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3 years ago

AB is tangent to circle D. Find the value of x.

Mathematics

1 answer:

Svet_ta [14]3 years ago

6 0

Answer:

c 15

Step-by-step explanation:

Tangent AB is tangent to circle D at point A. The angle made by a tangent to a circle and a radius of the circle at the point of tangency is a right angle. That means that angle is a right angle, and triangle ABD is a right triangle.

We can use the Pythagoren theorem.

a^2 + b^2 = c^2

x^2 + 20^2 = (x + 10)^2

x^2 + 400 = (x + 10)(x + 10)

x^2 + 400 = x^2 + 10x + 10x + 100

400 = 20x + 100

20x = 300

x = 15

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3 years ago

Find the mean, the median, and all modes for the data in the given frequency distribution. (Round your answers to one decimal pl

kvasek [131]

Answer: Mean = 7.8

Median = 9

Mode = 2,9

Step-by-step explanation: Mean is the average value of a data set. Mean from a frequency table is calculated as:

$E(X)=\frac{2(10)+3(9)+9(10)+11(7)+12(3)+15(4)+16(3)}{10+9+10+7+3+4+3}$

E(X) = 7.8

Mean for the given frequency distribtuion is 7.8.

Median is the central term of a set of numbers. Median in a frequency table is calculated as:

1) Find total number, n:

n = 10 + 9 + 10 + 7 + 3 + 4 + 3 = 46

2) Find position, using: $\frac{n+1}{2}$

$\frac{n+1}{2}=\frac{47}{2}$ = 23.5

Median is in the 23.5th position.

3) Find the position by adding frequencies: for this frequency distribution, 23.5th position is 9

Median for this frequency distribution is 9.

Mode is the number or value associated with the highest frequency.

In this frequency distribution, 2 and 9 points happen 10 times. So, mode is 2 and 9.

Mode for this distribution is 2 and 9.

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3 years ago