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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.
y = x³ + 3x² - x - 3
0 = x³ + 3x² - x - 3
0 = x²(x) + x²(3) - 1(x) - 1(3)
0 = x²(x + 3) - 1(x + 3)
0 = (x² - 1)(x + 3)
0 = (x² + x - x - 1)(x + 3)
0 = (x(x) + x(1) - 1(x) - 1(1))(x + 3)
0 = (x(x + 1) - 1(x + 1))(x + 3)
0 = (x - 1)(x + 1)(x + 3)
0 = x - 1 or 0 = x + 1 or 0 = x + 3
+ 1 + 1 - 1 - 1 - 3 - 3
1 = x or -1 = x or -3 = x
Solution Set: {-3, -1, 1}
Answer:
1st choice : 706.5 square inches
Step-by-step explanation:
circumference is pi times diameter
divide 94.2 by pi to get diameter = 29.9847912785
diameter 29.9847912785 divided by 2 is
14.9923956393 which is the radius
area is pi times radius times radius again
pi times 14.9923956393 times 14.9923956393 =
706.141834613
The answer should be around 28 square centi. rounding from about 27.71
