<span> (6y^2 + 4y + 5) – (3 – 7y + y^2)
= </span><span> 6y^2 + 4y + 5 – 3 + 7y - y^2
= 5</span>y^2 + 11y + 2
hope it helps
As you progress in math, it will become increasingly important that you know how to express exponentiation properly.
y = 2x3 – x2 – 4x + 5 should be written <span>y = 2^x3 – x^2 – 4^x + 5. The
" ^ " symbol denotes exponentiation.
I see you're apparently in middle school. Is that so? If so, are you taking calculus already? If so, nice!
Case 1: You do not yet know calculus and have not differentiated or found critical values. Sketch the function </span>y = 2x^3 – x^2 – 4^x + 5, including the y-intercept at (0,5). Can you identify the intervals on which the graph appears to be increasing and those on which it appears to be decreasing?
Case 2: You do know differentiation, critical values and the first derivative test. Differentiate y = 2x^3 – x^2 – 4^x + 5 and set the derivative = to 0:
dy/dx = 6x^2 - 2x - 4 = 0. Reduce this by dividing all terms by 2:
dy/dx = 3x^2 - x - 2 = 0 I used synthetic div. to determine that one root is x = 2/3. Try it yourself. This leaves the coefficients of the other factor, (3x+3); this other factor is x = 3/(-3) = -1. Again, you should check this.
Now we have 2 roots: -1 and 2/3
Draw a number line. Locate the origin (0,0). Plot the points (-1, 0) and (2/3, 0). This subdivides the number line into 3 subintervals:
(-infinity, -1), (-1, 2/3) and (2/3, infinity).
Choose a test number from each interval and subst. it for x in the derivative formula above. If the derivative comes out +, the function is increasing on that interval; if -, the function is decreasing.
Ask all the questions you want, if this explanation is not sufficiently clear.
Answer:
B
Step-by-step explanation:
The results of the survey are shown in the table.
It's required to calculate the following probabilities:
a) A customer is neutral
The row labeled as 'Neutral' has a total of 79 customers out of 367 in total.
The required probability is:
b) A customer is a walk-in
The first column labeled as 'Walk-in' has a total of 106 customers out of 367. The required probability is
c) A customer is dissatisfied and a walk-in.
We have to cross the row Dissatisfied with the column Walk-in. The number of customers that have both categories is 22 out of 367.
The required probability is:
d) A customer is very satisfied given he saw a TV ad.
This is a conditional probability, where the total is 111 because is the given condition. The customers that have both characteristics are 33, thus the required probability is:
e) A customer is satisfied or referred.
Total satisfied = 139
Total referred = 150
With both features = 62
Total customers with one or both features: 139 + 150 - 62 = 227
We have to subtract the common feature because it was counted twice.
The required probability is:
A=7 b =4 and c=9 Because the 7 is the base of the number
