The axis of symmetry is x=-b/2a for f(x), the axis of symmetry is x=0, because there is no b. when x=0, f(x)=4*0²-1=-1, so the vertex is (0, -1) because a in this case is 4, a positive number, the parabola opens upward, -1 is the lowest value.
for g(x), x=-(-8)/2*1=4, f(x)=4²-8*4+5=-11, the vertex is (4,-11) because a is 1 in this case, a positive number, the parabola opens upward, -11 is the lowest value.
for h(x), x=-(-12)/[2*(-3)]=-2, f(x)=-3*(-2)²-12(-2)+1=13, the vertex is (-2,13) because a is -3 in this case, a negative number, 13 is the largest value.
f(x)'s is obviously larger than g(x) (the graph of f(x) is above that of g(x)), but for h(x), since it opens downward from y=13, it overwraps with part of f(x) and g(x), I'm not sure how you can compare that.
but if we look at the vertex alone, g(x) is the least, then f(x), then h(x) is the largest. I hope all this makes sense.
The answer is actually A g(x) is the lowest amount, h(x) being the middle, and f(x) being the largest, I see where you were going with it, but I think you miscalculated f(x), because it is larger than h(x)
To find the answer, first you have to start by finding the percent of the circle in the sector. Convert the radians given to 108 degrees. 108 out of 360 is 30%.
Now, find the area of the circle. It's pi x r^2, so the area is 352.810.
Multiply this by 30% to find our area of 105.84 cm^2
Except k=7, any real number for k would cause the system of equations to have no solution.
Step-by-step explanation:
In general a system of equations can be represented as ax+by=c and dx+ey=f. In order this system of equations to have NO SOLUTIONS a/d=b/a≠c/f. In our example a=6, b=4, c=14, d=3, e=2 and f=k. To apply the formula above, 6/3=4/2≠14/k. Hence k≠7. It can be concluded that except k=7, any real number for k would cause the system of equations to have no solutions.
Just for information, if k=7 the system will have infinitely many solutions.
