72-42=30. Because you need to subtract the boys from the whole group. So, there are 30 girls.
Step-by-step explanation:
x, x+1, x+2 are the 3 consecutive positive integers.
(x+1)(x+2) = 2(x+1) + 2×(x+x+1+x+2)
x² + 3x + 2 = 2x + 2 + 2×(3x + 3)
x² + 3x + 2 = 2x + 2 + 6x + 6 = 8x + 8
x² - 5x - 6 = 0
we can solve this by finding the factoring.
that means we find a, b so that
(x - a)(x - b) = x² - 5x - 6 = 0
because then x = a and x = b are the 2 solutions of the quadratic equation.
we have
x² - ax - bx + ab = x² - (a+b)x + ab = x² - 5x - 6
a+b = 5
ab = -6
that means, either a or b must be 6 and the other -1.
so we get
(x - 6)(x + 1) = 0
x = 6
or
x = -1
since we are only looking for positive integers, the x = -1 solution is invalid, and we get only x = 6 as solution.
therefore the 3 consecutive positive integers are
6, 7, 8
The average rate of change over the interval is 2/9
<h3>How to determine the average rate of change?</h3>
The interval is given as:
-4 ≤ x ≤ 5
From the table, we have:
f(5) = 4
f(-4) = 2
The average rate of change is then calculated as:
This gives
Evaluate
Hence, the average rate of change over the interval is 2/9
Read more about average rate of change at:
brainly.com/question/23715190
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First you need to find the rule or 'equation' that this system goes by before we can solve what H' point is located.
So, to do so, label out the triangles points:
A(-7, 6), B(-5, 3), C(-1, 3) to A'(1, 4), B'(3, 1), C'(7, 1)
Now for A to A' which is -7 to 1 is a 8 point difference and A to A' which is 6 to 4 is a -2 point difference, indicating:
(x + 8, y - 2)
Now:
B(-5, 3) -> (-5 + 8, 3 - 2) = B'(3, 1)
C(-1, 3) -> (-1 + 8, 3 - 2) = C'(7, 1)
Now to simply solve for H to H':
We know H 's coordinates are: (-7, -5)
Now add in the rule and solve:
(-7 + 8, -5 - 2) = ?
Answer: (1, -7)
