Answer:
1. 8t
2. 510 + 6t
3. 510 - 2t
Step-by-step explanation:
1. Since the hare moves at a speed of 8 metres per second, the distance it moves from the starting line is d = speed × time = 8t
2. Since the rabbit moves at a speed of 6 metres per second, and gets a head start of 510 metres, the distance it moves from the starting line is d = 510 m + speed × time = 510 + 6t
3. The distance the tortoise is ahead of the hare is thus, distance moved by rabbit - distance moved by hare in time, t.
d' = 510 + 6t - 8t
= 510 - 2t
(-2,7) and (14,21)
Find the slope by using the formula

Plug in the numbers.

Write it in point slope form first
y - y1 = m(x - x1)
y - 7 = 7/8(x - -2)
y - 7 = 7/8x + 1.75
+ 7 +7
y = 7/8x + 8.75
Our final equation would be: <span>
y = 7/8x + 8.75</span>
<span>12xy - 9x - 8y + 6 = 3x(4y-3) - 2(4y-3) = (3x-2)(4y-3)</span>
Answer:

Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to

where
(h,k) is the vertex of the parabola
if a>0 -----> the parabola open upward (vertex is a minimum)
if a<0 -----> the parabola open downward (vertex is a maximum)
<u>Verify each case</u>
case A) 
The vertex is the point 

a>0 -----> the parabola open upward (vertex is a minimum)
The range is the interval--------> [5,∞)

case B) 
The vertex is the point 

a<0 -----> the parabola open downward (vertex is a maximum)
The range is the interval--------> (-∞,5]

case C) 
The vertex is the point 

a>0 -----> the parabola open upward (vertex is a minimum)
The range is the interval--------> [4,∞)

case D) 
The vertex is the point 

a<0 -----> the parabola open downward (vertex is a maximum)
The range is the interval--------> (-∞,4]
