Answer: E. 40
Step-by-step explanation:
The x-intercept of a line is when the y coordinate is equal to zero, so input zero in for y and solve for x to find the x-intercept.
1/2x + 3/5(0) = 20
1/2x = 20
x = 40
An equilateral triangle has all side lengths the same, and all angles are 60 degrees. Using this we can split the triangle along its altitude to get two right triangles with a hypotenuse of length 10 and a base of 1/2 of the original length, so 5. Now we can either use the Pythagorean theorem (a^2+b^2=c^2) or the fact that it is a 30 60 90 triangle (angles measure at 30 60 and 90 degrees) Pythagorean theorem is probably easier.
It stated that the squares of the two legs of a right triangle add to the square of the hypotenuse. So a(the altitude)^2+5(the base)^2=10(the hypotenuse)^2
A^2+5^2=10^2
A^2+25=100
A^2=75
A=sqrt(75)
A=5*sqrt(3)
Final answer:
The altitude of an equilateral triangle with side length 10 is 5sqrt(3), or about 8.66
145 because I added them and I did the correct answer
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:
8 people or 2/3 of the people choose another drink. Is that what you were asking?
