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2 years ago

The Diagram shows a polygon composed of rectangles

Mathematics

2 answers:

Igoryamba2 years ago

8 0

To find perimeter you add up all the sides so the answer is 210

vodka [1.7K]2 years ago

7 0

Answer:

210 feet

Step-by-step explanation:

Refer the attached figure

LK = 22 ft

KH=JI = 18 ft.

HG=14 ft.

CD=FE=16 ft.

AL=15 ft.

GF=CB = 5ft.

KJ=HI=10 ft.

CF=CB+BG+GF=5+15+5=25 ft. =DE

AB= LK+KH+HG=22+18+14= 54 ft.

Perimeter of polygon = Sum of all sides

Perimeter of polygon=AL+LK+KJ+JI+HI+HG+GF+FE+DE+CD+CB+BA

=15+22+10+18+10+14+5+16+25+16+5+54

=210

Hence the perimeter of the polygon is 210 feet.

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Find the distance from (4, −7, 6) to each of the following.

LenKa [72]

Answer:

(a) 6 units

(b) 4 units

(d) 9.22 units

(e) 7.21 units

(f) 8.06 units

Step-by-step explanation:

The distance d from one point (x₁, y₁, z₁) to another point (x₂, y₂, z₂) is given by;

d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Now from the question;

(a) The distance from (4, -7, 6) to the xy-plane

The xy-plane is the point where z is 0. i.e

xy-plane = (4, -7, 0).

Therefore, the distance d is from (4, -7, 6) to (4, -7, 0)

d = √[(4 - 4)² + (-7 - (-7))² + (0 - 6)²]

d = √[(0)² + (0)² + (-6)²]

d = √(-6)²

d = √36

d = 6

Hence, the distance to the xy plane is 6 units

(b) The distance from (4, -7, 6) to the yz-plane

The yz-plane is the point where x is 0. i.e

yz-plane = (0, -7, 6).

Therefore, the distance d is from (4, -7, 6) to (0, -7, 6)

d = √[(4 - 0)² + (-7 - (-7))² + (6 - 6)²]

d = √[(4)² + (0)² + (0)²]

d = √(4)²

d = √16

d = 4

Hence, the distance to the yz plane is 4 units

(c) The distance from (4, -7, 6) to the xz-plane

The xz-plane is the point where y is 0. i.e

xz-plane = (4, 0, 6).

Therefore, the distance d is from (4, -7, 6) to (4, 0, 6)

d = √[(4 - 4)² + (-7 - 0)² + (6 - 6)²]

d = √[(0)² + (-7)² + (0)²]

d = √[(-7)²]

d = √49

d = 7

Hence, the distance to the xz plane is 7 units

(d) The distance from (4, -7, 6) to the x axis

The x axis is the point where y and z are 0. i.e

x-axis = (4, 0, 0).

Therefore, the distance d is from (4, -7, 6) to (4, 0, 0)

d = √[(4 - 4)² + (-7 - 0)² + (6 - 0)²]

d = √[(0)² + (-7)² + (6)²]

d = √[(-7)² + (6)²]

d = √[(49 + 36)]

d = √(85)

d = 9.22

Hence, the distance to the x axis is 9.22 units

(e) The distance from (4, -7, 6) to the y axis

The x axis is the point where x and z are 0. i.e

y-axis = (0, -7, 0).

Therefore, the distance d is from (4, -7, 6) to (0, -7, 0)

d = √[(4 - 0)² + (-7 - (-7))² + (6 - 0)²]

d = √[(4)² + (0)² + (6)²]

d = √[(4)² + (6)²]

d = √[(16 + 36)]

d = √(52)

d = 7.22

Hence, the distance to the y axis is 7.21 units

(f) The distance from (4, -7, 6) to the z axis

The z axis is the point where x and y are 0. i.e

z-axis = (0, 0, 6).

Therefore, the distance d is from (4, -7, 6) to (0, 0 6)

d = √[(4 - 0)² + (-7 - (0))² + (6 - 6)²]

d = √[(4)² + (-7)² + (0)²]

d = √[(4)² + (-7)²]

d = √[(16 + 49)]

d = √(65)

d = 8.06

Hence, the distance to the z axis is 8.06 units

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2 years ago

∆ABC is translated 2 units down and 1 unit to the left. Then it is rotated 90° clockwise about the origin to form ∆A′B′C′.

RideAnS [48]

Answer:

The coordinates of image are A'(-2,1), B'(1,0) and C'(-1,0).

Step-by-step explanation:

From the figure it is clear that the coordinates of triangle are A(0,0), B(1,3) and C(1,1).

∆ABC is translated 2 units down and 1 unit to the left.

$(x,y)\rightarrow (x-1,y-2)$

$A(0,0)\rightarrow (0-1,0-2)=(-1,-2)$

$B(1,3)\rightarrow (1-1,3-2)=(0,1)$

$C(1,1)\rightarrow (1-1,1-2)=(0,-1)$

Then it is rotated 90° clockwise about the origin to form ∆A′B′C′.

$(x,y)\rightarrow (y,-x)$

$(-1,-2)\rightarrow A'(-2,1)$

$(0,1)\rightarrow B'(1,0)$

$(0,-1)\rightarrow C'(-1,0)$

Therefore the coordinates of image are A'(-2,1), B'(1,0) and C'(-1,0).

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1 year ago

Ben is eating some pretzels and an entire small package of mustard as a snack. Based on

olasank [31]

Please consider the attached graph.

We have been given that Ben is eating some pretzels and an entire small package of mustard as a snack. We are asked to find the equation that represents the relationship between the number of pretzels that Ben eats, x, and the total amount of sodium in his snack, y.

First of all, we will find the slope of the line using points (1,80) and (5,140).

$m=\frac{140-80}{5-1}$

$m=\frac{60}{4}$

$m=15$

Now we will use point-slope form of equation $y-y_1=m(x-x_1)$ , where m represents slope of line and point $(x_1,y_1)$ is on the line.

We will substitute $m=15$ and coordinates of point (1,80) in above equation.

$y-80=15(x-1)$

$y-80=15x-15$

$y-80+80=15x-15+80$

$y=15x+65$

Therefore, the equation $y=15x+65$ represents the relationship between the number of pretzels that Ben eats and the total amount of sodium in his snack.

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2 years ago

There are 20 children in the cast of a class play, and 8 of the children are boys. of the boys, 4 have a speaking part in the pl

likoan [24]

The probability that a child with a speaking part is chosen randomly would be 2:5.

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2 years ago

HELP MEEEEEEEEEE Package A contains 3 birthday cards and 2 thank-you notes and costs $9.60. Package B contains 8 birthday cards

hodyreva [135]

Answer:

Each birthday card costs $2.2 ⇒ answer c

Step-by-step explanation:

* Lets explain how to solve the problem

- Package A contains 3 birthday cards and 2 thank-you notes

- It costs $9.60

- Package B contains 8 birthday cards and 6 thank-you notes

- It costs $26.60

- x represents the cost of birthday card and y represents the cost of

thank-you note

* Lets change these information to two equations

∵ x represents the cost of each birthday cards

∵ y represents the cost of each thank-you notes

∵ Bag A contains 3 birthday cards and 2 thank-you notes

∵ Bag A costs $9.60

∴ 3x + 2y = 9.60 ⇒ (1)

∵ Bag B contains 8 birthday cards and 6 thank-you notes

∵ Bag B costs $26.60

∴ 8x + 6y = 26.60 ⇒ (2)

* Lets solve this system of equations to find x and y

- Multiply equation (1) by -3 to eliminate y

∵ -3(3x) + -3(2y) = -3(9.60)

∴ -9x - 6y = -28.8 ⇒ (3)

- Add equations (2) and (3)

∴ -x = -2.2

- Multiply both sides by -1

∴ x = 2.2

∵ x represents the cost of each birthday cards

∴ The cost of each birthday card is $2.2

* Each birthday card costs $2.2

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2 years ago

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