Answer:
w = 7 cm
Step-by-step explanation:
Volume = 252 cm³
Height, h = 3cm
Let width = w
Length, l = w + 5
Volume of rectangular prism, V = l * w * h
252 = (w + 5) * w * 3
252 = (w + 5) * 3w
252 = 3w² + 15w
3w² + 15w - 252 = 0
w² + 5w - 84 = 0
w² + 12w - 7w - 84 = 0
w(w + 12) - 7(w + 12) = 0
(w + 12) = 0 or (w - 7) = 0
w = - 12 or w = 7
w cannot be negative
Hence, w = 7 cm
Treat the matrices on the right side of each equation like you would a constant.
Let 2<em>X</em> + <em>Y</em> = <em>A</em> and 3<em>X</em> - 4<em>Y</em> = <em>B</em>.
Then you can eliminate <em>Y</em> by taking the sum
4<em>A</em> + <em>B</em> = 4 (2<em>X</em> + <em>Y</em>) + (3<em>X</em> - 4<em>Y</em>) = 11<em>X</em>
==> <em>X</em> = (4<em>A</em> + <em>B</em>)/11
Similarly, you can eliminate <em>X</em> by using
-3<em>A</em> + 2<em>B</em> = -3 (2<em>X</em> + <em>Y</em>) + 2 (3<em>X</em> - 4<em>Y</em>) = -11<em>Y</em>
==> <em>Y</em> = (3<em>A</em> - 2<em>B</em>)/11
It follows that

Similarly, you would find

You can solve the second system in the same fashion. You would end up with

Answer:(1/6)3
or 1/216
Step-by-step explanation:
You have a 1/6 chance of getting the first number.1/6
chance of the second and so on. Is it just
(16)3
Step-by-step explanation:
We have the original equation n ^ 2 + 5 * n - 24, when factoring we have:
(n + 8) * (n - 3)
Now by replacing the values:
n = 0
0 ^ 2 + 5 * 0 - 24 = - 24
(0 + 8) * (0 - 3) = - 24
n = 1
1 ^ 2 + 1 * 0 - 24 = - 18
(1 + 8) * (1 - 3) = -18
n = 2
2 ^ 2 + 5 * 2 - 24 = - 10
(2 + 8) * (2 - 3) = - 10
n = 3
3 ^ 2 + 5 * 3 - 24 = 0
(3 + 8) * (3 - 3) = 0
n = 4
4 ^ 2 + 5 * 4 - 24 = 12
(4 + 8) * (4 - 3) = 12