All categories

3 years ago

The length of one side of a square is (x + 2 1/4). If the perimeter is 14 units, what is the area?

Mathematics

1 answer:

Stels [109]3 years ago

7 0

The perimeter is the total of adding all of the side lengths together.

A square has 4 equal side lengths.

So the perimeter of a square is:

P = s + s + s + s or P = 4s

[P = perimeter s = side lengths of the square]

Since you know the side length of the square is (x + 2 1/4), you can replace s with (x + 2 1/4)

P = 4s

P = 4(x + 2 1/4) Multiply 4 into (x + 2 1/4)

P = 4x + 8 4/4

P = 4x + 9

Since you know the perimeter, you can plug it in.(you could have also plugged it in in the beginning)

P = 4x + 9

14 = 4x + 9 Subtract 9 on both sides

5 = 4x Divide 4 on both sides

5/4 = x

Now that you know x, find the side length of the square.

(x + 2 1/4)

(5/4 + 2 1/4)

2 6/4 = 3 2/4 = 3 1/2 units or 3.5 units

To find the area of a square, you multiply 2 of the sides together:

A = s · s

A = 3.5 · 3.5

A = 12.25 units²

You might be interested in

A container manufacturer plans to make rectangular boxes whose bottom and top measure x by 4x. The container must contain 12ft^3

zheka24 [161]

The height of the container should be equal to 2.57 cm, so as to minimize cost.

<h3>How to calculate the height?</h3>

First of all, we would determine the volume of the rectangular container by using this formula:

Volume = l × w × h

Where:

l represents the length.

w represents the width.

h represents the height.

Substituting the given parameters into the formula, we have;

Volume = x × 4x × h

Volume = 4x²h

At a volume of 12 ft³, we have:

12 = 4x²h

h = 12/4x²

h = 3/x²

For the total area of top and bottom, we have:

Area = (x × 4x) + (x × 4x)

Area = 4x² + 4x²

Area = 8x² sq. units.

Thus, the cost of top and bottom is given by:

Cost = 8x² × 1.50

Cost = $12x²

For the total area of all four sides, we have:

Area = (x × h) + (x × h) + (4x × h) + (4x × h)

Area = xh + xh + 4xh + 4xh

Area = 10xh sq. units.

Thus, the cost of all four sides is given by:

Cost = 10xh × 4.50

Cost = $45xh.

Also, the cost function would be given by:

C(x) = 12x² + 10xh

C(x) = 12x² + 10x(3/x²)

C(x) = 12x² + 30/x

Taking the first derivative, we have:

dC/dx = 24x - 30/x²

24x = 30/x²

24x³ = 30

x³ = 30/24

x = 1.08

Therefore, the height will be:

h = 3/x²

h = 3/1.08²

h = 3/1.1664

Height, h = 2.57 cm.

Read more on minimum height here: brainly.com/question/27308167

#SPJ1

5 0

2 years ago

Use pencil and paper to create a table of values for the equation, x - 2y = 6. Rearrange the equation into the y = mx + b form.

Lunna [17]

Answer:

y = 1/2x -3

x=-2 ⇒ y = -4

x=-1 ⇒ y = -3.5

x=0 ⇒ y = -3

x=1 ⇒ y = -2.5

x=2 ⇒ y = -2

Step-by-step explanation:

Hi, to answer this question we have to isolate y:

x - 2y = 6

-2y =6-x

y = (6-x)/-2

y = -3+1/2x

y = 1/2x -3

Now, we have to create a table with the next values (see attachment)

x=-2 ⇒ y = 1/2x -3 = 1/2(-2)-3= -4

x=-1 ⇒ y = 1/2x -3 = 1/2(-1)-3= -3.5

x=0 ⇒ y = 1/2x -3 = 1/2(0)-3= -3

x=1 ⇒ y = 1/2x -3 = 1/2(1)-3= -2.5

x=2 ⇒ y = 1/2x -3 = 1/2(2)-3= -2

Feel free to ask for more if needed or if you did not understand something.

7 0

3 years ago

part of the river she observed fell 1.68 millimeters per year for 1.5 years. Use the distributive property to calculate the exac

Alecsey [184]

1.68 mm per year for 1.5 years could be rewritten as
(2.00-0.32) mm per year for 1.5 yrs.

Multiply: (1.5 yrs)(2.00-0.32)(mm/yr) = 3 mm + 0.48 mm = 3.48 mm

This approach makes use of the distributive property of multiplication.

8 0

3 years ago

A? ________ is an arrangement of r objects chosen from n distinct objects without repetition and without regard to order

aliya0001 [1]

If we do not care about order, then a combination is an arrangement of r objects chosen from n distinct objects. It can often be seen written as:

$^{n}C_r$ or $\left(\begin{array}{cc}n\\r\end{array}\right)$

Its factorial form is:

$^{n}C_r = \frac{n!}{r!(n - r)!}$

3 0

3 years ago

How can you tell when a pattern shows counting on by tens?

velikii [3]

Answer:
The difference between successive terms is 10

Explanation:
To know the factor by which a certain pattern is increasing/decreasing, you need to subtract its successive terms.

If the subtraction gives you 10, this means that the pattern is increasing by 10

Examples:
10, 20, 30, 40, 50, .....
20 - 10 = 10
30 - 20 = 10
40 - 30 = 10
50 - 40 = 10
The difference between each two successive terms is 10. This means that each time we add 10 to the number we have in order to get the next one.
Therefore, this pattern is increasing by 10

37, 47, 57 , .....
47 - 37 = 10
57 - 47 = 10
The difference between each two successive terms is 10. This means that each time we add 10 to the number we have in order to get the next one.
Therefore, the pattern is increasing by 10

Hope this helps :)

7 0

3 years ago