A rectangle has a length that is 5 inches greater, №15229648, 28.04.2023 08:39

Mathematics

Arectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. the equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle. (x + 5)x = 104 x2 + 5x – 104 = 0 determine the solutions of the equation. what solution makes sense for the situation? x = what are the dimensions of the rectangle? width = inches length = inches

Step-by-step answer

P Answered by PhD

81

Keywords:

Rectangle, length, width, area, inches, equation, variable

For this case, we have a ractangle of area 104 square inches, they tell us that its length is 5 inches greater than the width. In addition, we have the following equation (x + 5) x = 104 where the variable "x" represents the width of the rectangle.

By definition, the area of a rectangle is given by:

A = l * x

Where:

l: It's the lenght x: It is the width

A = 104 square inches

For the width we have:

$(x + 5) x = 104\\x ^ 2 + 5x = 104\\x ^ 2 + 5x-104 = 0$

We find the solutions of the equation by factoring, that is, we look for two numbers that when multiplied give as result -104 and when summed give as result +5. So, those numbers are +13 and -8.

$13 * -8 = -104\\13-8 = + 5$

So, we have:

(x + 13) (x-8) = 0

The roots are:

$x_ {1} = - 13\\x_ {2} = 8$

The solution that makes sense for the width of the rectangle is: x_ {2} = 8

Thus, the width of the rectangle is x = 8 inches

If the thickness is 5 inches greater than the width, then:

$l = 5 + 8\\l = 13\ inches.$

Verifying the area, we have:

A = 13 * 8 = 104 square inches

ANswer:

$width = 8\ inches\\length = 13\ inches$

Mathematics

Arectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. the equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle. (x + 5)x = 104 x2 + 5x – 104 = 0 determine the solutions of the equation. what solution makes sense for the situation? x = what are the dimensions of the rectangle? width = inches length = inches

Step-by-step answer

P Answered by PhD

81

Keywords:

Rectangle, length, width, area, inches, equation, variable

For this case, we have a ractangle of area 104 square inches, they tell us that its length is 5 inches greater than the width. In addition, we have the following equation (x + 5) x = 104 where the variable "x" represents the width of the rectangle.

By definition, the area of a rectangle is given by:

A = l * x

Where:

l: It's the lenght x: It is the width

A = 104 square inches

For the width we have:

$(x + 5) x = 104\\x ^ 2 + 5x = 104\\x ^ 2 + 5x-104 = 0$

We find the solutions of the equation by factoring, that is, we look for two numbers that when multiplied give as result -104 and when summed give as result +5. So, those numbers are +13 and -8.

$13 * -8 = -104\\13-8 = + 5$

So, we have:

(x + 13) (x-8) = 0

The roots are:

$x_ {1} = - 13\\x_ {2} = 8$

The solution that makes sense for the width of the rectangle is: x_ {2} = 8

Thus, the width of the rectangle is x = 8 inches

If the thickness is 5 inches greater than the width, then:

$l = 5 + 8\\l = 13\ inches.$

Verifying the area, we have:

A = 13 * 8 = 104 square inches

ANswer:

$width = 8\ inches\\length = 13\ inches$

Mathematics

Arectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. the equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle. (x + 5)x = 104 x2 + 5x – 104 = 0 determine the solutions of the equation. what solution makes sense for the situation? x = what are the dimensions of the rectangle? width = inches length = inches

Step-by-step answer

P Answered by PhD

19

width = 8

length = 13

Step-by-step explanation:

All that is left to do is factor the results that you have

x^2 + 5x - 104 = 0

You need two numbers that are fairly close together (ignore the sign differ by 5) and multiply to 104.

The two numbers are 8 and 13

More formally stated, the quadratic can be factored to

(x + 13)(x - 8) = 0

x - 8 =0

x - 8 + 8 = 8 + 0

x = 8

x + 13 = 0 has no meaning.

That means that the width ( a positive number ) = 8

The length is 5 more = 13

Mathematics

Arectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. the equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle. (x + 5)x = 104 x2 + 5x – 104 = 0 determine the solutions of the equation. what solution makes sense for the situation? x = what are the dimensions of the rectangle? width =inches length =inches

Step-by-step answer

P Answered by Master

207

x=8, the width is 8 inches, and the length is 13 inches. Hope you guys are having a fabulous day:)

Mathematics

Determine the solutions of the equation. What solution makes sense for the situation? A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x +5)x = 104 represents the situation, where x represents the width of the rectangle. (x + 5)x = 104 x2 + 5x - 104 = 0 What are the dimensions of the rectangle? width= inches length = inches 5) Intro

Step-by-step answer

P Answered by Master

62

x=8

Width=8 inches

Length=13 inches

Mathematics

A rectangle has a length that is 5 inches greater than its width the equation is (x+5)x=104 x is the width what is the width and length of the rectangle

Step-by-step answer

P Answered by PhD

2

Width 8 inches

Length 13 inches.

Step-by-step explanation:

We have been given that a rectangle has a length that is 5 inches greater than its width and its area is 104 square inches. The equation (x+5)x=104 represents the situation, where x represents the width of the rectangle.

Let us solve for x to find the width of the rectangle.

Using distributive property, we will get:

x^2+5x=104

x^2+5x-104=104-104

x^2+5x-104=0

Now we will split the middle term as:

x^2+13x-8x-104=0

x(x+13)-8(x+13)=0

(x+13)(x-8)=0

Using zero product property, we will get:

x+13=0, x-8=0

x=-13, x=8

Since width cannot be negative, therefore, the width of the rectangle is 8 inches.

Length of the rectangle would be $x+5\Rightarrow 8+5=13$

Therefore, the length of the rectangle is 13 inches.

Mathematics

A rectangle has a length that is 5 inches greater than its width the equation is (x+5)x=104 x is the width what is the width and length of the rectangle

Step-by-step answer

P Answered by PhD

2

Width 8 inches

Length 13 inches.

Step-by-step explanation:

We have been given that a rectangle has a length that is 5 inches greater than its width and its area is 104 square inches. The equation (x+5)x=104 represents the situation, where x represents the width of the rectangle.

Let us solve for x to find the width of the rectangle.

Using distributive property, we will get:

x^2+5x=104

x^2+5x-104=104-104

x^2+5x-104=0

Now we will split the middle term as:

x^2+13x-8x-104=0

x(x+13)-8(x+13)=0

(x+13)(x-8)=0

Using zero product property, we will get:

x+13=0, x-8=0

x=-13, x=8

Since width cannot be negative, therefore, the width of the rectangle is 8 inches.

Length of the rectangle would be $x+5\Rightarrow 8+5=13$

Therefore, the length of the rectangle is 13 inches.

Mathematics

Arectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. the equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle. the first step in solving by factoring is to write the equation in standard form, setting one side equal to zero. what is the equation for the situation, written in standard form? x2 – 99 = 0 x2 – 99x = 0 x2 + 5x + 104 = 0 x2 + 5x – 104 = 0

Step-by-step answer

P Answered by Master

18

x^2 + 5x - 104 = 0

Step-by-step explanation:

(x + 5)x = 104 Original equation

x^2 + 5x = 104 Distributive property

x^2 + 5x - 104 = 0 Subtract, make the right side equal to 0

Mathematics

Arectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. the equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle. (x + 5)x = 104 x2 + 5x – 104 = 0 determine the solutions of the equation. what solution makes sense for the situation? x =

Step-by-step answer

P Answered by PhD

6

The answer is 8.

Step-by-step explanation:

We need to use the quadratic formula, that is ax2+bx+c=0

Where

$x=\frac{-b +/- \sqrt{b^{2}-4*a*c } }{2a}$

For the given equation x2+5x-104=0 we have

a=1, b=5, c= -104

If you solve that, we will have x=-13. x=8, two answers,

The first one, by being negative does not have physical sense (there are no negatives quantities when you measure the length of something)

So we use the anwser x=8

Mathematics

Arectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. the equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle. the first step in solving by factoring is to write the equation in standard form, setting one side equal to zero. what is the equation for the situation, written in standard form? choose one of the best answers. a. x² – 99 = 0 b. x² – 99x = 0 c. x² + 5x + 104 = 0 d. x² + 5x – 104 = 0 explain your answer? if your answers is wrong, it s going mark your

Step-by-step answer

P Answered by PhD

1

D

Step-by-step explanation:

(x + 5)x = 104

Distribute:

x² + 5x = 104

Subtract 104 from both sides:

x² + 5x − 104 = 0

A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches.

Step-by-step answer

Faq

Try asking the Studen AI a question.