Answer:
<h2>Leah is actually wrong, because those rectangles are similar.</h2>
Step-by-step explanation:
Remember that similarity is about having proportional sides and congruent angles. When we have congruent sides, then those rectangles are congruent not similar.
In this case, to find the similarity, Leah should compare bases and heights thorugh division, because the ratio between heights and the ratio between bases must be equal. So, let's divide.
![\frac{21}{6}=3.5](https://tex.z-dn.net/?f=%5Cfrac%7B21%7D%7B6%7D%3D3.5)
![\frac{7}{2}=3.5](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B2%7D%3D3.5)
As you can observe, both ratios are equal.
Therefore, those rectangles are congruent.
This is very easy question write all given and common
Answer:
x = 1/3
Step-by-step explanation:
1 = 1/x -2
add 2 to both sides
3 = 1/x
x = 1/3
Answer:
Stdivise 7 aep-by-step explanation:
![\displaystyle\lim_{(x,y)\to(0,0)}\frac{\left(x+23y)^2}{x^2+529y^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7B%28x%2Cy%29%5Cto%280%2C0%29%7D%5Cfrac%7B%5Cleft%28x%2B23y%29%5E2%7D%7Bx%5E2%2B529y%5E2%7D)
Suppose we choose a path along the
![x](https://tex.z-dn.net/?f=x)
-axis, so that
![y=0](https://tex.z-dn.net/?f=y%3D0)
:
![\displaystyle\lim_{x\to0}\frac{x^2}{x^2}=\lim_{x\to0}1=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto0%7D%5Cfrac%7Bx%5E2%7D%7Bx%5E2%7D%3D%5Clim_%7Bx%5Cto0%7D1%3D1)
On the other hand, let's consider an arbitrary line through the origin,
![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
:
![\displaystyle\lim_{x\to0}\frac{(x+23kx)^2}{x^2+529(kx)^2}=\lim_{x\to0}\frac{(23k+1)^2x^2}{(529k^2+1)x^2}=\lim_{x\to0}\frac{(23k+1)^2}{529k^2+1}=\dfrac{(23k+1)^2}{529k^2+1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto0%7D%5Cfrac%7B%28x%2B23kx%29%5E2%7D%7Bx%5E2%2B529%28kx%29%5E2%7D%3D%5Clim_%7Bx%5Cto0%7D%5Cfrac%7B%2823k%2B1%29%5E2x%5E2%7D%7B%28529k%5E2%2B1%29x%5E2%7D%3D%5Clim_%7Bx%5Cto0%7D%5Cfrac%7B%2823k%2B1%29%5E2%7D%7B529k%5E2%2B1%7D%3D%5Cdfrac%7B%2823k%2B1%29%5E2%7D%7B529k%5E2%2B1%7D)
The value of the limit then depends on
![k](https://tex.z-dn.net/?f=k)
, which means the limit is not the same across all possible paths toward the origin, and so the limit does not exist.