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anygoal [31]
3 years ago
15

Check up 1

Mathematics
1 answer:
zhenek [66]3 years ago
8 0

Answer:

a. The expression for the area of the gym is 15·x

b. The expression for the area of the cafeteria is 15·x + 45

c. The expression for the total area of the gym and the cafeteria is 30·x + 45

d. The expression for the total perimeter of the gym and the cafeteria is 36 + 4·x

Step-by-step explanation:

The parameters of the given figures are;

The width of the figure, w = 15

The breadth of the gym, b_{gym} = x

The breadth of the cafeteria, b_{cafeteria} = x + 3

The shape of the area of the gym = A rectangle

The shape of the area of the cafeteria = A rectangle

a. The expression for the area, 'A₁', of the gym is given by the area of a rectangle which is Width × Breadth

The area of the gym, A₁ = The width of the figure × The breadth of the gym

Therefore, we have; The area of the gym, A₁ = w × b_{gym}

A₁ = 15 × x

The area of the gym, A₁ = 15·x

b. The area of the cafeteria, A₂ = The width of the figure × The breadth of the cafeteria

The area of the cafeteria, A₂ = w × b_{cafeteria}

∴ A₂ = 15 × (x + 3) = 15·x + 45

The expression for the area of the cafeteria, A₂ = 15·x + 45

c. The expression for the total area of the gym and the cafeteria, 'A', is given as follows;

A = A₁ + A₂

∴ A = 15·x + 15·x + 45 = 30·x + 45

The expression for the total area of the gym and the cafeteria = 30·x + 45

d. The expression for the total perimeter of the gym and the cafeteria, 'P', is given as follows;

P = The perimeter of the rectangular area of the gym plus the area of the cafeteria

∴ P = 2 × 15 + 2 × (x + x + 3)

P = 30 + 4·x + 6

P = 36 + 4·x

The expression for the total perimeter of the gym and the cafeteria P = 36 + 4·x.

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todd Has a collection of 8cds and sally has a collection of 18 cds Todd is adding 9cds a month to his collection while sally is
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Answer:

Step-by-step explanation:

Let's create some equations first.

Say M = number of months, T = Todd and S = Sally.

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After one month (M = 1), Todd adds 9 cds.

This means can write the following equation:

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So after the first month (where M = 1), we can find out that Todd has

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For Sally, we know she adds 7 cds per month.

S = 18 + 7M

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This means we are trying to figure out what M = ? when Todd and Sally are equal.

So we want to find when T = S

Remember, earlier we wrote :

T = 8 + 9M

S = 18 + 7M

If T = S, this means:

8 + 9M = 18 + 7M

Gather the like terms and solve for M.

Subtract 8 from both sides.

9M = 10 + 7M

Subtract 7M from both sides

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Divide both sides by 2

M = 5.

So in 5 months, we are saying T = S (Todd and Sally will have the same number of cds).

Put M = 5 back into our earlier equations to find out how many cds they have after 5 months.

T = 8 + 9M

T = 8 + 9 x 5

T = 53

Therefore, after 5 months Todd and Sally will have 53 cds each :)

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3 years ago
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