module 7 lesson 14 quiz

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:

1080 minutes

Step-by-step explanation:

12x45: garys team

45x2=90 : hector's team

12x90=1080

80

Step-by-step explanation:

you take the square root of 82 squared minus 18 squared

Answer: The answer is 16

Step-by-step explanation: You divide the whole line segment by two to get only the half of the line segement.

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

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.

9514 1404 393

Answer:

  107/18

Step-by-step explanation:

Your calculator and/or knowledge of trig function values can help you evaluate this.

  = 4/3(1/3) +3/4 -3(3/4) +3(3) -2(1)

  = 4/9 +3/4 -9/4 +9 -2

  = 107/18

___

tan(30°) = 1/√3

tan(45°) = 1

tan(60°) = √3

sin(60°) = cos(30°) = √3/2

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.  

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:

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.

Answer:

Thomas age is 7

Step-by-step explanation:

X + 2x =21

3x=21

x=7

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

There was a little error in  t= -6 when "t"=2, I think you meant when   "r"= 2 when t =-6 so i corrected it before solving.

Answer:r= 7/3

Step-by-step explanation:

Step 1

r varies inversely as t  ,written mathematically can be expressed as

r ∝ 1/t

Introducing the constant of proportionality. K we have

r ∝ 1/t

r=Kt

Step 2

Now when r= 2 when t =-6, we have that

r=Kt

2 = K -6,

k=2/ -6= -1/3

Step 3

Find r when t  =-7

Using our equation,

r=Kt

r= -1/3 x-7

r= 7/3

Answer:

475272 will be your answer.

Step-by-step explanation:

just multiply.

Answer:

475272

Step-by-step explanation:

Brainliest?

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:

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

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:

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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Answer:

Please see photos for simplified result

Step-by-step explanation:

Answer:

0(2/3; 0)

Step-by-step explanation:

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 and Step-by-step explanation:

The answer would be D. 82%.

All we need to do is add together the amount that can swim.

We do this because all of the numbers added together equals 1, so the parts that are split off represent the percentages (in decimal form) of the total amount of people.

0.34 + 0.48 = 0.82.

Multiply by 100 and we get 82%.

#teamtrees #PAW (Plant And Water)

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