You can use the <u>determinant</u><u> (square root)</u> of a quadratic equation to determine the number and type of solutions of the equation.
> 0 → 2 real solutions
- if is a perfect square, then rational sol'ns
- if is not a perfect square, then irrational sol'ns
= 0 → 1 real solution (double root)
< 0 → 2 imaginary(complex) solutions
Answer:
-4
Step-by-step explanation:
We have the coordinates (6, 3) and (8, 4), allowing us to calculate the slope (or gradient). To do this, you divide the change in y by the change in x, which is 1/2 which is a half.
The form of a linear equation is y = mx + c, where m is the gradient and c is the y-intercept.
We have the gradient, so we can put it in the equation:
y = x/2 + c
We can now substitute in a pair of our coordinates and rearrange to find the y-intercept.
3 = 6/2 + c
3 = 3 + c
c = 0
Therefore the equation for our line is y = x/2.
We can now put in the y coordinate we were given to work out the corresponding x coordinate:
-2 = x/2
x = -4
Therefore n is -4.
Answer:
A
Step-by-step explanation:
Divide both numbers by 6. 1 inch per 7.5 ft.
Answer:
amount which will be withheld from John's pay for federal income tax this week is $54
Step-by-step explanation:
It is given that John Johnson's gross pay for a week is $520.95,
From table it is clear that his gross pay ( $520.95) lies between at least 520 but less than 530 category.
and he claimed one withholding allowance, therefore John Johnson has to pay $54 for federal income tax.
I hope this answer will help you
Answer:
55 mph
Step-by-step explanation:
Speed = Distance/Time so Time = Distance / Speed.
If the first speed is x mph, the first trip will take 660/x hours.
The second trip will take 660/(x+5) hours.
We want to find x such that (660/x) - 660/(x+5) = 1 (i.e. solving this equation for x).
Multiply both sides by x*(x+5):
660*(x+5) - 660x = x*(x+5)
660x + 3300 - 660x = x2 + 5x
x2 + 5x - 3300 = 0
(x - 55)*(x + 60) = 0
So either x = 55 or x = -60. Since x > 0, x = 55mph.
