Answer:
[-3, ∞)
Step-by-step explanation:
There are many ways to find the range but I will use the method I find the easiest.
First, find the derivative of the function.
f(x) = x² - 10x + 22
f'(x) = 2x - 10
Once you find the derivative, set the derivative equal to 0.
2x - 10 = 0
Solve for x.
2x = 10
x = 5
Great, you have the x value but we need the y value. To find it, plug the x value of 5 back into the original equation.
f(x) = x² - 10x + 22
f(5) = 5² - 10(5) + 22
= 25 - 50 +22
= -3
Since the function is that of a parabola, the value of x is the vertex and the y values continue going up to ∞.
This means the range is : [-3, ∞)
Another easy way is just graphing the function and then looking at the range. (I attached a graph of the function below).
Hope this helped!
Answer:
18 years
Step-by-step explanation:
The formula for computing accrued amount A for a principal of P at an interest rate of r(in decimal) compounded n times in a year for t years is given by
Note that r is percentage converted to decimal. So 3% = 3/100 = 0.03
We can rearrange the above equation to:
Taking logs on both sides
This gives
In this particular problem, n = 4, , A= 9600, P = 5600, r =0.03, so r/n = 0.03/4 = 0.0075
1 + r/n = 1+0.0075 = 1.0075
4t = log(9600/5600)/log(1.0075) = log(1.714) / log(1.0075) = 0.234 /0.00325 = 72
t = 72/4 = 18 years
Answer:
B: (4x - 7)(16x^2 + 28x + 49)
Step-by-step explanation:
64x^3-343 can be rewritten as 4^3x^3 - 7^3 or (4x)^3 - 7^3. This is the difference of two cubes. The appropriate formula for factoring such is
a^3 - b^3 = (a - b)(a^2 + ab + b^2). Therefore,
our (4x)^3 - 7^3 = (4x - 7)(16x^2 + 28x + 49). This is Answer B.
Lets look at the number. 76.78. In each of the different place holders the number is higher than 5. Lets do some examples. 74 rounded to the nearest whole number is going to be 70. 76 rounded to the whole number will be 80. The .78 in your question also contributes.
Answer: 80
Opposite operation of multiplication = division.
Simply divide 65 by 5.45
