A parabola is a quadratic function, and a quadratic can be expressed in vertex form, which is:
y=a(x-h)^2+k, where (h,k) is the vertex (absolute maximum or minimum point of the quadratic)
In this case we are given that (h,k) is (-5,80) so we have so far:
y=a(x--5)^2+80
y=a(x+5)^2+80, we are also told that it passes through the point (0,-45) so:
-45=a(0+5)^2+80
-45=25a+80 subtract 80 from both sides
-125=25a divide both sides by 25
-5=a, so now we know the complete vertex form is:
y=-5(x+5)^2+80
The x-intercepts occur when y=0 so:
0=-5(x+5)^2+80 add 5(x+5)^2 to both sides
5(x+5)^2=80 divide both sides by 5
(x+5)^2=16 take the square root of both sides
x+5=±√16 which is
x+5=±4 subtract 5 from both sides
x=-5±4 so the x-intercepts are:
x=-1 and -9
Answer: The running speed of Elena is 5 miles/hour and this can be determined by using the formula of speed.
Step-by-step explanation:
A circular running track 1/4 is a mile long.
Elena runs on this track, completing each lap in 1/20 of an hour.
Speed formula is used to determine the speed of Elena. The formula of speed is given by:
----- (1)
where S is the speed, D is the distance and T is the time taken by Elena to run a circle.
Now, put the value of distance D and time T in the equation (1).
Speed = 5 miles/hour
Therefore, the running speed of Elena is 5 miles/hour.
For more information, refer to the link given below:
brainly.com/question/22610586
Answer:
8,640
Step-by-step explanation:
Hope this helped
Answer:
None of the options are correct
О E. 289.2 cm
Step-by-step explanation:
Volume of a cylinder = v = л r² h
л = 3.1416 (aprox)
r = radius
h = height
8177 = 3.1416 * 3² * h
8177 = 3.1416 * 9 * h
8177 = 28.2744 * h
8177/282744 = h
h = 289.2 cm
Answer:
(2 a - b) (18 a - 9 b - 4)
Step-by-step explanation:
Factor the following:
9 (2 a - b)^2 - 4 (2 a - b)
Factor 2 a - b out of 9 (2 a - b)^2 - 4 (2 a - b):
(2 a - b) (9 (2 a - b) - 4)
9 (2 a - b) = 18 a - 9 b:
Answer: (2 a - b) (18 a - 9 b - 4)