Answer:
B) (1/2, -8)
Step-by-step explanation:
(1, -6) and (0, -10)
Midpoint formula:
((x1+x2)/2, (y1+y2)/2)
Solving for x:
(x1+x2)/2
(1 + 0)/2
1/2
Solving for y:
(y1+y2)/2
(-6-10)/2
(-16)/2
-8
Answer:
x = 387
Step-by-step explanation:
The wind acts in the opposite direction to the plane when the time is longer.
The wind acts in the same direction as the plane when the time is shorter.
Equation
d = r*t
Givens
- d = 1720
- x = plane's speed
- y = wind speed
- t1 = 5 hours
- t2 = 4 hours.
Substitution
- d = (x + y) * t
- 1720 = (x + y) * 4
- 1720 = (x - y) * 5
Since the two distances are the same, you can equate the right hand sides.
- (x + y) * 4 = (x - y)*5 Remove the brackets.
- 4x + 4y = 5x - 5y Add 5y to both sides
- 4x + 4y + 5y = 5x - 5y + 5y Combine all the terms.
- 4x + 9y = 5x Subtract 4x from both sides
- 9y + 4x - 4x = 5x - 4x Combine
- 9y = x
Now use one of the given equations with the distance
- 1720 = (x + y)*4 Substitute 9y for x
- 1720 = (9y + y) * 4 Combine
- 1720 = 10y * 4 Multiply the right
- 1720 = 40y Divide by 40
- 1720/40 = 40y/40 Do the division
- 43 = y y = wind speek
- 9y = x x = 9*y
- 9*43 = x
- x = 387 miles per hour.
Answer:
y = - 8x² + 6
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (0, 6), thus
y = a(x - 0)² + 6, that is
y = ax² + 6
To find a substitute (- 1, - 2) into the equation
- 2 = a(- 1)² + 6, that is
- 2 = a + 6 ( subtract 6 from both sides )
- 8 = a
y = - 8x² + 6
For the equation to be true, the events A and B must be mutually exclusive.
