Given that △XYZ is mapped to △X'Y'Z' using the rules (x, y)→(x+5, y−3) followed by (x, y)→(−x, −y) .
We know that (x,y) => (x+h,y+k) type operation represents translation so rule (x, y)→(x+5, y−3) will cause translation.
We know that (x,y) => (-x,-y) type operation represents rotation about origin so rule (x, y)→(−x, −y) will cause rotation.
So combining both results and comparing with given choices. we find that only 1st choice "△XYZ is congruent to △X'Y'Z' because the rules represent a translation followed by a rotation, which is a sequence of rigid motions."
is correct.
The correct box plot will have the "whiskers" extending to 24 and 49. The first quartile will be around 28.5 and the third quartile will be around 41.8. The median will be at 34.
**your question didn't include the box plots to choose from, so use this information to find which one it is :)
Answer:
Yes it is
Step-by-step explanation:
SOLUTION
Let the two integers be x and y.
Now, the product of x and y, is 80, that is
The quotient of x and y is 5, that is
From equation 2, make x, the subject, we have
Now substitute the x for 5y into equation 1, we have
![\begin{gathered} xy=80 \\ 5y\times y=80 \\ 5y^2=80 \\ \text{dividing by 5} \\ y^2=\frac{80}{5} \\ y^2=16 \\ \text{take square root of both sides } \\ \sqrt[]{y^2}=\sqrt[]{16} \\ \text{square cancels root} \\ y=4 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20xy%3D80%20%5C%5C%205y%5Ctimes%20y%3D80%20%5C%5C%205y%5E2%3D80%20%5C%5C%20%5Ctext%7Bdividing%20by%205%7D%20%5C%5C%20y%5E2%3D%5Cfrac%7B80%7D%7B5%7D%20%5C%5C%20y%5E2%3D16%20%5C%5C%20%5Ctext%7Btake%20square%20root%20of%20both%20sides%20%7D%20%5C%5C%20%5Csqrt%5B%5D%7By%5E2%7D%3D%5Csqrt%5B%5D%7B16%7D%20%5C%5C%20%5Ctext%7Bsquare%20cancels%20root%7D%20%5C%5C%20y%3D4%20%5Cend%7Bgathered%7D)
Now substitute y for 4 into any of the equations.
Let us use equation 1 again, we have
Hence the answer is 4, 20
