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.
Answer:
-3
Step-by-step explanation:
The length of a segment is
sqrt( ( y2-y1)^2 + (x2-x1) ^2) = 2 sqrt(10)
sqrt( ( a-4 - -1)^2 + (2a -4) ^2) = 2 sqrt(10)
sqrt( ( a-4 +1)^2 + (2a -4) ^2) = 2 sqrt(10)
Combine like terms
sqrt( ( a-3)^2 + (2a -4) ^2) = 2 sqrt(10)
Square each side
( a-3)^2 + (2a -4) ^2) = 4 *(10)
FOIL the left side
a^2 -6a +9 + 4a^2 -16a +16 = 40
Combine like terms
5a^2 -22a +25 = 40
Subtract 40 from each side
5a^2 -22a -15 =0
Factor
(a - 5) (5 a + 3) = 0
Using the zero product property
a-5 =0 5a +3 = 0
a = 5 5a = -3
a=5 a = -3/5
The product of the terms is
5 * -3/5 = -3
Answer:
i think its 60
Step-by-step explanation:
base times height then divide by 2
step 1: Given
step 2: Distributive Property
step 3: Combine Like terms
step 4: Subtraction Property of Order
step 5: Addition property of order
step 6: Division property of order
Step-by-step explanation:
We are given the inequality: 
We need to match each step with the reasons.
The given steps are:
1.
−38−3(x+5)>6x−17
So, Reason for step 1: Given
2.
−38−3x−15>6x−17
So, Reason for step 2: Distributive Property
3.
−3x−53>6x−17
So, Reason for step 3: Combine Like terms
4.
−9x−53>−17
So, Reason for step 4: Subtraction Property of Order
5.
−9x>36
So, Reason for step 5: Addition property of order
6.
x<−4
So, Reason for step 6: Division property of order
Keywords: Solving inequalities
Learn more about Solving inequalities at:
#learnwithBrainly
-180 is the answer
explanation: order of operations