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:
STEM ______ Leaf
2 ______ 0 0 2 4
3 _______ 6 8
4 _______ 2 7
5 ______ 5 7
6 ______ 1 2 3 5
Step-by-step explanation:
Given that data:
20, 24, 65, 36, 47, 55, 62, 20, 22, 63, 38, 42, 57, 61
STEM ______ Leaf
2 ______ 0 0 2 4
3 _______ 6 8
4 _______ 2 7
5 ______ 5 7
6 ______ 1 2 3 5
The unique numbers which starts each value is the stem while the second digit of each unique stem is the leaf.
Answer:
65625/4(x^5)(y²)
Step-by-step explanation:
Using binomial expansion
Formula: (n k) (a^k)(b ^(n-k))
Where (n k) represents n combination of k (nCk)
From the question k = 5 (i.e. 5th term)
n = 7 (power of expression)
a = 5x
b = -y/2
....................
Solving nCk
n = 7
k = 5
nCk = 7C5
= 7!/(5!2!) ------ Expand Expression
=7 * 6 * 5! /(5! * 2*1)
= 7*6/2
= 21 ------
.........................
Solving (a^k) (b^(n-k))
a = 5x
b = -y/2
k = 5
n = 7
Substituting these values in the expression
(5x)^5 * (-y/2)^(7-5)
= (3125x^5) * (-y/2)²
= 3125x^5 * y²/4
= (3125x^5)(y²)/4
------------------------------------
Multiplying the two expression above
21 * (3125x^5)(y²)/4
= 65625/4(x^5)(y²)
Answer:
the answer is 118
Step-by-step explanation:
since one pound is equal to 16 ounces you just convert