Answer:
3(5+x)
Step-by-step explanation:
15+3x
5*3 + 3*x
Factor out 3
3(5+x)
Answer: Option B.
Step-by-step explanation:
Here we can start with the relation
cos(x)^2 + sin(x)^2 = 1
multiply both sides by cos(x)
cos(x) = cos(x)^3 + sin(x)^2*cos(x) = cos(x)^2*(cos(xI + sin(x)^2/cos(x))
now we can replace sin(x)/cos(x) = tg(x)
cos(x) = cos(x)^2*(cos(x) + sin(x)*tan(x))
So the correct option is B
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:
Step-by-step explanation:
a) Set up the variables:
Let <u>x</u> represent the width; Then <u>2x</u> will represent the length.
b) What is the equation that represents the above situation?
<u>Use perimeter formula:</u>
As we set up w = x and l = 2x, and we know that the perimeter is 30 cm, we can build an equation by substituting the values we know or set up:
c) solve the equation
- 30 = 2( 2x + x)
- 30 = 2(3x)
- 30 = 6x
- x = 30/6
- x = 5
d) the length and width are?
- The width is 5 cm and the length is twice the width, 5*2 = 10 cm
Answer:
C
Step-by-step explanation:
2/3=66 therefore it also equals 2/3%
