Answer:
- not a function
- an x-value is repeated
Step-by-step explanation:
A function maps each value of the independent variable to one value of the dependent variable. If an input maps to two or more different outputs, the relation is not a function.
On a graph, two or more different output values for the same input will show up as points vertically aligned with each other. That is, a vertical line will intersect the graph in more than one place. When that happens, we say the graph <em>does not pass the vertical line test, so is not a function.</em>
<em>___</em>
On the graph of these points, we show the vertical line that intersects two of the points of the given relation. The relation fails the vertical line test.
The answer is C, because 8(x + 9) = 8x + 72. Since it now = y-2=8x+72 you add 2 to the other side which = : y=8x +74
Answer:
![\large\boxed{\dfrac{5x\sqrt{x}}{8y^4}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Cdfrac%7B5x%5Csqrt%7Bx%7D%7D%7B8y%5E4%7D%7D)
Step-by-step explanation:
![\sqrt{\dfrac{25x^9y^3}{64x^6y^{11}}}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b},\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}};\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=\dfrac{\sqrt{25}}{\sqrt{64}}\cdot \sqrt{x^{9-6}y^{3-11}}=\dfrac{5}{8}\sqrt{x^3y^{-8}}=\dfrac{5}{8}\sqrt{x^3}\cdot\sqrt{y^{-8}}\\\\\text{use}\ a^na^m=a^{n+m},\ (a^n)^m=a^{nm}\\\\=\dfrac{5}{8}\sqrt{x^{2+1}}\cdot\sqrt{y^{(-4)(2)}}=\dfrac{5}{8}\sqrt{x^2x}\cdot\sqrt{(y^{-4})^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cdfrac%7B25x%5E9y%5E3%7D%7B64x%5E6y%5E%7B11%7D%7D%7D%5Cqquad%5Ctext%7Buse%7D%5C%20%5Csqrt%7Bab%7D%3D%5Csqrt%7Ba%7D%5Ccdot%5Csqrt%7Bb%7D%2C%5C%20%5Csqrt%7B%5Cdfrac%7Ba%7D%7Bb%7D%7D%3D%5Cdfrac%7B%5Csqrt%7Ba%7D%7D%7B%5Csqrt%7Bb%7D%7D%3B%5C%20%5Cdfrac%7Ba%5Em%7D%7Ba%5En%7D%3Da%5E%7Bm-n%7D%5C%5C%5C%5C%3D%5Cdfrac%7B%5Csqrt%7B25%7D%7D%7B%5Csqrt%7B64%7D%7D%5Ccdot%20%5Csqrt%7Bx%5E%7B9-6%7Dy%5E%7B3-11%7D%7D%3D%5Cdfrac%7B5%7D%7B8%7D%5Csqrt%7Bx%5E3y%5E%7B-8%7D%7D%3D%5Cdfrac%7B5%7D%7B8%7D%5Csqrt%7Bx%5E3%7D%5Ccdot%5Csqrt%7By%5E%7B-8%7D%7D%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20a%5Ena%5Em%3Da%5E%7Bn%2Bm%7D%2C%5C%20%28a%5En%29%5Em%3Da%5E%7Bnm%7D%5C%5C%5C%5C%3D%5Cdfrac%7B5%7D%7B8%7D%5Csqrt%7Bx%5E%7B2%2B1%7D%7D%5Ccdot%5Csqrt%7By%5E%7B%28-4%29%282%29%7D%7D%3D%5Cdfrac%7B5%7D%7B8%7D%5Csqrt%7Bx%5E2x%7D%5Ccdot%5Csqrt%7B%28y%5E%7B-4%7D%29%5E2%7D)
![=\dfrac{5}{8}\sqrt{x^2}\cdot\sqrt{x}\cdot\sqrt{(y^{-4})^2}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=\dfrac{5}{8}x\sqrt{x}\cdot y^{-4}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{5x\sqrt{x}}{8y^4}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B5%7D%7B8%7D%5Csqrt%7Bx%5E2%7D%5Ccdot%5Csqrt%7Bx%7D%5Ccdot%5Csqrt%7B%28y%5E%7B-4%7D%29%5E2%7D%5Cqquad%5Ctext%7Buse%7D%5C%20%5Csqrt%7Ba%5E2%7D%3Da%5C%20%5Ctext%7Bfor%7D%5C%20a%5Cgeq0%5C%5C%5C%5C%3D%5Cdfrac%7B5%7D%7B8%7Dx%5Csqrt%7Bx%7D%5Ccdot%20y%5E%7B-4%7D%5Cqquad%5Ctext%7Buse%7D%5C%20a%5E%7B-n%7D%3D%5Cdfrac%7B1%7D%7Ba%5En%7D%5C%5C%5C%5C%3D%5Cdfrac%7B5x%5Csqrt%7Bx%7D%7D%7B8y%5E4%7D)
Answer:
x = 136º
Step-by-step explanation:
well, the sequence goes, 1100, to 1135, to 1170.... notice, is simply adding 35 to get the next term, so the common difference is 35, and the first term is 1100 of course.
![\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=1100\\ d=35\\ a_n=3725 \end{cases} \\\\\\ 3725=1100+(n-1)35\implies 3725=1100+35n-35 \\\\\\ 3725=1065+35n\implies 2660=35n\implies \cfrac{2660}{35}=n\implies 76=n](https://tex.z-dn.net/?f=%5Cbf%20n%5E%7Bth%7D%5Ctextit%7B%20term%20of%20an%20arithmetic%20sequence%7D%0A%5C%5C%5C%5C%0Aa_n%3Da_1%2B%28n-1%29d%5Cqquad%0A%5Cbegin%7Bcases%7D%0An%3Dn%5E%7Bth%7D%5C%20term%5C%5C%0Aa_1%3D%5Ctextit%7Bfirst%20term%27s%20value%7D%5C%5C%0Ad%3D%5Ctextit%7Bcommon%20difference%7D%5C%5C%5B-0.5em%5D%0A%5Chrulefill%5C%5C%0Aa_1%3D1100%5C%5C%0Ad%3D35%5C%5C%0Aa_n%3D3725%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A3725%3D1100%2B%28n-1%2935%5Cimplies%203725%3D1100%2B35n-35%0A%5C%5C%5C%5C%5C%5C%0A3725%3D1065%2B35n%5Cimplies%202660%3D35n%5Cimplies%20%5Ccfrac%7B2660%7D%7B35%7D%3Dn%5Cimplies%2076%3Dn)