Answer:
Part 1) The rate of change is 
Part 2) The initial value is 68
Part 3) The function rule to the linear model is 
Step-by-step explanation:
we know that
The linear equation in slope intercept form is equal to
where
m is the slope or unit rate
b is the y-intercept or initial value
step 1
Find the slope
take two points from the table
(0,68) and (15,85)
The formula to calculate the slope between two points is equal to
substitute the values
In a linear function , the slope is the same that the rate of change
therefore
The rate of change is
step 2
Find the y-intercept
we know that
The y-intercept is the value of y when the value of x is equal to zero
Looking at the table
For x=0, y=68
therefore
The y-intercept is
The y-intercept is also called the initial value
therefore
The initial value is 68
step 3
Determine the function rule to the linear model
we have
substitute
16 n^2 -10n + 129 = 8n^2 -8
We collect the terms:
8n^2 -10n + 137 = 0
The steps for completing the square:
1) Move the "non X" (or "non N") term to the right:
8n^2 -10n = -137
<span>2)<span> Divide the equation by the coefficient of N² which in this case is 8
n^2 -1.2n = </span></span><span><span>-17.125
</span>
3) Take the coefficient of "N"; divide it by 2; square it; add it to both sides of the equation.
-1.2 / 2 = -.6
-.6^2 = .36
</span>
n^2 -1.2n +.36 = <span>-17.125
+.36
Take the square root of both sides:</span>
(n-.6)*(n-.6) = sq root(
<span>
<span>
<span>
-16.765
</span>
</span>
</span>
)
That's about as far as I can go.
Answer: $40
Step-by-step explanation:
The key formula to use for this problem is the simple interest formula, which is 
; where I is the interest earned, p is the principal (initial) amount, r is the interest rate, and t is the amount of time that passes.
Since we know that both investments have the same interest rate, we can use the information from the first part of the problem to solve for the interest rate. Using algebra, we can rearrange the simple interest formula to solve for the interest rate: 
. We know that our interest earned is $24 and our principal amount is $300. To make things easier, we'll also convert months to years, which is easy to do since we know that 12 months = 1 year. This gives us our value for the amount of time that passes. Now, all we have to do is plug in our values into the rearranged equation above.
We should now have: 
Now, to find the interest earned from the $500 investment, we just need to plug in our values from the second part of the problem, along with our calculated interest rate of 0.08, into the original formula of
This should result in 
Therefore, James will receive $40 on his $500 investment after 12 months.
Answer:
no hacerlo yo mismo
Step-by-step explanation:
