Answer:
The graph of the equation 40.51x+12.45y=666.64 is attached with the answer where the horizontal axis represents the X axis and the vertical axis represents Y axis.
To plot the graph physically just find two points lying on the line. Mark the points on the graph sheet and then join them. This will give you the line represented by the equation.
To find points on the line assume the value of any one variable, substitute it in the equation, then solve the equation to find the value of other variable. For example : assume y = 1; substitute the value of y in the equation;
⇒ 40.51x + 12.45×1 = 666.64
⇒ 40.51x = 666.64 - 12.45
⇒ 40.51x = 654.19
⇒ x = 
⇒ x ≈ 16.149
Therefore point ( 16.149 , 1 ) lie on the graph of the equation.
***Only two points are required to plot this graph just because it represents a straight line, that we can conclude just by observing the equation. If in an equation the power of x is 1 or 0 and power of y is 1 or 0 then only it will represent a straight line in 2-D plane.***
Answer:
- y = 0.937976x +12.765
- $12,765
- $31,524
- the cost increase each year
Step-by-step explanation:
1. For this sort of question a graphing calculator or spreadsheet are suitable tools. The attached shows the linear regression line to have the equation ...
... y = 0.937976x + 12.765
where x is years since 2000, and y is average tuition cost in thousands.
2. The y-intercept is the year-2000 tuition: $12,765.
3. Evaluating the formula for x=20 gives y ≈ 31.524, so the year-2020 tuition is expected to be $31,524.
4. The slope is the rate of change of tuition with respect to number of years. It is the average increase per year (in thousands). It amounts to about $938 per year.
5. [not a math question]
Answer: There are 2346953264 ways to do so.
Step-by-step explanation:
Since we have given that
Total number of selected countries = 12
Number of selected countries from a block of 45 = 3
Number of selected countries from a block of 57 = 4
So, remaining number of selected countries from a block of 69.
So, 12-(3+4)=12-7=5
Now, we need to find the number of ways, so we will use "Combination" to select that number of countries.
So, it becomes.
Hence, there are 2346953264 ways to do so.
Answer:
Step-by-step explanation:
From the differential equation given:
The equation above can be re-written as:
Let assume that if function M(x,y) and N(x,y) are continuous and have continuous first-order partial derivatives.
Then;
M(x,y) dx + N (x,y)dy = 0; this is exact in R if and only if:
relating with equation M(x,y)dx + N(x,y) dy = 0
Then;
So;
Let's Integrate 
with respect to x
Then;
Now, we will have to differentiate the above equation with respect to y and set 
; we have:
Hence, 
Finally; the general solution to the equation is:
