A hamburger bun merchant can ship 8 large boxes or 10 small boxes of hamburger buns into a carton for shipping. In one shipment,
1 answer:
<h2>Answer:</h2>
56 large boxes and 40 small boxes.
<h2>Step-by-step explanation:</h2>To solve this problem, we need to use the concept of multiples. By definition, a multiple of a number is that number multiplied by an integer. For instance, 3, 6, 9, 12 are multiples of 3. So let's do a chart and list the multiples of large and small boxes:
From this, our goal is to select the number of small and large boxes such that the sum is 96 boxes of hamburger burns and the number of large boxes is greater than the number of small boxes. From the table, the correct solution is:
56 large boxes and 40 small boxes, and this meets our requirement, because 56 + 40 = 96 and 56 > 40
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Answer:
y = 2x³ +x² -3x +6
Step-by-step explanation:
The polynomial correlation function of a graphing calculator can work with the table of function values to give you the equation. (See attached)
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If you want to solve this by hand, you can write the equations for the unknown coefficients in the polynomial function, then solve those. First of all, notice that you are given the y-intercept, (0, 6), so you know one of the coefficients already. That leaves a system of 3 equations in 3 unknowns that need to be solved.
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<em>Writing the equations</em>
... ax³ +bx² +cx +6 = y . . . . the generic linear equation in a, b, c that you're writing
For x = -1:
... -a +b -c +6 = 8
For x = 1
... a + b + c + 6 = 6
For x = 2
... 8a +4b +2c +6 = 20
In augmented matrix terms, this set of linear equations looks like ...
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<em>Solving the equations</em>
There are a number of ways to solve these. Again, a graphing calculator often has solution functions, such as reducing a matrix to row-echelon form, that will solve this in a keystroke or two.
If you add the first two equations, you get ...
... 2b = 2 ⇒ b = 1
Substituting that into the first equation allows you to simplify it to ...
... -a -c = 1
Dividing the third equation by 2 (and substituting for b) makes it ...
... 4a +c = 5
Adding these equations gives ...
... 3a = 6 ⇒ a = 2
Then ...
... c = -a -1 = -2 -1 = -3
And our polynomial function is ...
... y = 2x³ +x² -3x +6
