2v=3-7
2v=-4 divide both sides
v=-2
Solve:
"<span>twice the number minus three times the reciprocal of the number is equal to 1."
3(1)
Let the number be n. Then 2n - ------- = 1
n
Mult all 3 terms by n to elim. the fractions:
2n^2 - 3 = n. Rearranging this, we get 2n^2 - n - 3 = 0.
We need to find the roots (zeros or solutions) of this quadratic equation.
Here a=2, b= -1 and c= -3. Let's find the discriminant b^2-4ac first:
disc. = (-1)^2 - 4(2)(-3) = 1 + 24 = 25.
That's good, because 25 is a perfect square.
-(-1) plus or minus 5 1 plus or minus 5
Then x = ------------------------------ = --------------------------
2(2) 4
x could be 6/4 = 3/2, or -5/4.
You must check both answers in the original equation. If the equation is true for one or the other or for both, then you have found one or more solutions.</span>
The math club could rent the room for up to 8 hours. I have also attached a picture of the work in case you need it.
Answer:
See below
Step-by-step explanation:
Remember that quadratic functions are parabolas when graphed. The solutions are where the parabola crosses the x-axis.
1. The vertex of the parabola in f(x) is (0, 9) which is above the x-axis and the parabola opens up. So the parabola does not cross the x-axis. Therefore the solutions are imaginary.
2. The vertex of the parabola in g(x) is (9, 0) which is on the x-axis and parabola opens up. Therefore, there is a double solution.
3. The vertex of the parabola in h(x) is (-1, -9) which is below the x-axis and the parabola opens up. Therefore, there are two real solutions.
I know this is a long explanation, but that is a way of looking at the problem.
Answer:
B: 22.5 degrees
Step-by-step explanation:
The interior angles of a pentagon add up to 540 degrees
(if you dont believe me you can turn a pentagon into three triangles, 3x180 = 540)
So you have four same angles say measure "x" degrees, and one final one that measures "5x" degrees, so 9x = 540, and x = 60
Unless I read the problem wrong, 60 degrees is the answer which is not an option :P
Edit: Yea I read it wrong, the final angle is 5 times the other four angles COMBINED, so that angle measures "20x" degrees.
The total would be 24x = 540, and so x = 22.5
