The system of equations 2x + 3y = 2 and y = (1/2)x + 3 have solutions at x = -2 and y = 2
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
From the system of equations 2x + 3y = 2 and y = (1/2)x + 3, the graph of the equation shows that the solution is at x = -2 and y = 2
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Answer:
in 2005, 17.3 percent of students are taking at least one online course
Step-by-step explanation:
f(5) = 2.6(5) +4.3 = 17.3
The definition of the function f(x) tells you that f(5) = 17.3 means 5 years after the year 2000, 17.3 percent of students are taking at least one online course.
Answers:
Part 1 (the ovals)
Domain = {-6,-1,1,5,7}
Range = {-4,-1,2,4}
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Part 2 (the table)
Domain = {1,-3,-2}
Range = {-2,5,1}
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Part 3 (the graph)
Domain = {1, 2, 3, 4, 5, 6}
Range = {-1, 0, 1, 2, 3, 6}
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Explanation:
Part 1 (the ovals)
The domain is the set of input values of a function. The input oval is the one on the left.
All we do is list the numbers in the input oval to get this list: {-6,-1,1,5,7}
The curly braces tell the reader that we're talking about a set of values.
So this is the domain.
The range is the same way but with the output oval on the right side
List those values in the right oval and we have {-4,-1,2,4}
Which is the range. That's all there is to it.
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Part 2 (The tables)
Like with the ovals in part 1, we simply list the input values. The x values are the input values. Notice how this list is on the left side to indicate inputs.
So that's why the domain is {1, -3, -2}. Optionally you can sort from smallest to largest if you want. Doing so leads to {-3, -2, 1}
The range is {-2,5,1} for similar reasons. Simply look at the y column
Side Note: we haven't had to do it so far, but if we get duplicate values then we must toss them.
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Part 3 (the graph)
Using a pencil, draw vertical lines that lead from each point to the x axis. You'll notice that you touch the x axis at the following numbers: 1, 2, 3, 4, 5, 6
So the domain is the list of those x values (similar to part 2) and it is {1, 2, 3, 4, 5, 6}
Erase your pencil marks from earlier. Draw horizontal lines from each point to the y axis. The horizontal lines will arrive at these y values: -1, 0, 1, 2, 3, 6
So that's why the range is {-1, 0, 1, 2, 3, 6}
Answer:
The number of roots for equation 
is 4 .
Step-by-step explanation:
Here, the given function polynomial is :
The Fundamental Theorem of Algebra says that a polynomial of degree n will have exactly n roots (counting multiplicity).
Now here, the degree if the polynomial is 4 (highest power of variable x).
So, according to the Fundamental Theorem, the given polynomial can have AT MOST 4 roots, counting Multiplicity.
Hence, the number of roots for equation is 4 .
