the tangent line squared is equal to the total length of the secant line times the external part of the secant line. IE:

(Length Tangent Line)² = (Length of Secant Line) x (Length of Secant External Segment)

In problem two this means that:

(x+8)8 = 13²

8x + 64 = 169

8x = 105

x = 13.125

3) This last problem needs the relationship of two chords. That relationship is that the product of the lengths of the segments of the chords should be equal. That is:

(Length of First Chord Segment 1) x (Length of First Chord Segment 2) = (Length of Second Chord Segment 1) x (Length of Second Chord Segment 2)

In problem 3 this says that:

10x = (5)(8)

10x = 40

x = 4

Hope this helps!

-Nathan

Answer 2

Need degrees on the circles. a,b,c,d; what do they refer to?