Is the relation a function? Why or why not?
1 answer:
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Answer:
The equation represents in R^2 c) a line
The equation represents in R^3 a) a plane
The equation represents in R^3 a) a plane
The equation represents d) a plane
The pair of equations represents a) a line
Step-by-step explanation:
Let's start by studying each question :
1)
In R^2 , with
∈ IR is the equation of all vertical lines
In this case, the only free variable is the variable ''y''
R^2 has two dimensions (x and y) so if we set we will have only one free variable in R^2 (which is a line in R^2). Therefore,
represents a line in R^2
Now, in R^3 we have three dimensions (x, y and z) so if we set we will have only two free variables (y and z) and
will represent a plane (which have two dimensions) in R^3.
2) The equation in R^3 has the free variable ''z'' and given that we select a value (for example for ''x'') the another value from the variable ''y'' is determined. Finally, we have the free variables ''z'' and ''x'', and the variable ''y'' restricted for our choice of the variable ''x''.
The equation in R^3 (given that we have two free variables) represents a plane.
Using the same reasoning, the equation represents a plane (given that it has two free variables : ''y'' and ''x'')
Finally, the pair of equations set values for ''y'' and ''z'' leading us ''x'' as the free variable. With only one free variable we will have a ''one dimensional'' geometric form. The one dimensional forms in R^3 are lines.
The final answer is a) a line.
Answer:
Step-by-step explanation:
Let b be the number of balloons and h be number of party hats.
We have been given that balloons cost $0.50 each, so cost of b balloons will be 0.50b.
We are also told that party hats each cost $1.25, so cost of h party hats will be 1.25h.
Further, Joe wants to spend exactly $20 on the party supplies. We can represent this information in an equation as:
Therefore, the equation represents the number of balloons ( b) and the number of party hats ( h) that Joe can buy spending exactly $20.