Can someone please help

The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square kilometers, find the dimensions

Art [367]

Hi there!

Answer:
length = 9 kilometres
Width = 12 kilometres

Let's solve this problem step by step!
To find our answer we need to set up and solve an equation.

Let the length of the rectangle be represented by x.
The width of the rectangle can therefore be expressed by 2x - 6.

The area of a rectangle can be found by using the formula:
A = width × length

Plug in the data from the formula
A = x (2x - 6).

Simplify using rainbow technique.
$x(2x - 6) = 2 {x}^{2} - 6x$

Now we've found the simplified expression that expresses the area of the rectangle. Therefore, we can now set up and start solve the equation.

$2 {x}^{2} - 6x = 108$
Subtract 108

$2 {x}^{2} - 6x - 108 = 0$
Divide by 2.

${x}^{2} - 3x - 54$
$(x - 9)(x + 6) = 0$
Rule AB = 0, gives A is 0 or B is 0.

$x - 9 = 0 \\ x = 9 \\ \\ x + 6 = 0 \\ x = - 6$

The length of the rectangle, which was represented by x, must be 9 (since it cannot be a negative number).

Length
$x = 9$
Width
$2x - 6 = 2 \times 9- 6 = 18 - 6 = 12$

Answer:
length = 9 kilometres
Width = 12 kilometres

~ Hope this helps you!

6 0

3 years ago

You buy a movie ticket for $5.25 and popcorn for $2.98. You pay with a 10-dollar bill. How much change will you get back?

slava [35]

Answer:

$1.77

Brainliest please?

Step-by-step explanation:

5.25+2.98=8.23

10-8.23=1.77

4 0

2 years ago

6. Commerce Bank hired Pete Drexel as its new branch office

hammer [34]

Question

How much did the bank spend on him that year?

Answer:

$60101.12

Step-by-step explanation:

Apart from salary of 59500.00 the company incurred additional charges which we add to give 421.27+85.25+94.60=$601.12

Total amount will be 59500.00+601.12=$60101.12

5 0

3 years ago

What number is 0.25% of 46?

cestrela7 [59]

Answer:

0.115

Step-by-step explanation:

First, multiply 0.25 x 46 to get 11.5

Then, multiply by 11.5 x 100 and get your answer.

You can find the percent of any number my doing this:

Multiplying the percent x the number then dividing by 100

hope this helps :)

3 0

3 years ago

20 points help help help

mrs_skeptik [129]

The perimeter of the shape is 94 cm and the area is 462 sq cm.

Step-by-step explanation:

Given,

The radius (r) = 14 cm

To find the area and perimeter of the given shape.

The given shape is $\frac{3}{4}$ of the full circle.

Formula

The perimeter of the circle = 2πr

The perimeter of the given shape = $\frac{3}{4}$ (2πr)+r+r = $\frac{3}{4}$ (2πr)+2r

The area of the circle = πr²

Now,

The perimeter of the given shape = $\frac{3}{4}$ (2× $\frac{22}{7}$ ×14)+2×14 = 94 cm

The area of the given shape = $\frac{3}{4}$ (πr²)

= $\frac{3}{4}$ × $\frac{22}{7}$ ×14² = 462 sq cm

7 0

3 years ago

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Can someone please help ​

Can someone please help