1) A quadratic will have no real roots when its discriminant is negative
Dividing by 4,
We have a positive coefficient on k^2 so this parabola is a CUP (concave up positive) so has a minimum at the vertex. If the vertex y value is less than zero, the inequality will be true in the range between the zeros.
That's true for
2) We look for the meet of the line and the parabola:
For two intersections we need a positive discriminant:
That's means two negative or two positive, so
or 
Answer:
Step-by-step explanation:
From the question we are told that
Sum of two angle =90
First angle is 15 less than twice the measure of the second angle.
Generally interpreting mathematically we have
Let x be the first angle and second angle y
Therefore
Therefore
Answer:
(6,3)
Explanation
On the x part of the point, you need to find the mean of 10 and 2 which is 6. On the y part of the point, you need to find the mean of 3 and 3 which is 3.
Thus, the point is (6,3)
Formula is:h ( t ) = a t² + v t + h o,where: a = - 16 ft/s², v = 60 ft/s and h o = 3 ft.When the toy rocket reach the ground: h ( t ) = 0.- 16 t² + 60 t + 3 = 0t 1/2 = ( - 60 +/- √( 60² - 4 · 3 · ( -16 ) ) / ( -32 )t 1/2 = ( - 60 +/- √(3600 + 192 ) ) / ( - 32 )t = ( - 60 - 61.58 ) / ( - 32 ) - another solution is negative.t = ( - 121.58 ) : ( - 32 ) = 3.80 sAnswer: C ) 3.80 s
