For this case we have that by definition, the domain of a function, is given for all the values for which the function is defined.
We have:
The given function is not defined when the denominator is equal to zero. That is to say:
To find the roots we factor, we look for two numbers that when multiplied give as a result "8" and when added as a result "-6". These numbers are:
Thus, the factored polynomial is:
That is to say:
Makes the denominator of the function 0.
Then the domain is given by:
All real numbers, except 2 and 4.
Answer:
x |x≠2,4
First you open 2 parenthesis with x in each one:
(x )(x )=0
Then, you place the sign of the second term (the x term) in the first parenthesis.
(x+ )(x )=0
Next, you multiply the signs of the x term and the sign of the constant (the third term).
Since + × - = -, then you place a -.
(x+ )(x- )=0
You look at the constant (-18) and the second term (3). What two numbers multiplied give you -18 but subtracted (since the signs inside the parenthesis are opposite) give you 3? Those numbers are 6 and 3.
Since the result of the substraction need to be 3, you place the 6 with the + sign and the 3 with the negative sign (if you think of it, 6-3=3 but 3-6 = -3. That's the reason behind placing the numbers)
(x+6)(x-3)=0
Therefore,
x+6=0 or x-3=0
x=-6 or x=3
Your roots are -6 and 3.
Answer:
Range =94
σ² = 1,141.564
Standard Deviation = 33.78703
Step-by-step explanation:
First off to find the range, we find the highest value and subtract it to the lowest value. In this situation the values are:
Highest = 99
Lowest = 5
Range = 99 - 5
Range = 94
Now to find the variance of the sample data set, we first need to find for the mean of the data.
The mean of the data with be the sum of all the numbers in the data set divided by the number of samples.
5 + 14 + 26 + 50 + 60 +72 + 79 + 88 + 93 +94 + 99
That would equal 680
Then you divide the number of samples and that is 11 so the next equation is 680 divided by 11
So the then-
Mean = 61.81818
Now to find the variance we simply use the formula:
Now to find the variance we simply use the formula:
σ²=
σ²=
σ²=
σ²=
Now to find the standard deviation, we take the variance and get the square root of it.
Standard Deviation=
Standard Deviation=
HOPE THIS HELPS :)
Answer:
60 in
Step-by-step explanation:
Area = length x width
Area is constant at 1440 in^2
For first rectangle: W1 and L1
For second rectangle: W2 and L2
W1 = 32 in
W2 = W1 - 8 in = 24 in
1440 in^2 = L1 x 32 in = L2 x 24 in
L1 = 45 in
L2 = 60 in