First, a bit of housekeeping:
<span>The meaning of four consecutive even numbers is 15. Wouldn't that be "mean," not meaning? Very different concepts!
The greatest of these numbers is _______ a^1
"a^1" means "a to the first power. There are no powers in this problem statement. Perhaps you meant just "a" or "a_1" or a(1).
The least of these numbers is ______a^2.
No powers in this problem statement. Perhaps you meant a_2 or a(2)
In this problem you have four numbers. All are even, and there's a spacing of 2 units between each pair of numbers (consecutive even).
The mean, or arithmetic average, of these numbers is (a+b+c+d) / 4, where a, b, c and d represent the four consecutive even numbers. Here this mean is 15. The mean is most likely positioned between b anc c.
So here's what we have: a+b+c+d
------------- = 15
4
This is equivalent to a+b+c+d = 60.
Since the numbers a, b, c and d are consecutive even integers, let's try this:
a + (a+2) + (a+4) + (a+6) = 60. Then 4a+2+4+6=60, or 4a = 48, or a=12.
Then a=12, b=14, c=16 and d=18. Note how (12+14+16+18) / 4 = 15, which is the given mean.
We could also type, "a(1)=12, a(2)=14, a(3) = 16, and a(4) = 18.
</span>
Answer:
f(x) = 4x + 11x2 - 104x + 105 = (x - 3)(x + 7)(4x - 5)
Step-by-step explanation:
f(x) = 4x^3 + 11x2 - 104x + 105
has the coefficients {4, 11 -104, 105}. We perform synthetic division using the given -7 as divisor:
-7 / 4 11 -104 105
-28 119 -105
-----------------------------------
4 -17 15 0
Since the remainder is zero (0), we have shown that -7 is a zero of f(x). The coefficients of the quotient (above) are {4, -17, 15}. Let's try factoring the corresponding polynomial again using synthetic division. Start out by using 5 as divisor and determining whether or not the remaindeer is zero:
5 / 4 -17 15
20 15
-------------------------
4 3 30 No, the remainder is 30 and so 5 is not a
root of this quadratic. Try the divisor 3 instead:
3 / 4 -17 15
12 -15
---------------------------
4 -5 0 Yes, the remainder is 0 and so 3 is a root.
Thus, the given f(x) = 4x + 11x2 - 104x + 105 factors as follows:
f(x) = 4x + 11x2 - 104x + 105 = (x - 3)(x + 7)(4x - 5). Notice that the coefficients of the last factor come from those we found above when using 3 as a divisor in synthetic division.
Is this suppose to be an equation or is there something missing here?
This the problem we are looking at: 6 pounds/18 = 72 ounces /?
To solve this, we have to make the unit of measurement the same. There are 16 ounces in 1 pound. So, there are 72 ounces in 4.5. To find that you just do 72 divided by 16. This is the new problem we are looking at: 6 pounds/18 = 4.5 pounds/?
To find ?, you must divided 6 divided by 4.5 to find the difference between the two to keep the same rate. That equals 1.33333333.
What is done to the numerator, you must do to the denominator to keep the same rate so now you divide 18 divided by 1.33333333 which equals 13.5
So for 72 ounces (4.5 pounds) it will cost $13.50
I hope this helps:)
Answer:
The above function value for 
shows that height of the ball before it was dropped i.e. at time = 0 seconds.
The height of the ball above the ground before it was dropped = 400 ft.
Step-by-step explanation:
Given:
The quadratic function that models the height of the baseball above the ground in feet , 
seconds after it was dropped is given as:
To find and interpret the meaning of the function value in contect of the problem.
Solution:
In order to find , we will replace 
in the given function as 
is a function of time .
Thus, we have:
(Answer)
The above function value for shows that height of the ball before it was dropped i.e. at time = 0 seconds.
The height of the ball above the ground before it was dropped = 400 ft.
