Question

Item 1
The Diamond Rule says two factors, m and n, must multiply to get to the top number and add to get to the bottom number.

What are the possible values for m and n?





9 and 4

-9 and 4

6 and 6

-6 and -6

-6 and 6

-9 and -4

Answer 1

The diamond rule creates a system of equation for variables m and n

The possible values of m and n are 8 and 4 or 4 and 8

How to determine the possible values of m and n.

The question is incomplete; so I will make use of the attached figure

When the diamond rule is applied to the figure, we have the following equations

$mn = 32$

$m + n = 12$

Make n the subject, in the second equation

$n = 12 - m$

The first equation becomes

$(12 - m)m = 32$

Expand

$12m - m^2 = 32$

Rewrite as:

$-m^2 + 12m - 32 = 0$

Multiply through by -1

$m^2 - 12m + 32 = 0$

Expand

$m^2 - 4m - 8m + 32 = 0$

Factorize

$m(m - 4) - 8(m - 4) = 0$

Factorize

$(m - 8)(m - 4) = 0$

Solve for m

m = 8 or m = 4

Recall that:

$n = 12 - m$

So, we have:

n = 12 - 8 or n = 12 - 4

Solve

n = 4 or n = 8

Hence, the possible values of m and n are 8 and 4 or 4 and 8 (using the attached figure)

Read more about equations at:

https://brainly.com/question/2972832