Can anyone me step by step on how to solve this problem?

see explanation

Step-by-step explanation:

The volume (V) of a cuboid is calculated using the formula

V = lbh ( l is length, b is breadth and h is height )

Equate the product of the dimensions to 374

2(x + 3)(x + 9) = 374 ( divide both sides by 2 )

(x + 3)(x + 9) = 187 ← expand factors on left side

x² + 12x + 27 = 187 ( subtract 187 from both sides )

x² + 12x - 160 = 0 ← in standard form

Factor by considering the factors of the constant term (- 160) which sum to give the coefficient of the x- term (+ 12)

The factors are + 20 and - 8, hence

(x + 20)(x - 8) = 0

Equate each factor to zero and solve for x

x + 20 = 0 ⇒ x = - 20

x - 8 = 0 ⇒ x = 8

solutions are x = - 20, x = 8

However x > 0 ⇒ x = 8 and

x + 3 = 8 + 3 = 11

x + 9 = 8 + 9 = 17

Dimensions are 2cm, 11 cm, 17 cm

you have to make an equation for the volume

volume = l × w × d

subsitute values given

2 × (x+3) × (x+9) = 374

multiply (x+3) and (x+9) first

2 × (x^2+12x+27) = 374

multiply left side by 2

2x^2 + 24x + 54 = 374

everything is divisible by 2 so you can divide by 2 on both sides to make it simpler

x^2 + 12x + 27 = 187

minus 187 on both sides to set equation equal to 0

x^2 + 12x - 160 = 0

factorise with two factors of -160 that add up to give 12

(x + 20)(x - 8) = 0

x + 20 = 0

x - 8 = 0

therefore

x = 8x = -20

however, x cannot be -20 as it is representing lengths, which cannot be negative.

so the solution we must use later on is 8.

the dimensions of the cuboid are

2

x + 3

x + 9

we know the value of x which is 8 so we substitute this.

dimensions:

2

8 + 3

8 + 9

therefore the dimensions of the cuboid are:

2cm, 11cm, 17cm

y = 2x² + 3x - 9

Step-by-step explanation:

Given αβ = - =

and α + β = - = -

Then a = 2, b = 3 and c = - 9, thus

y = 2x² + 3x - 9