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3 years ago

A polygon has the following coordinates: A(3,1), B(5,3), C(2,5), D(-1,5), E(-4,3), F(-2,1). Find the length of DC.

Mathematics

1 answer:

nlexa [21]3 years ago

7 0

To find the length of a line given two points, we are going to use the distance formula, which is defined below:

$D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

( $(x_1, y_1)$ and $(x_2, y_2)$ are the two points)

The points in this problem are (2, 5) and (-1, 5). We can find the distance of DC by substituting these values into the distance formula and simplifying, as shown below:

$D = \sqrt{(-1 - 2)^2 + (5 - 5)^2$

Substitute values into formula

$D = \sqrt{(-3)^2}$

Combine like terms and then simplify $0^2$ to 0

$D = \sqrt{9}$

Compute $(-3)^2 = 9$

$D = 3$

Compute $\sqrt{9} = 3$

The length of DC is 3.

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A six-sided die is rolled two times. What is the theoretical fractional probability that the first number is even and the second

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Answer:

The theoretical probability that the first number is even and the second number is odd is $\frac{1}{4}$ .

Step-by-step explanation:

Since each dice has six sides, and there are two die, the total amount of different outcomes are $6^2$ or 36. The probability of getting an even number on the first roll is $\frac{3}{6}$ or $\frac{1}{2}$ , and the probability of getting an odd number on the second roll is also $\frac{3}{6}$ or $\frac{1}{2}$ , so the probability of getting an even number on the first roll and an odd number on the second roll is $\frac{1}{2} * \frac{1}{2} = \frac{1}{4}$ .

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3 years ago

What is the standard deviation of the data set? 1, 4, 2, 2, 8, 7, 3 Round your answer to the nearest tenth.

fomenos

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Using the distance formula , find the distance from the center of your habitat to the point (x, y). Write this equation. Your an

alexdok [17]

Answer:

See explanation

Step-by-step explanation:

The distance formula is given by:

$d = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} }$

We want to find the distance between (a,b) and (x,y).

The center of the habitat is missing in the question.

Assuming the center is (a,b) where a and b are real numbers, then we can use the distance formula to obtain:

$d = \sqrt{(x - a)^{2} + {(y - b)}^{2} }$

For instance if the center of your habitat us (2,-1), then

$d = \sqrt{(x - 2)^{2} + {(y + 1)}^{2} }$

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3 years ago

<img src="https://tex.z-dn.net/?f=f%28x%29%3D-4x%5E%7B2%7D%2B5x" id="TexFormula1" title="f(x)=-4x^{2}+5x" alt="f(x)=-4x^{2}+5x"

JulijaS [17]

Answer:

Domain= (-inf,inf)/(-∞,∞)

Range= (-inf,25/16]

x-intercepts= (0,0), (5/4,0)

y-intercepts=(0,0)

vertex= maximum (5/8,25/16)

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3 years ago

Four dice, each numbered in the usual way from 1 to 6, are colored white, red, green and blue respectively. After casting them a

Delvig [45]

Suppose that the numbers that the boy being cast from the dice are 3 4 5 6.
3 stands for white, 4 stands for red, 5 stands for green and 6 stands for blue.
We need to interpret the statement given above. The set of numbers is 3 4 4 6 6 5.
First, we need to get the mean of this set. Add all the numbers and divide by the total number that the set has.
3+4+4+6+6+5= 28 / 6
= 4.67 The mean is 4.67
For the variance, we will use the mean above ( 4.67 )

1. Squared the mean and subtract how many numbers are present in the set.
4.67x4.67= 21.8089 /6 = 3.64 set aside this result
2. Next squared all the numbers present in the set and add the result

3x3= 9 , 4x4= 16, 4x4=16, 6x6=36, 6x6=36, 5x5=25

9+16+16+36+36+25= 138

3. Subtract the result of #2 with #1
138 - 3.64= 134.36 set this aside

4. Subtract 1 from the total numbers you have in your set

6 - 1= 5

5. Divide the result we have in #3 with the result of #4

134.36 / 5= 26. 872

So the variance is 26.872

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