29*2.4-36.5= 33.1 hrs before the freight train cought up.
Answer:
4,684 km
Step-by-step explanation:
Answer:
k = 7
Step-by-step explanation:
The given figures are lines f(x) and g(x)
For the line f(x), we have the y-intercept at (0, -3) and slope = (-1 - (-3))/(-3 - 0) = -2/3
Therefore, line f(x) = y - (-3) = -2/3·(x - 0) which gives f(x) = y = -3 - 2·x/3
For the line g(x), the y-intercept is (0, 4), and the slope is (4 - 2)/(0 - 3) = -2/3
The equation of the line g(x) is therefore, g(x) = y - 4 = -2/3·x, which simplifies to the slope and intercept form as g(x) = y = 4 - 2/3·x
Therefore, given that the transformation of f(x) to g(x) is given as g(x) = f(x) + k, we have;
k = g(x) - f(x) = 4 - 2/3·x - (-3 - 2·x/3) = 4 - 2/3·x + 3 + 2·x/3 = 7
∴ k = 7
<h3>
Answers:</h3><h3>x = sqrt(10)</h3><h3>y = sqrt(5)</h3>
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Explanation:
Naturally I start with x as that letter precedes y in the alphabet; however, it's easier to start with y because it is a leg of this triangle. We will then use the value of y to find x later.
For any 45-45-90 triangle, the two legs are the same length. So that's why we're able to quickly see that y = sqrt(5)
To get the hypotenuse, we multiply the leg length by sqrt(2). This trick only works for 45-45-90 triangles.
hypotenuse = leg*sqrt(2)
x = sqrt(5)*sqrt(2)
x = sqrt(5*2)
x = sqrt(10)
The rule I used is sqrt(a)*sqrt(b) = sqrt(a*b)
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An alternate path is to use the pythagorean theorem to find x
a^2+b^2 = c^2
(sqrt(5))^2 + (sqrt(5))^2 = x^2
5 + 5 = x^2
10 = x^2
x^2 = 10
x = sqrt(10)
Subtract 4 from 8, you get 4, then divide -2 from 4 and get 1, x=1
