Question

i know this is easy but i have done the middle one but dont know the first and last the miidle one is correct because its in green

Answer 1

a)

The box is a rectangular prism. The base measures 2x + 5 by x.

The area of the base is length times width, or (2x + 5) * x = 2x^2 + 5x.

The area of the base is 58, so

2x^2 + 5x = 58

Subtract 58 from both sides.

2x^2 + 5x - 58 = 0

b)

`x = (-b \pm √(b^2 - 4ac))/(2a)`

`x = (-5 \pm √(5^2 - 4(2)(-58)))/(2(2))`

`x = (-5 \pm √(25 + 464))/(4)`

`x = (-5 \pm √(489))/(4)`

`x = (-5 + √(489))/(4)` The other answer is negative and can be discarded.

`x = (-5 + 22.11)/(4)`

`x = 4.28`

x = 4.28

c) The volume of the box is the area of the base multiplied by the height.

The height is x - 2. 4.28 - 2 = 2.28. The height is 2.28 cm.

V = 58 * 2.28

V = 132.14

The volume is 132.14 cm^3