That bracket symbol, with an r in it, means "the absolute value of r".
So r's absolute value is -2 meaning r is two units from zero
r= 2
<h2>
Greetings</h2>
Step-by-step explanation:
1.
When trying to find the weekly rate, we need to simply divide the t by 52:
P = ![120(1.016)^{\frac{t}{52} }](https://tex.z-dn.net/?f=120%281.016%29%5E%7B%5Cfrac%7Bt%7D%7B52%7D%20%7D)
2.
To find the weekly growth rate, we need to recall one of the indicies laws:
![a^{bc} = (a^{b})^{c}](https://tex.z-dn.net/?f=a%5E%7Bbc%7D%20%3D%20%28a%5E%7Bb%7D%29%5E%7Bc%7D)
So the ![120(1.016)^{\frac{t}{52} }](https://tex.z-dn.net/?f=120%281.016%29%5E%7B%5Cfrac%7Bt%7D%7B52%7D%20%7D)
Can be rearranged to:
![120(1.016^\frac{1}{52} )^{t}}](https://tex.z-dn.net/?f=120%281.016%5E%5Cfrac%7B1%7D%7B52%7D%20%29%5E%7Bt%7D%7D)
Which gives the result:
120 x (![1.016^\frac{1}{52} = 1.0003](https://tex.z-dn.net/?f=1.016%5E%5Cfrac%7B1%7D%7B52%7D%20%3D%201.0003)
120(1.0003)![^t](https://tex.z-dn.net/?f=%5Et)
Or 120( 1 + 0.0003)![^t](https://tex.z-dn.net/?f=%5Et)
So the weekly growth rate is 0.0003 x 100 = 0.03
So it is 0.03%
<h2>Hope this helps!</h2>
Answer:
-17x=234
Step-by-step explanation:
Given that:
![\dfrac{2x}{3}-\dfrac{5x}{9}-\dfrac{x}{6}-\dfrac{5x}{12}=\dfrac{13}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B2x%7D%7B3%7D-%5Cdfrac%7B5x%7D%7B9%7D-%5Cdfrac%7Bx%7D%7B6%7D-%5Cdfrac%7B5x%7D%7B12%7D%3D%5Cdfrac%7B13%7D%7B2%7D)
![\dfrac{72x-60x -18x-45x }{108} = \dfrac{13}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B72x-60x%20-18x-45x%20%7D%7B108%7D%20%3D%20%5Cdfrac%7B13%7D%7B2%7D)
![\dfrac{-51x }{108} = \dfrac{13}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B-51x%20%7D%7B108%7D%20%3D%20%5Cdfrac%7B13%7D%7B2%7D)
![-102x = 1404](https://tex.z-dn.net/?f=-102x%20%3D%20%20%20%201404)
![-\dfrac{102x}{6} = \dfrac{1404}{6}](https://tex.z-dn.net/?f=-%5Cdfrac%7B102x%7D%7B6%7D%20%3D%20%5Cdfrac%7B1404%7D%7B6%7D)
-17x = 234
It is the distributivity of the multiplication from the subtraction
8*(d-5)=8*d-8*5=8d-40
Step-by-step explanation:
<u>Step 1: Factor the equation</u>
![f(x) = -16x^{2} + 22x + 3\\f(x) = -(8x + 1)(2x - 3)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-16x%5E%7B2%7D%20%2B%2022x%20%2B%203%5C%5Cf%28x%29%20%3D%20-%288x%20%2B%201%29%282x%20-%203%29)
<u>Step 2: Find the x-intercepts of the graph of f(x)</u>
<u />![-8x - 1 + 1 = 0 + 1\\-8x / -8 = 1 / -8\\x = -1/8](https://tex.z-dn.net/?f=-8x%20-%201%20%2B%201%20%3D%200%20%2B%201%5C%5C-8x%20%2F%20-8%20%3D%201%20%2F%20-8%5C%5Cx%20%3D%20-1%2F8)
![2x - 3 + 3 = 0 + 3\\2x / 2 = 3 / 2\\x = 3/2](https://tex.z-dn.net/?f=2x%20-%203%20%2B%203%20%3D%200%20%2B%203%5C%5C2x%20%2F%202%20%3D%203%20%2F%202%5C%5Cx%20%3D%203%2F2)
<u>Step 3: Describe the end behavior of the graph of f(x)</u>
Since the function is to the power of 2, that means that it is a parabola. And since the leading coefficient is negative, means that the arrows will be pointing down therefore, the end behavior of this graph is as x goes to infinity, f(x) goes to negative infinity and as x goes to negative infinity, f(x) goes to negative infinity.
<u>Step 4: What are the steps you would use to graph f(x)</u>
The first step that I would do is factor the equation. Then I would find the x-intercepts of the graph and plot them on the graph. I would then plug in 0 for all of the x values to get the y intercept. After doing that I would get the vertex using the vertex formula plotting it on the graph. Finally, I would connect all of the dots together to form the graph of the equation.