Julie was looking at the architect's blueprint of her house. The scale on the blueprint was inch = 1 foot. On the blueprint, wha
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Answer:
In order to maximize profit, the company should sell each widget at $22.68.
Step-by-step explanation:
The amount of profit <em>y</em> made by the company for selling widgets at <em>x</em> price is given by the equation:
And we want to find to price for which the company should sell in order to maximize the profit.
Since our equation is a quadratic with a negative leading coefficient, its maximum will occur at the vertex point.
The vertex of a quadratic is given by the formulas:
In this case, <em>a</em> = -34, <em>b</em> = 1542, and <em>c </em>= -10037.
Find the <em>x-</em>coordinate of the vertex:
So, in order to maximize profit, the company should sell each widget at $22.68.
Extra Notes:
In order to find the maximum profit, substitute the price back into the equation:
9514 1404 393
Answer:
45
Step-by-step explanation:
Let x and y represent the tens and ones digits, respectively. The 5 times the sum of digits is 5(x+y). The value of the digit-reversed number is (10y+x), so the required relation is ...
5(x +y) = (10y +x) -9
The other relationship between the digits is given as ...
4y = 1/2(10x)
A graphing calculator shows the solution to these equations is (x, y) = (4, 5).
The two-digit number is 45.
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<em>Additional comment</em>
You can solve these equations in any of a variety of ways. Using a graphing calculator to find integer solutions is fast and easy, so is one of my favorites. Here, the coefficients on one equation are not easy multiples of those in the other, so substitution and/or elimination can get messy. In this situation, I like to use the "cross-multiplication" method, which starts with the equations in general form:
- 4x -5y +9 = 0
- 5x -4y +0 = 0
From the coefficients of these equations, differences of cross products are formed:
- d1 = 4(-4) -(5)(-5) = 9
- d2 = -5(0) -(-4)(9) = 36
- d3 = 9(5) -0(4) = 45
Then the solutions are the solutions to 1/d1 = x/d2 = y/d3:
- x = d2/d1 = 36/9 = 4
- y= d3/d1 = 45/9 = 5
(x, y) = (4, 5) ⇒ the number is 45.
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This method is one of several variations of Cramer's Rule, the general solution of systems of linear equations using matrix methods.
Step-by-step explanation:
answer is in photo above
