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bekas [8.4K]
3 years ago
11

Find the correct plugged in formula for each figure.

Mathematics
1 answer:
Mars2501 [29]3 years ago
8 0

Answer:

Area = 40 ( 84)+ 2 *(294)

Step-by-step explanation:

There is only one figure in the attached image and the solution (surface area) is as follows:

The shape can be sub-divided into:

1. Rectangle

Dimension: 40 by 35

2. Rectangle

Dimension: 40 by 28

3. Rectangle

Dimension: 21 by 40

4. 2 triangles

Base: 21 and Height: 28

Calculate area of each and add them up to get the surface area of the figure.

1. Rectangle

Dimension: 40 by 35

A_1 = 40 * 35

2. Rectangle

Dimension: 40 by 28

A_2 = 40 * 28

3. Rectangle

Dimension: 21 by 40

A_3 = 40 * 21

4. 2 triangles

Base: 21 and Height: 28

A_4 = 2 * \frac{1}{2} * 21 * 28

So, the area is:

Area = A_1 +...+A_4

Area = 40 * 35 + 40 * 28 +40 * 21 + 2 * \frac{1}{2} * 21 * 28

Factor out 40

Area = 40 ( 35 +  28 + 21 )+ 2 * \frac{1}{2} * 21 * 28

Area = 40 ( 84)+ 2 * \frac{1}{2} * 21 * 28

Area = 40 ( 84)+ 2 *(294)

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The formula for the volume of pyramid is,

V=\frac{Bh}{3}

Here, B is base area and height of pyramid.

The volume expression for group 4 is,

V=\frac{1}{3}\cdot(\frac{8\cdot4}{2})\cdot9

Here, expression,

\frac{8\cdot4}{2}

represents the base area and 9 represent the height of pyramid.

So height of the pyramid created by group 4 is 9.

Answer: 9

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1 year ago
A collection of 20 coins made up of only nickels, dimes, and quarters has a total value of $3.35. If the dimes were nickels, the
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Answer:  The required number of quarters in the collection is 11.

Step-by-step explanation:  Given that a collection of 20 coins made up of only nickels, dimes and quarters has a total value of $3.35.

If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of $2.75.

We are to find the number of quarters in the collection.

Let x, y and z represents the number of nickels, dimes and quarters respectively in the collection.

We will be using the following values of nickels, dimes and quarters in form of dollar :

1 nickel = $ 0.05,   1 dime = $ 0.10   and    1 quarter = $0.25.

Then, according to the given information, we have

x+y+z=20\\\\\Rightarrow x=20-y-z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\0.05x+0.10y+0.25z=3.35\\\\\Rightarrow 5x+10y+25z=335\\\\\Rightarrow x+2y+5z=67~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\0.05y+0.25x+0.10z=2.75\\\\\Rightarrow 5y+25x+10z=275\\\\\Rightarrow y+2z+5x=55~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)

Substituting the value of x from equation (i) in equations (ii) and (iii), we have

(20-y-z)+2y+5z=67\\\\\Rightarrow y+4z=47\\\\\Rightarrow y=47-4z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)

and

y+2z+5(20-y-z)=55\\\\\Rightarrow -4y-3z=-45\\\\\Rightarrow y=\dfrac{45-3z}{4}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(v)

Comparing the values of y from equations (iv) and (v), we get

47-4z=\dfrac{45-3z}{4}\\\\\Rightarrow 188-16z=45-3z\\\\\Rightarrow 16z-3z=188-45\\\\\Rightarrow 13z=143\\\\\Rightarrow z=\dfrac{143}{13}\\\\\Rightarrow z=11.

Thus, the required number of quarters in the collection is 11.

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2 years ago
Exactly 512 tickets were sold for the talent show at Cypress Middle School. The number of student tickets sold was three times t
ioda

Answer:

384 student tickets and 128 adult tickets

Step-by-step explanation:

S for student and A for adult

s+a=512

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Step-by-step explanation:

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Solve the equation and you get 4. Simple!

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