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3 years ago

What number do you divide by 12 to get 9

Mathematics

2 answers:

Law Incorporation [45]3 years ago

8 0

Work backwards. 12*9=108
check: 108/12=9

finlep [7]3 years ago

5 0

Well I don't know. Let's figure it out together.

You said (a number) divided by 12 gives you 9 .

A fraction is the easiest way to show division, so
you can write this equation:

   (number) / 12 = 9

Now you can multiply each side of the equation by 12 .
When you do that, you have ...

   number = 9 x 12

   <em>number =    108</em> .

Now you know how to find it. That's even better than just
having the answer.

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3 years ago

4x-4y+4z=8<br> 9x+3y+z=6<br> 16x+4y+z=2

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Answer:

(x, y, z) = (-1, 3, 6)

Step-by-step explanation:

The augmented matrix for the system is ...

$\left[\begin{array}{ccc|c}4&-4&4&8\\9&3&1&6\\16&4&1&2\end{array}\right]$

Your graphing or scientific calculator can tell you the solution to this system is ...

(x, y, z) = (-1, 3, 6)

If you want to solve this by hand, it can work well to divide the first equation by 4 to get ...

x -y +z = 2

This can be subtracted from the other two equations to eliminate z.

(9x +3y +z) -(x -y +z) = (6) -(2) ⇒ 8x +4y = 4

(16x +4y +z) -(x -y +z) = (2) -(2) ⇒ 15x +5y = 0

These two equations can be reduced to standard form:

2x +y = 1
3x +y = 0

Subtracting the first equation from the second, we have ...

(3x +y) -(2x +y) = (0) -(1) ⇒ x = -1

Substituting into the first gives y:

2(-1) +y = 1

y = 3 . . . . . . . add 2

Then we can find z from the reduced first equation above:

z = 2 -x +y = 2 -(-1) +3 = 6

Then the solution is (x, y, z) = (-1, 3, 6).

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3 years ago