Tim spends 1/3 each weekday sleeping and 7/24 in school. We can write 1/3 as 8/24 so we have a common denominator. Now we can see that Tim sleeps for 1/24 time of a weekday more then he spends in school.
I hope that's what you meant.
Mentally
As they are numbers which you can do mental math with since they are whole numbers.
Cross multiply the denominators by the numerators. In other words, 12 times 3 and 7 times x (x, being our missing number).
We end up with 36 and 7x.
Divide both sides by 7.
36/7x = 5.14
x = 5.14
Hope this helps!
Domain: x>-5 ; It goes on from -5.
Range: y>-1 ; It goes on from -1.
Function: Slope is 6/7 ;
<h3><u><em>
y=6/7 x , when x>-5</em></u></h3>
The quadratic equation for this would be f(x) = 5x^2 - 10x - 120.
In order to find that, we need to start by taking our x intercept values and setting them equal to zero.
x = 6 ----> subtract 6 from both sides
x - 6 = 0
x = -4 ----> add 4 to both sides
x + 4 = 0
Now that we have both of these zero terms, we can multiply them to get a standard form.
f(x) = (x - 6)(x + 4)
And while this will give us the zeros we need, it will no give us the lead coefficient. So we must multiply by the desired lead coefficient.
f(x) = 5(x - 6)(x + 4)
f(x) = 5(x^2 - 6x + 4x - 24)
f(x) = 5(x^2 - 2x - 24)
f(x) = 5x^2 - 10x - 120
