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3 years ago

Find the distance between the points: (-3, -4) and (5, 5)

Mathematics

1 answer:

zimovet [89]3 years ago

6 0

Answer:d = √ ((X2-X1)2+(Y2-Y1)2)

d = √ (5--3)2+(5--4)2

d = √ ((8)2+(9)2)

d = √ (64+81)

d = √ 145

Xm=(X1+X2)/2

Xm=(-3+5)/2=1

Ym=(Y1+Y2)/2

Ym=(-4+5)/2=0.5

Slope = (Y2-Y1) = (5--4) = (9) = 1.125

(X2-X1) (5--3) (8)

The midpoint is: (1,0.5)

y = mx + b

y = 1.13x + b

-4 = 1.13×-3 + b

-4 = -3.38 + b

-4--3.38 = b

-0.63 = b

y= 1.13x-0.63

0= 1.13x-0.63

-1.13x= -0.63

x= -0.63/-1.13 = 0.56

y= 1.13×0-0.63

y= -0.63

Step-by-step explanation:

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How many different simple random sampmes of size 5 can be obtained from a pppulation whose size is 43?

Nesterboy [21]

Answer:

Number of random samples = 962598

Step-by-step explanation:

A random sample represents the responses for a certain survey of a part of the population.

A sample size is the part of the population being surveyed.

For a population $N$ the number of different random samples that can be chosen for a sample size $x$ can be calculated as = $NCx$

This can be calculated as :

$NCx=\frac{N!}{x!(N-x)!}$

Given:

Population size = 43

Sample size = 5

Number of random samples = $43C5$

⇒ $\frac{43!}{5!(43-5)!}$

⇒ $\frac{43!}{5!(38)!}$

⇒ $\frac{43\times42\times41\times40\times39}{5\times4\times3\times2\times1}$ [Canceling out the common terms]

⇒ $962598$ (Answer)

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3 years ago

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VladimirAG [237]

Answer: First option.

Step-by-step explanation:

You can idenfity in the figure that $\angle FCE$ is formed by two secants that intersect outside of the given circle.

It is important to remember that, by definition:

$Angle\ formed\ by\ two\ Secants=\frac{1}{2}( Difference\ of\ intercepted\ Arcs)$

Knowing this, you can set up the following equation:

$m\angle FCE=\frac{1}{2}(BD-FE)$

Therefore, you must substitute values into the equation and then evaluate, in order to find the measure of the angle $\angle FCE$ .

This is:

$m\angle FCE=\frac{1}{2}(112\°-38\°)\\\\m\angle FCE=37\°$

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Step-by-step explanation:

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