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natulia [17]
3 years ago
5

What is the perimeter in square units of the rectangle shown on the coordinate grid?

Mathematics
2 answers:
Likurg_2 [28]3 years ago
5 0

Answer:

A

Step-by-step explanation:

The opposite sides of a rectangle are congruent.

Calculate the lengths of 2 of the sides using the distance formula and multiply by 2

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 2, 10) and (x₂, y₂ ) = (2, 7)

d = \sqrt{(2+2)^2+(7-10)^2}

   = \sqrt{4^2+(-3)^2}

   = \sqrt{16+9} = \sqrt{25} = 5

Repeat

with (x₁, y₁ ) = (- 8, 2) and (x₂, y₂ ) = (- 2, 10)

d = \sqrt{(-2+8)^2+(10-2)^2}

  = \sqrt{6^2+8^2}

   = \sqrt{36+64} = \sqrt{100} = 10

Hence

Perimeter = (2 × 5) + (2 × 10) = 10 + 20 = 30 units → A

Rashid [163]3 years ago
4 0

In order to find the Perimeter of the Rectangle, First we need to find the Length and Width of the Rectangle.

Distance between two points (x₁ , y₁) and (x₂ , y₂) is given by :

\bigstar\;\; \mathsf{Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}

There are two lengths in a rectangle. Let us find any one length of the rectangle.

I'm considering the length with co-ordinates (-8 , 2) and (-2 , 10)

Here :  x₁ = -8 and x₂ = -2 and y₁ = 2 and y₂ = 10

Substituting the values in the distance formula, We get :

\mathsf{\implies Length = \sqrt{[-2 - (-8)]^2 + [10 - 2]^2}}

\mathsf{\implies Length = \sqrt{[-2 + 8]^2 + [8]^2}}

\mathsf{\implies Length = \sqrt{[6]^2 + [8]^2}}

\mathsf{\implies Length = \sqrt{36 + 64}}

\mathsf{\implies Length = \sqrt{100}}

\mathsf{\implies Length = 10}

There are two widths in a rectangle. Let us find any one width of the rectangle.

I'm considering the width with co-ordinates (-2 , 10) and (2 , 7)

Here :  x₁ = -2 and x₂ = 2 and y₁ = 10 and y₂ = 7

Substituting the values in the distance formula, We get :

\mathsf{\implies Width = \sqrt{[2 - (-2)]^2 + [7 - 10]^2}}

\mathsf{\implies Width = \sqrt{[2 + 2]^2 + [-3]^2}}

\mathsf{\implies Width = \sqrt{[4]^2 + [-3]^2}}

\mathsf{\implies Width = \sqrt{16 + 9}}

\mathsf{\implies Width = \sqrt{25}}

\mathsf{\implies Width = 5}

Perimeter of a Rectangle is given by : 2[Length + Width]

:\implies  Perimeter of the given rectangle = 2[10 + 5]

:\implies  Perimeter of the given rectangle = 2[15]

:\implies  Perimeter of the given rectangle = 30

<u>Answer</u> : Perimeter of the given rectangle is 30 square units

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A roller coaster can accommodate 18 riders in 8 minutes. Complete the table with equivalent ratios.
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Answer:

36 riders in 16 minutes, 54 riders in 24 minutes, and 72 riders in 32 minutes.

Step-by-step explanation:

The roller coaster can accommodate 9 riders every 4 minutes. 36 riders in 16 minutes, 54 riders in 24 minutes, and 72 riders in 32 minutes all follow the common ratio.

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3 years ago
A major cab company in Chicago has computed its mean fare from O'Hare Airport to the Drake Hotel to be $28.75 , with a standard
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Answer:

Following are the solution to the given choices:

Step-by-step explanation:

Using chebyshev's theorem :

\to P(|(x-\mu)|\leq k \sigma)\geq 1- \frac{1}{k^2}\\\\here \\ \to \mu=28.75\\\\ \to \sigma=4.44

In point a)  

\to |(x-\mu)|= |20.17-28.75|=8.58 and \sigma=4.44 \\\\so, \\k= \frac{ |(x-\mu)| }{\sigma}

  = \frac{8.58}{4.44} \\\\ =1.9 \\\\ =2

value= (1- \frac{1}{k^2}) \times 100 \% =75\%

In point b)

\to (1- \frac{1}{k^2}) \times 100 \% =84\% \\\\\to (1- \frac{1}{k^2})=0.84 \\\\\to \frac{1}{k^2} =0.16 \\\\\to \frac{1}{k}=0.4\\\\ \to k=2.5 \\\\\to |(x-\mu)| \leq k \sigma  \\\\= |(x-\mu)|\leq 2.5 \times 4.44  \\\\  = |(x-\mu)|\leq 1.11 \\\\ =  (28.75\pm 11.1) \\\\\to \text{fares lies between}(17.65,39.85)

In point c)

\to 99.7 \% \\ lie \ between=28.75 \pm z(.03)\times \sigma \\\\ =28.75\pm 2.97 \times 4.44\\\\=(28.75\pm 13.1)\\\\=(15.65,41.85)\\

In point d)

using standard normal variate

x=20.17\\\\  z=-2 \\\\x=37.13\\\\ z=2\\\\\to P(20.17

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Answer:

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Step-by-step explanation:

For finding the price we pay during a sale, we focus on the percent we pay. If 22% off is the sale, then we spend 78% or 100-22-78. We use this percent byb  multiplying the price with a decimal. We convert percents into decimals by dividing the percent number by 100. For example, 78% divided by 100 becomes 0.78.

8. Percent off is 22%. We pay 78%=0.78.

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9. Percent off is 33%. We pay 67%=0.67.

89(0.67)=$59.63

10. Percent off is 44%. We pay 56%=0.56.

23.99(0.56)=$13.43

11. Percent off is 75%. We pay 25%=0.25.

279.99(0.25)=$70

12. See explanation above.

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3 years ago
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