Answer:
The system that can be used is:
Step-by-step explanation:
We have that:
x is the price of a package of sugar cookies, y is the price of a package of oatmeal cookies.
Shaikha sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56.
This means that:
Khalid sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60.
This means that
System that can be used:
The system that can be used is:
Answer:
<u>Using below system of inequalities</u>
<u>Following the rules </u>
- 1. Finding x- and y - intercepts
- 2. Connecting with dotted line for each as no equal symbol present in any inequality
- 3. Shade respective regions
- 4. Solution is the intersection of the shades regions
- 5. Select any three points in the solution region
<u>Line 1</u>
- y > 2x - 3
- x- intercept: y = 0 ⇒ 0 = 2x - 3 ⇒ 2x = 3 ⇒ x = 1.5
- y - intercept: x = 0 ⇒ y = -3
- Shaded region is above the line (or to the left)
<u>Line 2</u>
- y < x + 1
- x- intercept: y = 0 ⇒ 0 = x + 1 ⇒ x = -1
- y - intercept: x = 0 ⇒ y = 1
- Shaded region is below the line (or to the right)
<u>Selected points are:</u>
The correct statement is the first figure, that is:
To prove this, we need to solve each side of the inequality and see that, in fact, the term on the left side is greater than the term on the right. So:
As you can see 0.0038728 is less than 3343.4728, so this is the only answer that is true. The rest of the choices are false! Recall that Inequality tells us about the relative size of two values. Inequality refers the term greater or less than (this may include or not the equality)
Let x be the number of times they raise the price on the newspaper. Then the new cost of the newspaper is
Let y be the newspaper they sell, then the income will be
Now, we know that the circulation is of 500, assuming that they sold every newspaper at the original price now the number the will sell will be
Plugging the value of y in the first expression we have that the income will be
Then the income is given by the function
To find the maximum value of this functions (thus the maximum income) we need to take the derivative of the function,
no we equate the derivative to zero and solve for x.
This means that we have an extreme value of the function when x=9. Now we need to find out if this value is a maximum or a minimum. To do this we need to take the second derivative of the function, then
Since the second derivative is negative in the point x=9, we conclude that this value is a maximum of the function.
With this we conclude that the number of times that they should raise the price to maximize the income is 9. This means that they will raise the price of the newspaper (9)($0.05)=$0.45.
Therefore the price to maximize the income is $0.35+$0.45=$0.80.