Answer:
<em>Numbers: 6 and -2</em>
Step-by-step explanation:
<u>Equations</u>
This question can be solved by inspection. It's just a matter of factoring 12 into two factors that sum 4. Both numbers must be of different signs and they are 6 and -2. Their sum is indeed 6-2=4 and their product is 6*(-2)=-12.
However, we'll solve it by the use of equations. Let's call x and y to the numbers. They must comply:
![x+y=4\qquad\qquad [1]](https://tex.z-dn.net/?f=x%2By%3D4%5Cqquad%5Cqquad%20%5B1%5D)
![x.y=-12\qquad\qquad [2]](https://tex.z-dn.net/?f=x.y%3D-12%5Cqquad%5Cqquad%20%5B2%5D)
Solving [1] for y:
Substituting in [2]
Operating:
Rearranging:
Solving with the quadratic formula:
With a=1, b=-4, c=-12:
The solutions are:
This confirms the preliminary results.
Numbers: 6 and -2
Y = x + 3 is the answer
the y-intercept is 3, so the answer should have a "+ 3" in it
when you are trying to determine the gradient (the x), you can use two methods
first method:
picture/sketch the line. If the line is going upwards (from left to right), it's positive. If the line is going downwards (from left to right), it's negative. However, this method only works for this question, you should try using the second method more
second method:
use the formula: (y - y) / (x - x)
So, you use the y from one of the brackets and subtract the y from the other bracket. Then, you put it over the x ,from the same bracket as the first y, and subtract the x from the second bracket. If you are confused, look at the picture. (Sorry for the messy explanation)
y = x + 4/x
replace x with -x. Do you get back the original equation after simplifying. if you do, the function is even.
replace y with -y AND x with -x. Do you get back the original equation after simplifying. If you do, the function is odd.
A function can be either even or odd but not both. Or it can be neither one.
Let's first replace x with -x
y = -x + 4/-x = -x - 4/x = -(x + 4/x)
we see that this function is not the same because the original function has been multiplied by -1
. Let's replace y with -y and x with -x
-y = -x + 4/-x
-y = -x - 4/x
-y = -(x + 4/x)
y = x + 4/x
This is the original equation so the function is odd.
I don't fully understand the question but I hope this helps...
I believe this would mean he made $1405 that day.
123 5/10 becuase everything on the left side of the dcimal is a whole number and everything on the right side is a fraction. The 5 is in the 10 place so the denominator would be 10 and the numerator would be 5. Your answer is 123 5/10 or simplified, 123 1/2
