Graph the following system X+y=4 X-y=2
1 answer:
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Answer:
Please see attached image and all steps below for both parts
Step-by-step explanation:
Task 1
The following system of equations includes a linear equation and a quadratic one:
it can be solved by using substitution in the second equation of the variable "y" by the linear expression of the first equation:
and this product of two factors will e zero when either factor is zero, that is: when x = 0, or when x = 9 [to make zero the binomial(x - 9)]
There are two solutions: x = 0 and x = 9.
When we graph both expressions in the system, we see that the line intercepts the parabola at the points (0, 2) and (9, 11). See attached image.
Task 2
Part 1:
Let's pick 30 as a number larger than 25. 30 can be written as 40 - 10
So we can use:
to calculate its square.
Part 2:
let's choose a=9 and b=10 so we use:
Honestly I can see an argument for 7 shelves or for 8 shelves.
When you do the calculation;
You get 7.15 shelves. Clearly you cannot have .15 of a shelf so the logician in me wants to say you need 8 shelves!
But if the assignment is aimed estimation skills, (Which is what I assume is being implied by the title of the assignment), then the easier calculation of
is probably what the teacher was hoping for.
You might have been accidentally been calculating
. Remember division is NOT communitive! i.e.
.
From the image;
The first step was to see that 59 can not go into 4..resulting in the zero above the 4, multiplying 0 by 59 and subtracting 0 from 4.
The second step begins by bringing down the 2, seeing that 59 can not go into 42..resulting in the zero above the 2, multiplying 0 by 59 and subtracting 0 from 42.
The third step begins by bringing down the 2, seeing that 59 can go into 422 7 times (I tested this on the right by a short multiplication problem)..resulting in the 7 above the 2, multiplying 7 by 59 and subtracting 413 from 42.
This process continues....
When you do the calculation;
But if the assignment is aimed estimation skills, (Which is what I assume is being implied by the title of the assignment), then the easier calculation of
You might have been accidentally been calculating
From the image;
The first step was to see that 59 can not go into 4..resulting in the zero above the 4, multiplying 0 by 59 and subtracting 0 from 4.
The second step begins by bringing down the 2, seeing that 59 can not go into 42..resulting in the zero above the 2, multiplying 0 by 59 and subtracting 0 from 42.
The third step begins by bringing down the 2, seeing that 59 can go into 422 7 times (I tested this on the right by a short multiplication problem)..resulting in the 7 above the 2, multiplying 7 by 59 and subtracting 413 from 42.
This process continues....