Answer: Choice A
The number line graph is visually showing every number that is 19 or smaller; hence ![x \le 19](https://tex.z-dn.net/?f=x%20%5Cle%2019)
Note the use of a closed or filled in circle at the endpoint (in contrast to an open circle). This indicates we are including the endpoint 19 as part of the solution set, and that's why we go for "or equal to" as part of the inequality sign.
The correct works are:
.![\frac{Blue(s + h) - Blue(s)}{h} = 4s + 2h](https://tex.z-dn.net/?f=%5Cfrac%7BBlue%28s%20%2B%20h%29%20-%20Blue%28s%29%7D%7Bh%7D%20%3D%204s%20%2B%202h)
<h3>Function Notation</h3>
The function is given as:
![Blue(s) = 2s^2 + 3](https://tex.z-dn.net/?f=Blue%28s%29%20%3D%202s%5E2%20%2B%203)
The interpretation when Steven is asked to calculate Blue(s + h) is that:
Steven is asked to find the output of the function Blue, when the input is s + h
So, we have:
![Blue(s + h) = 2(s + h)^2 + 3](https://tex.z-dn.net/?f=Blue%28s%20%2B%20h%29%20%3D%202%28s%20%2B%20h%29%5E2%20%2B%203)
Evaluate the exponent
![Blue(s + h) = 2(s^2 + 2sh + h^2) + 3](https://tex.z-dn.net/?f=Blue%28s%20%2B%20h%29%20%3D%202%28s%5E2%20%2B%202sh%20%2B%20h%5E2%29%20%2B%203)
Expand the bracket
![Blue(s + h) = 2s^2 + 4sh + 2h^2 + 3](https://tex.z-dn.net/?f=Blue%28s%20%2B%20h%29%20%3D%202s%5E2%20%2B%204sh%20%2B%202h%5E2%20%2B%203)
So, the correct work is:
![Blue(s + h) = 2s^2 + 4sh + 2h^2 + 3](https://tex.z-dn.net/?f=Blue%28s%20%2B%20h%29%20%3D%202s%5E2%20%2B%204sh%20%2B%202h%5E2%20%2B%203)
<h3>Simplifying Difference Quotient</h3>
In (a), we have:
![Blue(s + h) = 2s^2 + 4sh + 2h^2 + 3](https://tex.z-dn.net/?f=Blue%28s%20%2B%20h%29%20%3D%202s%5E2%20%2B%204sh%20%2B%202h%5E2%20%2B%203)
![Blue(s) = 2s^2 + 3](https://tex.z-dn.net/?f=Blue%28s%29%20%3D%202s%5E2%20%2B%203)
The difference quotient is represented as:
![\frac{f(x + h) - f(x)}{h}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%20%2B%20h%29%20-%20f%28x%29%7D%7Bh%7D)
So, we have:
![\frac{Blue(s + h) - Blue(s)}{h} = \frac{2s^2 + 4sh + 2h^2 + 3 - 2s^2 - 3}{h}](https://tex.z-dn.net/?f=%5Cfrac%7BBlue%28s%20%2B%20h%29%20-%20Blue%28s%29%7D%7Bh%7D%20%3D%20%5Cfrac%7B2s%5E2%20%2B%204sh%20%2B%202h%5E2%20%2B%203%20-%202s%5E2%20-%203%7D%7Bh%7D)
Evaluate the like terms
![\frac{Blue(s + h) - Blue(s)}{h} = \frac{4sh + 2h^2}{h}](https://tex.z-dn.net/?f=%5Cfrac%7BBlue%28s%20%2B%20h%29%20-%20Blue%28s%29%7D%7Bh%7D%20%3D%20%5Cfrac%7B4sh%20%2B%202h%5E2%7D%7Bh%7D)
Evaluate the quotient
![\frac{Blue(s + h) - Blue(s)}{h} = 4s + 2h](https://tex.z-dn.net/?f=%5Cfrac%7BBlue%28s%20%2B%20h%29%20-%20Blue%28s%29%7D%7Bh%7D%20%3D%204s%20%2B%202h)
Hence, the correct work is:
![\frac{Blue(s + h) - Blue(s)}{h} = 4s + 2h](https://tex.z-dn.net/?f=%5Cfrac%7BBlue%28s%20%2B%20h%29%20-%20Blue%28s%29%7D%7Bh%7D%20%3D%204s%20%2B%202h)
Read more about function notations at:
brainly.com/question/13136492
Use Cymath !! best math app !
Answer: -3/2
Step-by-step explanation:
The axis of symmetry, and thus the x-coordinate of the vertex, is given by ![x=-\frac{b}{2a}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7Bb%7D%7B2a%7D)
So, the answer is ![x=-\frac{9}{2(3)}=\boxed{-\frac{3}{2}}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B9%7D%7B2%283%29%7D%3D%5Cboxed%7B-%5Cfrac%7B3%7D%7B2%7D%7D)
Answer:
Lisa's team have played 24 home games and 25 away games.
Step-by-step explanation:
Given:
Let
represents games played at home.
also
represent games played away.
Total number of games played = 49
∴ ![x+y=49 \ \ \ \ equation \ 1](https://tex.z-dn.net/?f=x%2By%3D49%20%5C%20%5C%20%5C%20%5C%20%20equation%20%5C%201)
Now according to given data:
Number of home games won = ![\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D)
Number of away game won = ![\frac{2}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D)
Total games won =26
Hence
![\frac{2}{3}x+\frac{2}{5}y=26\\\\\frac{2\times 5}{3\times 5}x+\frac{2\times 3}{5\times 5}y=26\\\\\frac{10}{15}x+\frac{6}{15}y=26\\\\\frac{10x+6y}{15}=26\\\\10x+6y= 26\times 15\\10x+6y = 390\\2(5x+3y)=390\\5x+3y=\frac{390}{5}\\\\5x+3y=195 \ \ \ \ equation \ 2\\](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7Dx%2B%5Cfrac%7B2%7D%7B5%7Dy%3D26%5C%5C%5C%5C%5Cfrac%7B2%5Ctimes%205%7D%7B3%5Ctimes%205%7Dx%2B%5Cfrac%7B2%5Ctimes%203%7D%7B5%5Ctimes%205%7Dy%3D26%5C%5C%5C%5C%5Cfrac%7B10%7D%7B15%7Dx%2B%5Cfrac%7B6%7D%7B15%7Dy%3D26%5C%5C%5C%5C%5Cfrac%7B10x%2B6y%7D%7B15%7D%3D26%5C%5C%5C%5C10x%2B6y%3D%2026%5Ctimes%2015%5C%5C10x%2B6y%20%3D%20390%5C%5C2%285x%2B3y%29%3D390%5C%5C5x%2B3y%3D%5Cfrac%7B390%7D%7B5%7D%5C%5C%5C%5C5x%2B3y%3D195%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%202%5C%5C)
Now multiplying equation 1 by 3 we get,
![3(x+y)=3\times49\\3x+3y=147 \ \ \ \ \ equation \ 3\\](https://tex.z-dn.net/?f=3%28x%2By%29%3D3%5Ctimes49%5C%5C3x%2B3y%3D147%20%5C%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%203%5C%5C)
Now Subtracting equation 2 by equation 3 we get,
![(5x+3y=195)-(3x+3y=147)\\2x=48\\x= \frac{48}{2}=24](https://tex.z-dn.net/?f=%285x%2B3y%3D195%29-%283x%2B3y%3D147%29%5C%5C2x%3D48%5C%5Cx%3D%20%5Cfrac%7B48%7D%7B2%7D%3D24)
Substituting value of x in equation 1 we get.
![x+y=49\\24+y=49\\y=49-24=25](https://tex.z-dn.net/?f=x%2By%3D49%5C%5C24%2By%3D49%5C%5Cy%3D49-24%3D25)
Hence Lisa's team have played 24 home games and 25 away games.