What must be the length of ZY in order for ZY to be tangent
to circle X at point Y?
14 units
15 units
16 units
17 units

15 units

Step-by-step explanation:

The picture of the question in the attached figure

we know that

Triangle XYZ is a right triangle, because segment ZY is tangent to circle X at point Y

so

Applying the Pythagorean Theorem

we have

substitute the given values

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.