<em>Question:</em>
<em>Abraham has visited at least 50 countries; he plans to visit five new countries per year (Y) for the next several years. Which inequality and solution shows the amount of years they will take for Abraham to meet his goal.</em>
Answer:
Step-by-step explanation:
Given
------ at least
Required
Represent as an inequality
"at least" means 
So the countries he has visited can be represented as thus;
If
1 year = 5 countries
y years would be 5y countries
So, in y years; he'd have visited
To determine the value of y.
We have that
<em>in the world</em>
<em>Substitute 195 for Countries</em>
<em>Collect Like Terms</em>
<em>Divide through by 5</em>
<em>Reorder</em>
This means that; he'll visit all countries in at most 29 years' time
K is the slope of the line formed by connecting the points.
Use slope formula:
where the 2 points are the end points of the line (First and last going Left to right)
Substitute into slope formula
You can check if this is correct by going back to graph and going "up 7" and "over 2" to get from one point to the next.
Answer:
Maximum area = 800 square feet.
Step-by-step explanation:
In the figure attached,
Rectangle is showing width = x ft and the side towards garage is not to be fenced.
Length of the fence has been given as 80 ft.
Therefore, length of the fence = Sum of all three sides of the rectangle to be fenced
80 = x + x + y
80 = 2x + y
y = (80 - 2x)
Now area of the rectangle A = xy
Or function that represents the area of the rectangle is,
A(x) = x(80 - 2x)
A(x) = 80x - 2x²
To find the maximum area we will take the derivative of the function with respect to x and equate it to zero.
= 80 - 4x
A'(x) = 80 - 4x = 0
4x = 80
x = 
x = 20
Therefore, for x = 20 ft area of the rectangular patio will be maximum.
A(20) = 80×(20) - 2×(20)²
= 1600 - 800
= 800 square feet
Maximum area of the patio is 800 square feet.
2 - 7 = -5
8i - 2i = 6i
-5 + 6i is your answer
hope this helps
