Explain how the associative property can be used to mentally find the volume of the prisms shown

A prism is a solid object having two identical bases, hence the same cross section along the length. This is a rectangular prism its base is a rectangle. multiplying the three dimensions of a rectangular prism: length, width and height, gives us the volume of a prism:

Therefore, Associative Property can be used to mentally find the volume of the prisms shown by selecting the easier way of the multiplication. For instance, we can say that:

In whose case:

To operate this mentally is not an easy way, but what if we rotate this shape? so we say that:

Then, the volume can be found as:

There are two forms of finding the result. First, multiplying 18 by 20 and then the result by 5, but as in the previous case this is a tricky way to do mentally:

Hence, here we can use Associative Property multiplying 20 by 5 and then the result by 18:

This last arrangement is easier because 20 x 5 is easy to remember given that the result is 100. Then, by multiplying this result by 18 then we get 1800.

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.

add an !

step-by-step explanation: