At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path. The bicyclist head
2 answers:
Answer:
Rates of two bicyclists are 18 km per hour and 14 km per hour.
Step-by-step explanation:
At 9:00 on Saturday morning, two bicyclists passes each other in opposite directions on a bicycle path.
Let the speed of a bicyclist heading north is = x km per hour
It is given that the speed of the bicyclist heading south is 4 km per hours less than the speed of the bicyclist heading north.
Therefore speed of bicyclist heading south will be = (x - 4) km per hour
After 1 hour and 15 minutes or 1.25 hours these bicyclists are 40 km apart.
Since distance = speed × time
So the equation will be
x(1.25) + (x - 4)(1.25) = 40
(1.25)(x - 4 + x) = 40
(1.25)(2x - 4) = 40
2x - 4 =
2x = 32 + 4
2x = 36
x = 18 km per hour will be the speed of the bicyclist heading north.
Speed of the bicyclist heading south = (x - 4) km per hour
= 18 - 4
= 14 km per hour
Therefore, rates of two bicyclists are 18 km per hour and 14 km per hour.
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The output y is
Explanation:
The expression is
We need to determine the output y, when the value of input is x is 5.
That is, substituting in
, we get,
Multiplying the value within the bracket, we have,
Subtracting the terms, we get,
Thus, the value of output y is
Answer:
The final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.
Step-by-step explanation:
General Formula
<em>A way to solve this problem is as follows</em>:
The general formula for this is taking into account that:
The <em>starting point</em> is number 784.
The most important key is the solution for this answer is that:
Where <em>x</em> is a number that we need to find. Then
[1]
Is 784 increased or decreased after all?
We also need to evaluate the following: if a quantity decreases a percentage, and then increases in another percentage, what is the final percentage? In this case, we have first that 784 decreases by 1% and then increases by 4%. As a result 784 will +4% - 1% = +3%, that is, 784 will increase in 3%.
Finding the result
If 784 increases by 3%, we have:
Which is equal to
Solving for <em>x</em>, we first multiply by 784 to both sides of the previous formula:
Remember that if we add, subtract, multiply, divide... to both sides of the equation, we do not "alter" this equation.
Subtracting 784 to both sides:
Multiplying by -1 to both sides:
We have to remember that:
Then
Therefore, using formula [1], an increase of 3% is
Since an increase of 3% is 23.52, we have to add this to the starting point 784, and finally the amount is 784 + 23.52 = 807.52.
As a result, the final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.
In a more <em>terse way</em> of solving this problem, we can say that:
Increase of 4% = 784 * 0.04 = 31.36.
Decrease of 1% = 784 * 0.01 = 7.84.
Difference = 31.36 - 7.84 = 23.52.
Then, we need to add this value to 784, and 784 + 23.52 = 807.52 (the same result).
<h2>Answer:</h2><h2>Step-by-step explanation:</h2>
I've drawn a graph in order to a better understanding of this problem. We know that:
BC is perpendicular to AC
∠DBE = 2x - 1
∠CBE = 5x - 42
Let's call the intersection of line BC and AC the point P, so:
∠P=90°
And points B, P and C form the triangle ΔBPC. On the other hand, ∠CBE and ∠PCB are Alternate Interior Angles, so:
∠PCB = ∠CBE = 5x - 42
Moreover:
∠PBC = 2x - 1 - (5x - 42)
∠PBC = 2x - 1 - 5x + 42
∠PBC = -3x + 41
The internal angles of any triangle add up to 180°. Hence for ΔBPC:
90° + ∠PBC + ∠PCB = 180°
90° - 3x + 41 + 5x - 42 = 180°
2x + 89 = 180
2x = 91
x = 45.5°