Answer:
6 chickens, 11 cows.
Step-by-step explanation:
x - chickens
y - cows
x + y = 17
2x + 4y = 56 <-- chickens have 2 legs, cows have 4.
y = -x + 17
Substitute (-x+17) for y in the second equation.
2x + 4(-x + 17) = 56
2x -4x + 68 = 56
2x = 12
<u>x = 6 chickens</u>
Now substitute 6 for x
6 + y = 17
<u>y = 11 cows</u>
For this case we have the following equation:
x ^ 2 + 18x + 32 = 0
Rewriting we have:
x ^ 2 + 18x = -32
By completing squares we have:
x ^ 2 + 18x + (18/2) ^ 2 = -32 + (18/2) ^ 2
Rewriting:
x ^ 2 + 18x + (9) ^ 2 = -32 + (9) ^ 2
x ^ 2 + 18x + 81 = -32 + 81
x ^ 2 + 18x + 81 = 49
(x + 9) ^ 2 = 49
Answer:
(x + 9) ^ 2 = 49
option 1
6m3 - 16m2 + 15m - 40<span> Simplify —————————————————————
2m2 + 5
</span>Checking for a perfect cube :
<span> 4.1 </span> <span> 6m3 - 16m2 + 15m - 40</span> is not a perfect cube
Trying to factor by pulling out :
<span> 4.2 </span> Factoring: <span> 6m3 - 16m2 + 15m - 40</span>
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 15m - 40
Group 2: <span> -16m2 + 6m3</span>
Pull out from each group separately :
Group 1: (3m - 8) • (5)
Group 2: <span> (3m - 8) • (2m2)</span>
-------------------
Add up the two groups :
<span> (3m - 8) • </span><span> (2m2 + 5)</span>
<span>Which is the desired factorization</span>
<span>3m-8 is the answer</span>
Intuitively, the answer is 3, but to confirm, remember that the constant of proportionality k is y/x,
y = 3x Divide both sides by x
y/x = k = 3
Thee constant of proportionality is B) 3
