Answer:
Below in bold.
Step-by-step explanation:
A. −16x2 + 24x + 16 = 0
-8(2x2 - 3x - 2) = 0
-8(2x + 1 )(x - 2) = 0
x = -0.5, 2.
So the x-intercepts are (-0/5, 0) and (2, 0).
B. As the leading coefficients is negative (-16) the vertex of the graph will be a Maximum.
To find its coordinates we convert the function to vertex form:
f(x) = −16x2 + 24x + 16
= -16(x^2 - 1.5x) + 16
Completing the square on contents of the parentheses:
= -16 [(x - 0.75)^2 - 0.75^2] + 16
= -16(x - 0.75)^2 - 16 * -0.75^2 + 16
= -16(x - 0.75)^2 + 9 + 16
= -16(x - 0.75)^2 + 25.
So the coordinates of the vertex are (0.75, 25)
Students in 2014 = (100% + 33%) × 2,300
students in 2014 = 133% × 2,300
students in 2014 = 133/100 × 2,300
students in 2014 = 3,059
There are 3,059 students in 2014
Answer:
y>−1
Step-by-step explanation:
y-6>-7
Add 6 to both sides
y-6+6 > -7+6
Simplify
y>-1
Answer:
10
Step-by-step explanation:
the radius is from center out.
Step-by-step explanation:
Let the original speed of the train be x km/h.
Time taken to cover a distance of 360 km = 360/x hours.
New speed of the train = (x+5) km/h.
Time taken to cover a distance of 360 km at new speed = 360/x+5 hours.
Since, the train takes 1 hour less time,
∴360/x - 360/ x+5 = 1
⇒360 (5) = x² + 5x
⇒1800 = x² + 5x
⇒x² + 5x - 1800 = 0
⇒x² + 45x - 40x - 1800 = 0
⇒x (x+45) - 40( x +45) = 0
⇒(x+45) (x-40) = 0
⇒x = (-45), 40
But since speed cannot be in negative.
∴x = 40 km/hr.
Hence, the original speed of the train is 40 km/h.
