A quadrilateral MUST be a parallelogram if it has one pair of opposite sides both parallel and congruent. A quadrilateral MUST be a parallelogram if it has both pairs of its opposite angles congruent (or equal in measure). A quadrilateral MUST be a parallelogram if it has both diagonals bisecting each other.
E) 2
Remember that the first derivative of a function is the slope of the function at any specified point. We've been told that f(0) = -5 and that f'(x) is always less than or equal to 3. So let's look at the available options and see what the average slope would have to be in order to get the specified value of f(2).
A) -10: (-10 - -5)/(2 - 0) = -5/2 = -2.5
B) -5: (-5 - -5)/(2 - 0) = 0/2 = 0
C) 0: (0 - -5)/(2 - 0) = 5/2 = 2.5
D) 1: (1 - -5)/(2 - 0) = 6/2 = 3
E) 2: (2 - -5)/(2 - 0) = 7/2 = 3.5
Now taking into consideration the mean value theorem, the value of the function f'(x) has to have the value equal to the average slope between the two points at at least one point between the two given values. For options A, B, C, and D it's possible for f'(x) to return values that make that slope possible. However, for option E, the mean value theorem indicates that f'(x) has to have the value of 3.5 for at least 1 point between x=0 and x=2. And since we've been told that f'(x) is less than or equal to 3 for all possible values of x, that is in conflict and f(2) can not have the value of 2.
Answer:
D. 126
Step-by-step explanation:
Hello there,
The equation that we have to factor is as follows:
2x² + 3x - 54
In order to factor this we first multiply (-54) by 2 and try to find two factor pairs that can be add up to 3.
For this we would use 12 * -9 which gives you -108 when multiplied and when added you would get 3.
2x² + 12x - 9x -54
2x(x + 6) -9(x +6)
(2x - 9) (x + 6)
Now the factor pairs would be: (2x - 9)(x + 6)
Hope I helped,
Amna
Okay, so let's find the average
People with 92: 18(92)
People with 84: 12(84)
1656 + 1008 = 2664
So then we divide by 30
2664 / 30: 88.8
The average is a score of 88.8
