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Vlad [161]
3 years ago
6

the length of a rectangle is 3cm more than the width. find the length and the width if the perimeter of the rectangle is 98cm.

Mathematics
1 answer:
laila [671]3 years ago
7 0

The perimeter of a rectangle is <u>length + length + width + width</u>.

We know that the length of a rectangle is 3cm more than its width, which gives us the equation:  (l for length and w for width)

l = 3 + w

We also know that the perimeter of the rectangle is 98cm, which gives us the equation:

98 = 2l + 2w         (equation for perimeter of a rectangle as noted above)

We can divide both sides of this equation by 2 to get:

49 = l + w

Now we'll stick l = 3 + w into the above equation, which gives us:

49 = 3 + w + w

which simplifies to 49 = 3 + 2w.

Now we'll subtract 3 from both sides:

49 - 3 = 46

3 + 2w - 3 = 2w

which gives us 46 = 2w.

Dividing both sides by 2 gives us 23 = w.

Substituting w = 23 into the equation l = 3 + w gives us:

l = 3 + 23

l = 26cm.

Let's check our answer.  26cm is 3cm more than 23cm.  26cm + 26cm + 23cm + 23cm gives us 98cm.  The length is 26cm and the width is 23cm.


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18.66 quarts of paint is needed to paint the swimming pool with two coats of paint

<em><u>Solution:</u></em>

Given that,

<em><u>A swimming pool is in the shape of a rectangular prism</u></em>

Length = 20 feet

Width = 10 feet

Height = 5 feet

<em><u>Find the surface area of prism</u></em>

A=2(wl+hl+hw)

Where, "l" is the length and "w" is the width and "h" is the height

A = 2(10 \times 20 + 5 \times 20 + 5 \times 10)\\\\A = 2(200+100+50)\\\\A = 2 \times 350\\\\A = 700

Thus surface area area of prism is 700 square feet

Given that,

One quart of water-resistant paint covers 75 square feet

Therefore,

1 quart paint = 75 square feet

x quart = 700 square feet

This forms a proportion

1 \times 700 = 75 \times x\\\\x = \frac{700}{75}\\\\x = 9.33

Thus 9.33 quarts of paint is needed to cover 700 square feet

How many quarts should you buy to paint the swimming pool with two coats of paint

For two coats of paint we need = 9.33 + 9.33 = 18.66 quarts of paint

4 0
3 years ago
Given the first term and the common difference find the first five terms and the explicit formula
Zielflug [23.3K]

Answer:

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____________________________________

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Maureen earned some money doing odd jobs last summer and put it in a savings account that earns 9% interest compounded quarterly
ivolga24 [154]

Answer:

Maureen earned $123.19 doing odd jobs

Step-by-step explanation:

The compound interest formula is given by:

A(t) = P(1 + \frac{r}{n})^{nt}

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

In this question:

Compounded quarterly means that n = 4

10 years, so t = 10

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There is $300.00 in the account, which means that A = 300

How much did Maureen earn doing odd jobs?

This is P.

A(t) = P(1 + \frac{r}{n})^{nt}

300 = P(1 + \frac{0.09}{4})^{4*10}

(1.0225)^{40}P = 300

P = \frac{300}{(1.0225)^{40}}

P = 123.19

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