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1 year ago

Find the area of the polygon. 7 cm 14 cm 14 cm 7 cm 7 cm 7 cm

Mathematics

1 answer:

kvasek [131]1 year ago

7 0

The area of the polygon is 470596 units²

<h3>What is Area of Regular polygon?</h3>

The region occupied by it in a two-dimensional plane. The areas or formulas for areas of different types of polygon depends on their shapes.

Given that: side are 7 cm,14 cm,14 cm,7 cm,7 cm,7 cm

Area of Polygon= 7*14*14*7*7*7

= 343*195*7

= 470596 units²

The area of polygon is 470596 units²

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21 students in a dass wear spectacles. This is 60% of the total number of

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Answer:

There are 35 students in the class

Step-by-step explanation:

We would divide 21 by 60%

21/0.6 = 35 students.

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A triangle is formed from the points L(-3, 6), N(3, 2) and P(1, -8). Find the equation of the following lines:

Dima020 [189]

Answer:

Part A) $y=\frac{3}{4}x-\frac{1}{4}$

Part B) $y=\frac{2}{7}x-\frac{5}{7}$

Part C) $y=\frac{2}{7}x+\frac{8}{7}$

see the attached figure to better understand the problem

Step-by-step explanation:

we have

points L(-3, 6), N(3, 2) and P(1, -8)

Part A) Find the equation of the median from N

we Know that

The median passes through point N to midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

L(-3, 6) and P(1, -8)

substitute the values

$M(\frac{-3+1}{2},\frac{6-8}{2})$

$M(-1,-1)$

step 2

Find the slope of the segment NM

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

N(3, 2) and M(-1,-1)

substitute the values

$m=\frac{-1-2}{-1-3}$

$m=\frac{-3}{-4}$

$m=\frac{3}{4}$

step 3

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{3}{4}$

$point\ N(3, 2)$

substitute

$y-2=\frac{3}{4}(x-3)$

step 4

Convert to slope intercept form

Isolate the variable y

$y-2=\frac{3}{4}x-\frac{9}{4}$

$y=\frac{3}{4}x-\frac{9}{4}+2$

$y=\frac{3}{4}x-\frac{1}{4}$

Part B) Find the equation of the right bisector of LP

we Know that

The right bisector is perpendicular to LP and passes through midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

L(-3, 6) and P(1, -8)

substitute the values

$M(\frac{-3+1}{2},\frac{6-8}{2})$

$M(-1,-1)$

step 2

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

L(-3, 6) and P(1, -8)

substitute the values

$m=\frac{-8-6}{1+3}$

$m=\frac{-14}{4}$

$m=-\frac{14}{4}$

$m=-\frac{7}{2}$

step 3

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-\frac{7}{2}$

$m_2=\frac{2}{7}$

step 4

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{2}{7}$

$point\ M(-1,-1)$ ----> midpoint LP

substitute

$y+1=\frac{2}{7}(x+1)$

step 5

Convert to slope intercept form

Isolate the variable y

$y+1=\frac{2}{7}x+\frac{2}{7}$

$y=\frac{2}{7}x+\frac{2}{7}-1$

$y=\frac{2}{7}x-\frac{5}{7}$

Part C) Find the equation of the altitude from N

we Know that

The altitude is perpendicular to LP and passes through point N

step 1

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

L(-3, 6) and P(1, -8)

substitute the values

$m=\frac{-8-6}{1+3}$

$m=\frac{-14}{4}$

$m=-\frac{14}{4}$

$m=-\frac{7}{2}$

step 2

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-\frac{7}{2}$

$m_2=\frac{2}{7}$

step 3

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{2}{7}$

$point\ N(3,2)$

substitute

$y-2=\frac{2}{7}(x-3)$

step 4

Convert to slope intercept form

Isolate the variable y

$y-2=\frac{2}{7}x-\frac{6}{7}$

$y=\frac{2}{7}x-\frac{6}{7}+2$

$y=\frac{2}{7}x+\frac{8}{7}$

7 0

3 years ago

Point C is on the segment AB which has endpoints A(-1, 0) and B(3, 8). Point C is three times as far from point A as it is from

Viefleur [7K]

Answer:

C = (2, 6)

Step-by-step explanation:

The coordinates of point C can be found as the weighted average of the endpoint coordinates. The weights are the reverse of the relative segment lengths.

For AC : CB = 3 : 1, we have ...

C = (A +3B)/(1+3) = ((-1, 0) +3(3, 8))/4 = (-1+9, 0+24)/4

C = (2, 6)

8 0

3 years ago

First line joins ordered pairs negative 4, 3 and 2, negative 3. Second line joins negative 4, negative 3 and 2, 3. Part A shaded

elena55 [62]

The part that represents the solution to the inequality will be Part B shaded below first line and above second line.

<h3>How to depict the inequality?</h3>

From the information given, the equation of the first line will be:

y - 3 = (-3 - 3/2 + 4)(x + 4)

y - 3 = -1(x + 4)

y + x = -4 + 3

x + y = -1

The equation of the second line will be:

y + 3 = -1(x + 4)

y = x + 4 - 3

y = x + 1

This is plotted on the graph attached.

From the systems of equations, the statement that is correct about the two systems of equations is that They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A.

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4 0

2 years ago