Answer:
Putting the value of x = (5-i√5)÷5 in 5x²-10x+6=0.
We get,
⇒ 25 + (i√5)² - 10i√5 - 50 + 10i√5 + 30 = 0
⇒ (i√5)² + 5 = 0 {∵ i² = -1}
⇒ - 5 + 5 = 0
⇒ 0 = 0
Thus, (5-i√5) ÷ 5 is the solution of 5x²-10x+6=0.
Answer:
1,440,000
Step-by-step explanation:
1249 is rounded to 1200 because 49 is less than half of 100.
1194 is rounded to 1200 because 94 is more than half of 100.
1200 x 1200 = 1,440,000
Answer:
16
+ 2t - 6
Step-by-step explanation:
simplify
combine like terms
16 + 2t - 6
Answer:
6
Step-by-step explanation:
Cost per item is found by dividing the cost by the number of items. If the woman bought n items for $120, the cost of each item is $120/n. If the woman bought 24 more items, n+24, at the same price, then the cost per item is $120/(n+24). The problem statement tells us this last cost is $16 less than the first cost:
120/(n+24) = (120/n) -16
Multiplying by n(n+24) gives ...
120n = 120(n+24) -16(n)(n+24)
0 = 120·24 -16n^2 -16·24n . . . . . . subtract 120n and collect terms
n^2 +24n -180 = 0 . . . . . . . . . . . . . divide by -16 to make the numbers smaller
(n +30)(n -6) = 0 . . . . . . . . . . . . . . factor the quadratic
The solutions to this are the values of n that make the factors zero: n = -30, n = 6. The negative value of n has no meaning in this context, so n=6 is the solution to the equation.
The woman bought 6 items.
_____
Check
When the woman bought 6 items for $120, she paid $120/6 = $20 for each of them. If she bought 6+24 = 30 items for the same money, she would pay $120/30 = $4 for each item. That amount, $4, is $16 less than the $20 she paid for each item.
