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2 years ago

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Mathematics

2 answers:

galben [10]2 years ago

5 0

Answer:

length of line segment PQ is 5 units

Step-by-step explanation:

Tangent secant theorem

MN² = QN x PN

6² = 4(x+4)

36 = 4x + 16 Plug in values into exponents

20 = 4x Subtract 16 from both sides

x = 5 Divide by 4 to isolate the variable

MrRa [10]2 years ago

4 0

Answer:

5 units

Step-by-step explanation:

The product of the length of the secant segment and its external part equals the square of the length of the tangent segment.

4 * (4+x) = 6^2

Distribute

16 +4x = 36

Subtract 16 from each side

16-16+4x = 36-16

4x= 20

Divide each side by 4

4x/4 = 20/4

x=5

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Answer:

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Step-by-step explanation:

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2 years ago

What are the mean absolute deviation and population standard deviation of this data set? Round to the nearest tenth if necessary

tekilochka [14]

Answer:

For a data set of N elements:

{x₁, x₂, ..., xₙ}

The mean is:

$M = \frac{x_1 + x_2 + ... + x_n}{N}$

The mean absolute deviation is:

$MAD = \frac{|x_1 - M| + ... + |x_n - M|}{N}$

And the population standard deviation is:

$PSD = \frac{\sqrt{|x_1 - M|^2 + ... + |x_n - M|^2} }{\sqrt{N}}$

In this case, our set has 5 elements, and the set is:

{2, 4, 6, 9, 14}

The mean of this set is:

$M = \frac{2 + 4 + 6 + 9 + 14}{5} = 7$

The mean absolute deviation is:

$MAD = \frac{|2 - 7| + |4 - 7| + |6 - 7|+ |9 - 7| + |14 - 7| }{5} = 3.6$

And the population standard deviation is:

$PSD = \sqrt{\frac{|2 - 7|^2 + |4 - 7|^2 + |6 - 7|^2+ |9 - 7|^2 + |14 - 7|^2 }{5}} = 4.2$

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anyanavicka [17]

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lakkis [162]

Answer:

y = (x-3)^2 -16

Step-by-step explanation:

y = x^2 -6x-7

We need to complete the square

b= -6

b/2 = -6/2 = -3

(b/2) ^2 = (-3)^2 =9

Add 9 then subtract 9 to balance the equation

y = x^2 -6x +9 -9 -7

y = (x^2 -6x+9) -16

The terms in parentheses is (x-b/2)^2

y = (x-3)^2 -16

This is in vertex form

The vertex is (3,-16)

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