39/1.5 = 26 km per hour
51/3 = 17 km per hour
Then you need the mean. 26+17/2 = 21.5 km per hour
If the original angle is x degrees then its supplement is 180 - x degrees.
we have the equation:-
180 - x = 3x + 20
160 = 4x
x = 40
The original angle is 40 degrees and its supplement is 140 degrees
Answer:
x = -8 and x = 4
Step-by-step explanation:
given
f(x) = (x+8) (x - 4)
recall that at any point on the x-axis, y = 0 [i.e f(x) = 0]
hence to find where the graph crosses the x-axis, we simply substitue f(x) = 0 into the equation and solve for x
f(x) = (x+8) (x - 4)
0 = (x+8) (x - 4)
Hence
either,
(x+8) = 0 ----> x = -8 (first crossing point)
or
(x-4) = 0 ------> x = 4 (second crossing point)
Hence the graph crosses the x-axis at x = -8 and x = 4
To find the gradient of the tangent, we must first differentiate the function.
The gradient at x = 0 is given by evaluating f'(0).
The derivative of the function at this point is negative, which tells us <em>the function is decreasing at that point</em>.
The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so
Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).
So the point (0, -1) lies on the tangent. Substituting into the tangent equation:
Answer:
22 hours (B)
Step-by-step explanation:
John's velocity = 55mph
Sally's velocity = 65mph
John's time taken = x
Sally's time taken = x - 4
since they must cover the same distance.
and, distance = vel × time
Sally's vel × time = John's vel × time
55x = 65(x-4)
55x = 65x - 220
-10x = -220
x = 22 hours.
Therefore, Sally catches up after 22 hours
