



In matrix multiplication, the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix.

Multiply each element of the 1st row of the 1st matrix by the corresponding element of the 1st column of the 2nd matrix. Then add these products to obtain the element in the 1st row, 1st column of the product matrix.

The remaining elements of the product matrix are found in the same way.

Simplify each element by multiplying the individual terms.

Now, sum each element of the matrix.

First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.
The sum

can be written as:

,
<span>
from the binomial expansion formula: </span>

.
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>
</span>



.
This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.
At x=5.4, the expression

, which is equivalent to

, takes it smallest value.
Substituting, we would find

=32.4 This is the smallest value of the expression.
For x=5.4, y=-3x+18=-3(5.4)+18=1.8.
Answer: (5.4, 1.8)
Answer:
<u>-5 ± √5² - 4 · 1 · 4</u>
2 · 1
Step-by-step explanation:
ax²+bx+c=0 (quadratic equation)
x=<u> -b ± √b² - 4ac</u>
2a
a= 1
b= 5
c= 4
-<u>5 ± √5² - 4 · 1 · 4</u>
2 · 1
Answer:
19
Step-by-step explanation:
Matt ended up with 26.
We reverse the steps he did to get the original number that both people thought of.
26 / 2 = 13
13 - 7 = 6
6 is the original number.
Tikka did the same operations but in the reverse order so...
6 X 2 = 12
12 + 7 = 19
Simplifying
30c + -45d
Factor out the Greatest Common Factor (GCF), '15'.
15(2c + -3d)
Final result:
15(2c + -3d)