The rate of change of Pete's height from 3 to 5 years can be determined as,
Thus, the required rate of change from 3 to 5 years is 4 in/year.
Answer:
A
Step-by-step explanation:
Hihi. So, this is a nice application of interest rates as well as properties of exponentials/logarithms. As you know, the basic equation for interest rates is A= Pe^(rt) where A is your final amount, P is your initial, r is your rate of interest, and t is the time the money was accumulating interest. After cleaning up, you get in a situation due to you having e still lying around. Luckily, if you take the natural log of e, all you have left behind is the previous exponent. Thus, you can take the natural log of both sides, divide by 4, and then simplify to see that your final interest rate is ~6%
<span>x^2 + 15x + 56.25 = 105.25
"Completing the square" is one of many different techniques for solving a quadratic equation. What you do is add a constant to both sides of the equation such that the lefthand side can be factored into the form a(x+d)^2. For instance, squaring (X+D) = X^2 + 2DX + D^2. Notice the 2DX term. That is the same term as the 15x term in the problem. So 2D = 15, D = 7.5. And D^2 = 7.5^2 = 56.25.
So we have
x^2 + 15x + 56.25 = 49 + 56.25
Which is
x^2 + 15x + 56.25 = 105.25
Which is the answer desired.
Now the rest of this is going beyond the answer. Namely, it's answering the question "Why does complementing the square help?"
Well, we know that the left hand side of the equation can now be written as
(x+7.5)^2 = 105.25
Now take the square root of each side
(x+7.5) = sqrt(105.25)
And let's use both the positive and negative square roots.
So
x+7.5 = 10.25914226
and
x+7.5 = -10.25914226
And let's find X.
x+7.5 = 10.25914226
x = 2.759142264
x+7.5 = -10.25914226
x = -17.75914226
So the roots for x^2 + 15x - 49 is 2.759142264, and -17.75914226</span>
Answer:
Kenneth will earn about $ 504 the next week
Step-by-step explanation:
The first thing we will have to figure out is how much Kenneth earns per hour. Then we can get how much he will earn when he wors for 42 hours.
to get Kenneth's wage per hour, we will divide the sum he is paid in the first week by the number of hours he worked that week.
This is 450/ 37.5 = 12 dollars per hour.
Kenneth earns $12 per hour.
If Kenneth works for 42 hours, he will earn 42 X 12 = $ 504 the next week
