The correct answer is Option C. Ty saved $14 and he earns $9 each week. How many weeks will it take till he has $100?
Further explanation:
Given equation is:
9x+14
We will look at the options one by one
<u>A.9 dogs and 14 dogs and 14 cats cost $100</u>
If this option has to be considered, there will be atleast two variables involved one for the dogs and one for the cats while the given equation only involves one variable so this is not the correct option.
<u>B. Ty wants to buy 14 dogs, but they cost $100, how much more does he need?</u>
The given scenario cannot be linked to given equation if x represents dogs the equation will be something like 14x=100 so this option is not the correct answer.
<u>C. Ty saved $14 and he earns $9 each week. How many weeks will it take till he has $100?</u>
The number 14 will be constant as this is the value which is used only once while ty earns 9 dollar per week if x represents number of weeks then the equation to represent the scenario will be
9x+14=100
The value of x will give us the number of weeks required.
The correct answer is Option C. Ty saved $14 and he earns $9 each week. How many weeks will it take till he has $100?
Keywords: Linear equations, linear inequality
Learn more about linear equations at:
#LearnwithBrainly
Since the 2 and x^1/4 are multiplying we can do the math separately and then just multiply them afterwards
2^-4 is the same as 1/(2^4) which is 1/16
(x^1/4)^-4 (POWER RULES REVIEW)
2 exponents of same base you just add (basically multiply the two)
so x^(1/4x-4) = x^(-1)
which is just 1/x
so the answer is 1/16x
(6x4)(4x3)
Hope this helps you. I accidentally wrote my answer in the comment box.
Answer:
64
Step-by-step explanation:
Youd do 8x8 because the base of the triangles are 8 and a square has equal sides all around
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)
