Ten(10) adults and 3 children attend a local concert for $59. Four(4) adults and 3
1 answer:
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To expand two terms such as these, we can use the method called FOIL (stands for First, Outer, Inner, Last). Here is what I mean:
We have two terms: (x - 2)(x - 1)
We should first multiply the First two terms of each term in order to complete the F stage:
(x)*(x) =
So then, we take the two outer terms and multiply them together to complete the O stage:
(x)*(-1) = -x
So far we have two things that we have calculated; at the end of the FOIL process we will have four.
To keep going with the FOIL, we now multiply the two inner terms to complete the I stage:
(-2)*(x) = -2x
Last but not least, we need to complete the L stage - so we multiply the two last terms of each term:
(-2)*(-1) = 2
Now that we have our four terms, let us add them together and combine like terms:
Since -x and -2x both have the x portion in common and they are added together, we can add them to create one single term:
-x + (-2x) = -3x
So now that we have our terms completed, we can combine into one polynomial equation:
or 
We have two terms: (x - 2)(x - 1)
We should first multiply the First two terms of each term in order to complete the F stage:
(x)*(x) =
So then, we take the two outer terms and multiply them together to complete the O stage:
(x)*(-1) = -x
So far we have two things that we have calculated; at the end of the FOIL process we will have four.
To keep going with the FOIL, we now multiply the two inner terms to complete the I stage:
(-2)*(x) = -2x
Last but not least, we need to complete the L stage - so we multiply the two last terms of each term:
(-2)*(-1) = 2
Now that we have our four terms, let us add them together and combine like terms:
Since -x and -2x both have the x portion in common and they are added together, we can add them to create one single term:
-x + (-2x) = -3x
So now that we have our terms completed, we can combine into one polynomial equation:
Answer:
We have the system of equations:
y=1/3x+5
y=2/3x+5
To solve it graphically, we need to graph both lines and see in which point the lines intersect.
You can see the graph below, and you can see that the lines intersect in the point (0, 5)
Now, we can also solve this analytically.
We can use the fact that for the solution, we need y = y.
Then we can write:
(1/3)*x + 5 = (2/3)*x + 5
First, we can subtract 5 in both equations to get:
(1/3)*x = (2/3)*x
This only has a solution when x = 0.
Replacing x = 0 in one of the equations, we get:
y = (1/3)*0 + 5 = 5
Then the solution is x = 0, and y = 5, as we already could see in the graph.
