Determine the value of x in the figure. answers: A) x = 90 B) x = 40 C) x = 45 D) x = 135
1 answer:
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<h3>Answer: 220 combinations</h3>
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Explanation:
We have 12*11*10 = 1320 permutations possible. This is where order matters. However, order does not matter with swim teams as there are no positions or ranks. All that matters is the group overall (rather than any individual in the group).
Consider the set {A,B,C}. We have 3*2*1 = 6 ways to arrange this set of letters. When considering a permutation, there are 6 permutations but only 1 combination since order doesnt matter and ABC is the same as BAC. Therefore, we divide 1320 over 6 to get the final answer of 1320/6 = 220.
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You can use the combination formula with n = 12 and r = 3. Doing so will give the following:
As you can see, we get the same result and note how 1320/6 is also present as well.
Answer:
A function is increasing when the gradient is positive
A function is decreasing when the gradient is negative
<u>Question 7</u>
If you draw a tangent to the curve in the interval x < -2 then the tangent will have a positive gradient, and so the function is increasing in this interval.
If you draw a tangent to the curve in the interval x > -2 then the tangent will have a negative gradient, and so the function is decreasing in this interval.
If you draw a tangent to the curve at the vertex of the parabola, it will be a horizontal line, and so the gradient at x = -2 will be zero.
The function is increasing when x < -2
The function is decreasing when x > -2
<u>Additional information</u>
We can actually determine the intervals where the function is increasing and decreasing by differentiating the function.
The equation of this graph is:
The function is increasing when
The function is decreasing when
This concurs with the observations made from the graph.
<u>Question 8</u>
This is a straight line graph. The gradient is negative, so:
The function is decreasing for all real values of x
But if they want the interval for the grid only, it would be -4 ≤ x ≤ 1
<u>Question 9</u>
If you draw a tangent to the curve in the interval x < -1 then the tangent will have a negative gradient, and so the function is decreasing in this interval.
If you draw a tangent to the curve in the interval x > -1 then the tangent will have a positive gradient, and so the function is increasing in this interval.
If you draw a tangent to the curve at the vertex of the parabola, it will be a horizontal line, and so the gradient at x = -1 will be zero.
The function is decreasing when x < -1
The function is increasing when x > -1