Question 5 the area of a rectangle is 35 ft2 , and the length of the rectangle is 3 ft more than twice the width. find the dimensions of the rectangle.

Let's assume w represent the width of the rectangle.

Given that, the length of the rectangle is 3 ft more than twice the width.

So, we can write:

Length = 3 + 2w

And area = 35

So, length * width = 35

(3+2w) * w = 35

3w +2w²=35 By distribution property.

3w + 2w²-35 = 0 Subtract 35 from each sides.

2w² + 3w - 35 = 0

Next step is to solve the above equation by factoring to get the vaue of w.

To factor the above trinomial, multiply the constant -35 with the leading coefficient 2.

So, -35*2 = -70.

Next step is to breakdown -70 into two multiples so that their addition will result the coefficient of w=3.

So, -70 = -7 * 10

And addition of -7 and 10 will give 3.

So, next step is to replace 3w with -7w + 10w. Therefore,

2w² - 7w + 10w - 35 = 0

(2w² - 7w) + (10w - 35) = 0 Make the group of two terms.

w (2w - 7) + 5 (2w - 7) = 0 Take out the common factor from each group.

(2w - 7) ( w + 5) = 0 Again take out the common factor (2w-7).

So, 2w -7 =0 and w + 5 =0 Set both the factor equal to 0.

2w = 7 and w = -5

w = 7/2

So, w = 3.5 because width cannot be negative 5.

Now plug in w=3.5 in 3 + 2w to get the length.

So, length = 3 + 2(3.5)

= 3 + 7

= 10

Hence the dimension of the rectangle is 10 ft and 3.5 ft.

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|