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.
Hello!
You first have to find the area of the square grid
To find this you multiply the sides
14 * 14 = 196
Next you have to find the area of the triangle
To find the area of a triangle you use the equation

h is height
b is base
Put in the values you know

Multiply

The area of the triangle is 49 inches squared
You divide the area of the triangle by the area of the square
196 / 49 = 4
The answer is 4 triangles
Hope this helps!
Answer: B) It represents the product of two irrational numbers and is equivalent to an irrational number.
Step-by-step explanation:
1. By a definition an irrational number cannot be written as a simple fraction.
2. Keeping this information on mind:
(Cannot be written as a simple fraction. It is an irrational number).
(Cannot be written as a simple fraction. It is an irrational number).
3. When you multiply this irrational number, you obtain:

4.
is an irrational number.
5. Therefore, the answer is the option B,
The term of this sequence is:
<span>-(17/30)n^5+(113/12)n^4-(173/3)n^3+(1915/12)n^2-(5813/30)n+85 </span>
<span>Therefore,term number 7 is:-146/1=-146 </span>