The median is going to be 75 since it is in the middle of the box.
Answer:
Step 2
Step-by-step explanation:
Michelle's step in trying to solve the equation is given below:
![\begin{aligned} t-\dfrac35&=\dfrac45\\\\ t-\dfrac35+\dfrac35&=\dfrac45+\dfrac35&\green{\text{Step } 1}\\\\ t&=1&\blue{\text{Step } 2} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20t-%5Cdfrac35%26%3D%5Cdfrac45%5C%5C%5C%5C%20t-%5Cdfrac35%2B%5Cdfrac35%26%3D%5Cdfrac45%2B%5Cdfrac35%26%5Cgreen%7B%5Ctext%7BStep%20%7D%201%7D%5C%5C%5C%5C%20t%26%3D1%26%5Cblue%7B%5Ctext%7BStep%20%7D%202%7D%20%5Cend%7Baligned%7D)
Michelle made a mistake in Step 2.
The right hand side of Step 1: ![\dfrac45+\dfrac35\neq 1](https://tex.z-dn.net/?f=%5Cdfrac45%2B%5Cdfrac35%5Cneq%201)
Rather, the correct sum is:
![\dfrac45+\dfrac35=\dfrac75\\\\=1\dfrac25](https://tex.z-dn.net/?f=%5Cdfrac45%2B%5Cdfrac35%3D%5Cdfrac75%5C%5C%5C%5C%3D1%5Cdfrac25)
Answer:
![y = {x}^{2} - 2](https://tex.z-dn.net/?f=y%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20-%202)
Or if you want with the value of h too.
![y = {(x - 0)}^{2} - 2](https://tex.z-dn.net/?f=y%20%3D%20%20%7B%28x%20-%200%29%7D%5E%7B2%7D%20%20-%202)
Step-by-step explanation:
![y = a {(x - h)}^{2} + k](https://tex.z-dn.net/?f=y%20%3D%20a%20%7B%28x%20-%20h%29%7D%5E%7B2%7D%20%20%2B%20k)
Find the value of h and k by using the formula.
![h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a}](https://tex.z-dn.net/?f=h%20%3D%20%20-%20%20%5Cfrac%7Bb%7D%7B2a%7D%20%20%5C%5C%20k%20%3D%20%20%5Cfrac%7B4ac%20-%20%20%7Bb%7D%5E%7B2%7D%20%7D%7B4a%7D%20)
From y = x²-2
![a = 1 \\ b = 0 \\ c = - 2](https://tex.z-dn.net/?f=a%20%3D%201%20%5C%5C%20b%20%3D%200%20%5C%5C%20c%20%3D%20%20-%202)
Substitute these values in the formula.
![h = - \frac{0}{2(1)} \\ h = 0](https://tex.z-dn.net/?f=h%20%3D%20%20-%20%20%5Cfrac%7B0%7D%7B2%281%29%7D%20%20%5C%5C%20h%20%3D%200)
Therefore, h = 0.
![k = \frac{4(1)( - 2) - {0}^{2} }{4(1)} \\ k = \frac{ - 8}{4} \\ k = - 2](https://tex.z-dn.net/?f=k%20%3D%20%20%5Cfrac%7B4%281%29%28%20-%202%29%20-%20%20%7B0%7D%5E%7B2%7D%20%7D%7B4%281%29%7D%20%20%5C%5C%20k%20%3D%20%20%5Cfrac%7B%20-%208%7D%7B4%7D%20%20%5C%5C%20k%20%3D%20%20-%202)
Therefore, k = - 2.
From the vertex form, the vertex is at (h, k) = (0,-2). Substitute h = 0, a = 1 and k = -2 in the equation.
![y = a {(x - h)}^{2} + k \\ y = 1 {(x - 0)}^{2} - 2 \\ y = {(x)}^{2} - 2 \\ y = {x}^{2} - 2](https://tex.z-dn.net/?f=y%20%3D%20a%20%7B%28x%20-%20h%29%7D%5E%7B2%7D%20%20%2B%20k%20%5C%5C%20y%20%3D%201%20%7B%28x%20-%200%29%7D%5E%7B2%7D%20%20-%202%20%5C%5C%20y%20%3D%20%20%7B%28x%29%7D%5E%7B2%7D%20%20-%202%20%5C%5C%20y%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20-%202)
These type of equation where b = 0 can also be both standard and vertex form.
Answer:
<em>a) </em>
<em />
<em>b) The coordinates of P are</em>
<em />![\displaystyle \left( \frac{3\pi}{2},1\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cleft%28%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%2C1%5Cright%29)
Step-by-step explanation:
<u>Translation</u>
The dashed line shows the graph of the function
![y = \sin x](https://tex.z-dn.net/?f=y%20%3D%20%5Csin%20x)
This function has a maximum value of 1, a minimum value of -1, and a center value of 0.
a)
Graph G shows the same function but translated by 2 units up, thus the equation of G is:
![\boxed{G(x)= \sin x + 2}](https://tex.z-dn.net/?f=%5Cboxed%7BG%28x%29%3D%20%5Csin%20x%20%2B%202%7D)
b) The coordinates of P correspond to the value of
![x = \frac{3\pi}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B3%5Cpi%7D%7B2%7D)
The value of G is
![\displaystyle G(\frac{3\pi}{2})= \sin \frac{3\pi}{2} + 2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20G%28%5Cfrac%7B3%5Cpi%7D%7B2%7D%29%3D%20%5Csin%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%20%2B%202)
Since
![\sin \frac{3\pi}{2}=-1](https://tex.z-dn.net/?f=%5Csin%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%3D-1)
![\displaystyle G(\frac{3\pi}{2})= -1+ 2=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20G%28%5Cfrac%7B3%5Cpi%7D%7B2%7D%29%3D%20-1%2B%202%3D1)
The coordinates of P are
![\displaystyle \left( \frac{3\pi}{2},1\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cleft%28%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%2C1%5Cright%29)
Answer: The 3 is the numerator.
The top number is always the numerator.