A designer is creating a rug for an oddly-shaped room. His design for the rug is shown below. If each blue square represents 1 square foot, how much cloth will the tailor need for the rug?

Given:

One diagonal of the kite is three times as long as the other diagonal.

The area of the kite is 48 square meters.

To find:

The length of each diagonal.

Solution:

We know that, the area of the kite is:

[tex]A=\dfrac{d_1d_2}{2}[/tex]

Where, [tex]d_1,d_2[/tex] are two diagonals of a kite.

It is given that, one diagonal of the kite is three times as long as the other diagonal.

Let [tex]d_1=3d_2[/tex]. Then the area of the kite is:

[tex]A=\dfrac{3d_2d_2}{2}[/tex]

[tex]A=\dfrac{3d_2^2}{2}[/tex]

The area of the kite is 48 square meters.

[tex]\dfrac{3d_2^2}{2}=48[/tex]

[tex]3d_2^2=2(48)[/tex]

[tex]d_2^2=\dfrac{96}{3}[/tex]

[tex]d_2^2=32[/tex]

Taking square root on both sides, we get

[tex]d_2=\sqrt{32}[/tex]       [It is only positive because side length cannot be negative]

[tex]d_2=4\sqrt{2}[/tex]

Now,

[tex]d_1=3d_2[/tex]

[tex]d_1=3(4\sqrt{2})[/tex]

[tex]d_1=12\sqrt{2}[/tex]

Therefore, the diagonals of the kite are [tex]4\sqrt{2}[/tex] units and [tex]12\sqrt{2}[/tex] units.

Answer:

0(2/3; 0)

Step-by-step explanation:

Answer:

x=-3/2 x=2

Step-by-step explanation:

2x(1-x)=x-6

2x-2x^2=x-6

subtract x from both sides

add 6 to both sides

x-2x^2+6=0

reorganize

-2x^2+x+6=0

factor

2x+3=0

x-2=0

solve both

2x+3=0

2x=-3

x=-3/2

now the other one

x-2=0

x=2

Sorry, I don't speak spanish.

Answer:

where is the question?

Step-by-step explanation:

I don't see anything If he then " consider this right triangle determine whether each equation is correct select yes or no for each equation"

Answer:

Please see photos for simplified result

Step-by-step explanation:

Answer:

d is the ans

Step-by-step explanation:

D is the answer

Answer:

Diameter of the pipe ≈ 6.77 ft

Step-by-step explanation:

Volume of a cylinder = πr²h

Here, r = Radius of the cylindrical pipe

h = Length of the pipe

Volume of the pipe = 900 ft³

Length of the pipe = 25 ft

By substituting the given values in the formula,

900 = π(r)²(25)

r² = [tex]\frac{900}{25\pi}[/tex]

r = √11.459

r = 3.385

Diameter = 2(radius)

                = 2(3.385)

                = 6.77 ft

The diameter of the cylinderi is 6.77ft

the formula for calculating thevolume of a cylinder is given as

V = pi d²/4 × h

Given the following

V = 900ft³

h = 25ft

Substitute the given parameters

900 = 3.14 × d²/4 × 25

900 = 19.625d²

d² = 45.859

d = 6.77ft

Hence the diameter of the cylinderi is 6.77ft

learn more on cylinder here: https://brainly.com/question/23935577

there are 6+9+10=25 equal parts, so Ben has 9/25 of the total.

Answer:

Hey!

The X Value is 3, while the Y value is 6. In other words, it looks like this:

3, 6

Step-by-step explanation:

Hey!

The X Value is 3, while the Y value is 6. In other words, it looks like this:

3, 6

Answer:

(0.5,1.5)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hard to tell how the question should read.

40/100 = 40%

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Proportion means writing in fraction form as numerator and denominator.

40/100 = 40%

The proportion of 40 and 100 is 40%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have.

40 and 100.

Proportion means writing in fraction form as numerator and denominator.

So,

If we write 40/100 we get 40%.

This means 40 out of 100.

Thus,

40/100 = 40%

The proportion of 40 and 100 is 40%.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ5

Answer:

6 cm

Step-by-step explanation:

Volume of a Prism = base area x height =

Base area = length x width =  12 x 2 = 24 cm^2

Volume = 24 x 3 = 72 cm^3

Volume of a pyramid = 1/3( l x w x h)

72 = 1/3( 6x6 x h)

Multiply both sides of the equation by 3

216 = 36 x h

divide both sides by 36

h = 6

Answer:

1. 60 2. 120

Step-by-step explanation:

plz give brailiest

Answer:

1. 60

2. 120

Step-by-step explanation:

the opposite angle is 60

180 - 60 = 120

Answer:

p-o

u-t

e-l

s-d

r-w

b-z

a-n

Step-by-step explanation:

Answer:

The new surface area would be 9 times larger than the original surface area.

Step-by-step explanation:

Here we do not know what was the original shape, but we will see that it does not matter.

Let's start with a square of side length L.

The original area of this square will be:

A = L^2

Now if each dimension is tripled, then all the sides of the square now will be equal to 3*L

Then the new area of the square is:

A' = (3*L)^2 = (3*L)*(3*L) = 9*L^2 = 9*A

So the new surface area is 9 times the original one.

Now, if the figure was a circle instead of a square?

For a circle of radius R, the area is:

A = pi*R^2

where pi = 3.14

Now if the dimensions of the circle are tripled, the new radius will be 3*R

Then the new area of the circle is:

A' = pi*(3*R)^2 = pi*9*R^2 = 9*(pi*R^2) = 9*A

Again, the new area is 9 times the original one.

If the figure is a triangle?

We know that for a triangle of base B and height H, the area is:

A = B*H/2

If we triple each measure, we will have a base 3*B and a height 3*H

Then the new area is:

A' = (3*B)*(3*H)/2 = (3*3)*(B*H/2) = 9*(B*H/2) = 9*A

Again, the new area is 9 times the original area.

So we can conclude that for any shape, the new area will be 9 times the original area.

Answer:

x = 15

Step-by-step explanation:

We know that 4x° + 8x° make a straight angle of 180°.

4x° + 8x° = 180°

12x° = 180°

12x = 180

x = 180/12 = 15

Answer:

x=15

Step-by-step explanation:

I gotcha bro

The line C is straight and straight lines are 180°

so 180° = 4x + 8x = 12x ----> 180 = 12x ---> then divide both sides by 12

180/12 = 15   and 12x/12 = x

so 15 = x or x = 15

Answer:

1080 minutes

Step-by-step explanation:

12x45: garys team

45x2=90 : hector's team

12x90=1080

Answer:

98ft.

Step-by-step explanation:

Question is asking for the total square feet of laminate wood to cover the entire retail store. Add all the sides together to get your answer.

Step-by-step Answer:

C and D are both correct as fractions. Numbers are NOT irrational because they are a fraction. And concluding decimals are both rational numbers. By using a known formula you can convert reaptedly decimals to a fraction.  

80

Step-by-step explanation:

you take the square root of 82 squared minus 18 squared

Answer:

Thomas age is 7

Step-by-step explanation:

X + 2x =21

3x=21

x=7

Answer:

Respuesta. entonces como respuesta deben colocarse 14 filas por 14 columnas de baldosas para que quede un cuadrado. SALUDOS!

Number of 1/2-inch cubes length-wise = 8 1/2 ÷ 1/2 = 17

Number of 1/2-inch cubes width-wise = 5 1/2 ÷ 1/2 = 11

Number of 1/2-inch cubes height-wise = 2 1/2 ÷ 1/2 = 5

Number of 1/2-inch cubes = 17 x 11 x 5 = 935

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Answer: 935 1/2-inch cubes are needed.

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