Answer:
The answer is 9.
Step-by-step explanation:
Because 7 + 9 + 11 + 13 = 40, 9 is the 2nd number in the problem.
Answer:
a² + b² = 22
Step-by-step explanation:
(a + b)² = a² + 2ab + b² ← substitute a + b = 6 and ab = 7
6² = a² + 2(7) + b²
36 = a² + 14 + b² ( subtract 14 from both sides )
22 = a² + b²
Solve the following system using elimination:
{3 a + 4 b = 2 | (equation 1)
{5 a + 9 b = 1 | (equation 2)
Swap equation 1 with equation 2:
{5 a + 9 b = 1 | (equation 1)
{3 a + 4 b = 2 | (equation 2)
Subtract 3/5 × (equation 1) from equation 2:
{5 a + 9 b = 1 | (equation 1)
{0 a - (7 b)/5 = 7/5 | (equation 2)
Multiply equation 2 by 5/7:
{5 a + 9 b = 1 | (equation 1)
{0 a - b = 1 | (equation 2)
Multiply equation 2 by -1:
{5 a + 9 b = 1 | (equation 1)
{0 a+b = -1 | (equation 2)
Subtract 9 × (equation 2) from equation 1:
{5 a+0 b = 10 | (equation 1)
{0 a+b = -1 | (equation 2)
Divide equation 1 by 5:
{a+0 b = 2 | (equation 1)
{0 a+b = -1 | (equation 2)
Collect results:
Answer: {a = 2
{b = -1
To be sure that you get all the items you want of the same color you will have to grab the minimum amount of fruits to exhaust all other possibilities. So for this case you would need to grab a total of 3+5+7+1 = 16 for Yellow, 5+7+2+1 = 15 for Green.
Now of course it's possible to get your solution in less than the above numbers but it's only 100% change once you take all the other options out of existence.
