The GCF is 36 since 36 can go into 144 (:
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The amount of metal needed to make the metal stud for the costume is 12 unit²
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
Given that the meatal stud does not have a base, hence:
Amount of metal needed = sum of area of triangular faces = 4(1/2 * 2 * 3) = 12 unit²
The amount of metal needed to make the metal stud for the costume is 12 unit²
Find out more on equation at: brainly.com/question/2972832
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Answer:
5 students are left out in the arrangement.
Step-by-step explanation:
If the number of rows = the number of columns
Then there must be an equal arrangement
Since the total number of students in the school is 2121
Then, the students that are left out in this arrangement = 2121 - (√2121 X √2121
Note the result of the square root would only consider the whole number, the digits after the decimal point signifies the remaining number that can't fit into the arrangement
so, √2121 = 46.05 (so 46 would be used)
= 2121 - (46 X 46)
= 2121 - 2116 = 5
Therefore 5 students are left out in the arrangement.
let's notice something on this hyperbola, the fraction that is positive, is the fraction with the "y" variable, that simply means that the hyperbola is opening vertically, namely runs over the y-axis or it has a vertical traverse axis, which means, that, the foci will be a certain "c" distance from the center over the y-axis, well, with that mouthful, let's proceed.
![\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ asymptotes\quad y= k\pm \cfrac{a}{b}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bhyperbolas%2C%20vertical%20traverse%20axis%20%7D%20%5C%5C%5C%5C%20%5Ccfrac%7B%28y-%20k%29%5E2%7D%7B%20a%5E2%7D-%5Ccfrac%7B%28x-%20h%29%5E2%7D%7B%20b%5E2%7D%3D1%20%5Cqquad%20%5Cbegin%7Bcases%7D%20center%5C%20%28%20h%2C%20k%29%5C%5C%20vertices%5C%20%28%20h%2C%20k%5Cpm%20a%29%5C%5C%20c%3D%5Ctextit%7Bdistance%20from%7D%5C%5C%20%5Cqquad%20%5Ctextit%7Bcenter%20to%20foci%7D%5C%5C%20%5Cqquad%20%5Csqrt%7B%20a%20%5E2%20%2B%20b%20%5E2%7D%5C%5C%20asymptotes%5Cquad%20y%3D%20k%5Cpm%20%5Ccfrac%7Ba%7D%7Bb%7D%28x-%20h%29%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\cfrac{(y-3)^2}{1}-\cfrac{(x+2)^2}{4}=1\implies \cfrac{[y-3]^2}{1^2}-\cfrac{[x-(-2)]^2}{2^2}=1~~ \begin{cases} h=-2\\ k=3\\ a=1\\ b=2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ c=\sqrt{a^2+b^2}\implies c=\sqrt{1+4}\implies c=\sqrt{5} \\\\\\ \stackrel{\textit{so then the foci are at}}{(-2~~,~~3\pm \sqrt{5})}\qquad \qquad \qquad \stackrel{\textit{and its vertices are at }}{(-2~~,~~3\pm 1)}\implies \begin{cases} (-2,4)\\ (-2,2) \end{cases}](https://tex.z-dn.net/?f=%5Ccfrac%7B%28y-3%29%5E2%7D%7B1%7D-%5Ccfrac%7B%28x%2B2%29%5E2%7D%7B4%7D%3D1%5Cimplies%20%5Ccfrac%7B%5By-3%5D%5E2%7D%7B1%5E2%7D-%5Ccfrac%7B%5Bx-%28-2%29%5D%5E2%7D%7B2%5E2%7D%3D1~~%20%5Cbegin%7Bcases%7D%20h%3D-2%5C%5C%20k%3D3%5C%5C%20a%3D1%5C%5C%20b%3D2%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20c%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%5Cimplies%20c%3D%5Csqrt%7B1%2B4%7D%5Cimplies%20c%3D%5Csqrt%7B5%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bso%20then%20the%20foci%20are%20at%7D%7D%7B%28-2~~%2C~~3%5Cpm%20%5Csqrt%7B5%7D%29%7D%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Band%20its%20vertices%20are%20at%20%7D%7D%7B%28-2~~%2C~~3%5Cpm%201%29%7D%5Cimplies%20%5Cbegin%7Bcases%7D%20%28-2%2C4%29%5C%5C%20%28-2%2C2%29%20%5Cend%7Bcases%7D)
now let's check for the asymptotes.
![\bf y=3\pm \cfrac{1}{2}[x-(-2)]\implies y=3\pm \cfrac{1}{2}(x+2) \\\\[-0.35em] ~\dotfill\\\\ y=3+ \cfrac{1}{2}(x+2)\implies y=3+\cfrac{x+2}{2}\implies y=\cfrac{6+x+2}{2} \\\\\\ y=\cfrac{x+8}{2}\implies y=\cfrac{1}{2}x+4 \\\\[-0.35em] ~\dotfill\\\\ y=3- \cfrac{1}{2}(x+2)\implies y=3-\cfrac{(x+2)}{2}\implies y=\cfrac{6-(x+2)}{2} \\\\\\ y=\cfrac{6-x-2}{2}\implies y=\cfrac{-x+4}{2}\implies y=-\cfrac{1}{2}x+2](https://tex.z-dn.net/?f=%5Cbf%20y%3D3%5Cpm%20%5Ccfrac%7B1%7D%7B2%7D%5Bx-%28-2%29%5D%5Cimplies%20y%3D3%5Cpm%20%5Ccfrac%7B1%7D%7B2%7D%28x%2B2%29%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20y%3D3%2B%20%5Ccfrac%7B1%7D%7B2%7D%28x%2B2%29%5Cimplies%20y%3D3%2B%5Ccfrac%7Bx%2B2%7D%7B2%7D%5Cimplies%20y%3D%5Ccfrac%7B6%2Bx%2B2%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20y%3D%5Ccfrac%7Bx%2B8%7D%7B2%7D%5Cimplies%20y%3D%5Ccfrac%7B1%7D%7B2%7Dx%2B4%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20y%3D3-%20%5Ccfrac%7B1%7D%7B2%7D%28x%2B2%29%5Cimplies%20y%3D3-%5Ccfrac%7B%28x%2B2%29%7D%7B2%7D%5Cimplies%20y%3D%5Ccfrac%7B6-%28x%2B2%29%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20y%3D%5Ccfrac%7B6-x-2%7D%7B2%7D%5Cimplies%20y%3D%5Ccfrac%7B-x%2B4%7D%7B2%7D%5Cimplies%20y%3D-%5Ccfrac%7B1%7D%7B2%7Dx%2B2)
Answer:
I cant see it....
Step-by-step explanation:
