a teacher wishes to keep the students books in the cardboard which is 69.9cm long,24cm wide and 36.01cm high estimate how many exercise books he can put if each exercise book is 22cm long 19.5cm wide and 0.9cm thick

156

Step-by-step explanation:

We are given that

Length of cardboard, l=69.9 cm

Width of cardboard, b=24 cm

Height of cardboard, h=36.01 cm

Length of book, l=22 cm

Width of book, b=19.5 cm

Thickness of book, h=0.9 cm

Volume of cuboid=lbh

Using the formula

Volume of cardboard=

Volume of one book=

Number pf exercise book=

Number of exercise book=

Number of exercise book=156

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.