Answer:
y=3(x-7)^2+4
Step-by-step explanation:
Answer:
- the value of the function changes sign in the interval
- the function is monotonic in the interval
Step-by-step explanation:
All polynomial functions are continuous, so we know from the intermediate value theorem that if the expression on the left changes sign in the interval [-2, 1] then there will be a zero in that interval. If the function is monotonic in the interval, there can only be one zero.
a) For f(x) = x^3 +x +3 = (x^2 +1)x +3, the values at the ends of the interval are ...
f(-2) = (4+1)(-2) +3 = -7
f(-1) = (1 +1)(-1) +3 = 1
The function value goes from -7 to +1 in the interval, so there exists at least one root in that interval.
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b) The derivative of the function is ...
f'(x) = 3x^2 +1
This is positive for any x, so is positive in the interval [-2, -1]. That is, the function is continuously increasing in that interval, so cannot have more than one crossing of the x-axis. There is exactly one root in the interval [-2, -1].
Answer: There is a 30% chance Ricky will pull out a quarter
Step-by-step explanation:
This problem is quite simple, really. Okay, so first we're gonna figure out how many items in total there are. He has 3 quarters, 5 dimes, and 2 nickels. So 3+5+2 is equal to 10. Since there is 3 quarters out of the 10 different options, here is how many quarters are in the bag (aka the probability that Ricky will pull out a quarter): 3/10. 3/10 is the same thing as 30%, so there is a 30 percent chance Ricky will pull out a quarter.
Answer:
Lets start with the given system of linear equations In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa). So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 ...
Step-by-step explanation: