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2 years ago

similarities between finding the perimeter and area of a polygon with and without the coordinate plane

Mathematics

1 answer:

Lapatulllka [165]2 years ago

6 0

<h2>Answer:</h2>

A Polygon is shape with straight sides and must be closed. Polygon sides never touch and are classified according to the number of its sides. So:

A Triangle is any polygon with exactly 3 sides
A Quadrilateral is any polygon with exactly 4 sides.
A Pentagon is any polygon with exactly 5 sides.
An Hexagon is any polygon with exactly 6 sides.
A Heptagon is any polygon with exactly 7 sides.
An Octagon is any polygon with exactly 8 sides.
A Nonagon is any polygon with exactly 9 sides.
Decagon is any polygon with exactly 10 sides.

<h3>1. WITH THE COORDINATE PLANE:</h3>

If you have the coordinate plane, there are several ways to calculate the perimeter and area. If the polygon meaning that every side must have the same length and every angle must have the same measure, you just need the coordinates of two points and by using the distance formula you can calculate the length of that side. Then you must multiply the number of sides by that distance and this is the perimeter, but if the polygon is irregular you must calculate the length of each side of the polygon using the distance formula and then make the sum. To compute the area, you must divide the entire polygon in triangles, rectangles, parallelograms, etc, and then calculating the area of each figure using the formulas known for each type of figure.

<h3>2. WITHOUT THE COORDINATE PLANE:</h3>

If you don't have the coordinate plane, you need to have the length of each side to calculate the perimeter or each side should be calculated by using trigonometry and other mathematical skills. If the polygon is regular or is a known figure (trapezoid, parallelogram, triangle) you can use the formulas you know to compute the area of that figure. On the other hand, if the polygon is irregular you should divide the polygon in other simple figures and calculate each area and then making the sum.

_______________________

<em>In conclusion,</em><em> for both ways you need to have the length of each side to find the perimeter and can use well known formulas to find the area of the figure.</em>

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Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. If th

ioda

Answer:

The bottom cutoff heights to be eligible for this experiment is 66.1 inches.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean of 69.0 inches and a standard deviation of 2.8 inches.

This means that $\mu = 69, \sigma = 2.8$

What is the bottom cutoff heights to be eligible for this experiment?

The bottom 15% are excluded, so the bottom cutoff is the 15th percentile, which is X when Z has a pvalue of 0.15. So X when Z = -1.037.

$Z = \frac{X - \mu}{\sigma}$

$-1.037 = \frac{X - 69}{2.8}$

$X - 69 = -1.037*2.8$

$X = 66.1$

The bottom cutoff heights to be eligible for this experiment is 66.1 inches.

8 0

2 years ago

Solve the following quadratic by<br> completing the square.<br> y = x^2 - 6x+7

kozerog [31]

Answer:

$x= 3+\sqrt{2}, \quad x= 3 -\sqrt{2}$

Step-by-step explanation:

<u>Given quadratic equation</u>:

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

To complete the square, begin by adding and subtracting the square of half the coefficient of the term in x:

$\implies y = x^2 - 6x+\left(\dfrac{-6}{2}\right)^2-\left(\dfrac{-6}{2}\right)^2+7$

$\implies y = x^2 - 6x+\left(-3\right)^2-\left(-3\right)^2+7$

$\implies y = x^2 - 6x+9-9+7$

Factor the perfect square trinomial:

$\implies y=(x-3)^2-9+7$

$\implies y=(x-3)^2-2$

To solve the quadratic, set it to zero and solve for x:

$\implies (x-3)^2-2=0$

$\implies (x-3)^2-2+2=0+2$

$\implies (x-3)^2=2$

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

$\implies x-3= \pm\sqrt{2}$

$\implies x-3+3= 3\pm\sqrt{2}$

$\implies x= 3\pm\sqrt{2}$

Therefore, the solution to the given quadratic equation is:

$x= 3+\sqrt{2}, \quad x= 3 -\sqrt{2}$

6 0

4 months ago

Read 2 more answers

Please help me with this

tester [92]

$\rm\blue{Answer:}$

x = 70°

<u>Explanation</u> :

To find : Value of x

Here, given angles are :

35°, 75° and x

Knowledge Required to solve it :

The sum of all the angles of a triangle is 180°.

Now,

35°+75°+x=180°

⇒110°+x=180°

⇒x=180°-110°

⇒x=70°

.°. x=70°

5 0

2 years ago

What is the slope of a line parallel to the line whose equation is 52 +y = -9. Fully

inna [77]

Answer:

Step-by-step explanation:

3.0

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2 years ago

Find the equation of a line with an x-intercept (2,0) and a y-intercept

cricket20 [7]

Since that is only one set of numbers, you would have to start on the origin, then move right on the x-axis twice because the first number is 2, and stay there for the other half of the equation since the other number is 0.

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2 years ago