Step-by-step explanation:
on line AB
X + 117 = 180 ( Angle sum property )
X = 63°
and
X+Y = 90° (given )
63° + Y = 90°
Y = 27°
To finish the demonstration that the quadrilateral JKLM is a rhombus we need to prove that side JK is congruent with side LM.
The length of a segment with endpoints (x1, y1) and (x2, y2) is calculated as follows:
![\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=%5Csqrt%5B%5D%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Substituting with points L(1,6) and M(4,2) we get:
![\begin{gathered} LM=\sqrt[]{(4-1)^2+(2-6)^2} \\ LM=\sqrt[]{3^2+(-4)^2} \\ LM=\sqrt[]{9+16^{}} \\ LM=5 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20LM%3D%5Csqrt%5B%5D%7B%284-1%29%5E2%2B%282-6%29%5E2%7D%20%5C%5C%20LM%3D%5Csqrt%5B%5D%7B3%5E2%2B%28-4%29%5E2%7D%20%5C%5C%20LM%3D%5Csqrt%5B%5D%7B9%2B16%5E%7B%7D%7D%20%5C%5C%20LM%3D5%20%5Cend%7Bgathered%7D)
Given that opposite sides are parallel, all sides have the same length, and, from the diagram, the quadrilateral is not a square, we conclude that it is a rhombus.
Ashely reads 3 chapters in her book each night. Jordon reads 8 chapters in a book each night. Will reads 2 chapters per night, but they are very long. How many chapters do they read per night all together?
A(x) = 17 - 8x. Hope this helps!
John owes 15 dollars to Bill, then another 2 dollars to Joey. How much money does John have?
Since John has 0 dollars to give, he has (-15)+(-2) =-17 dollars (as 15+2=17, so the same can be applied negatively) as the first 17 dollars he gets has to be given to Bill and Joey
