Draw a triangle on your paper and extend the base of the triangle so it extends past the base angle. The base angle inside the triangle is the interior angle and the one outside the triangle between the extended line and the outside of the interior angle is the exterior angle. A straight line has a measure of 180 degrees. That means that the interior angle + the exterior angle = 180. So they are supplementary by definition of supplementary angles. A is the only choice above that applies.
bearing in mind that parallel lines have exactly the same slope, hmmm what's the slope of that equation above anyway?
![\bf -x+y=5\implies y=x+5\implies y = \stackrel{\stackrel{m}{\downarrow }}{1}x+5\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}](https://tex.z-dn.net/?f=%5Cbf%20-x%2By%3D5%5Cimplies%20y%3Dx%2B5%5Cimplies%20y%20%3D%20%5Cstackrel%7B%5Cstackrel%7Bm%7D%7B%5Cdownarrow%20%7D%7D%7B1%7Dx%2B5%5Cimpliedby%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20slope-intercept~form%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y%3D%5Cunderset%7By-intercept%7D%7B%5Cstackrel%7Bslope%5Cqquad%20%7D%7B%5Cstackrel%7B%5Cdownarrow%20%7D%7Bm%7Dx%2B%5Cunderset%7B%5Cuparrow%20%7D%7Bb%7D%7D%7D%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D)
so we're really looking for the equation of a line whose slope is 1 and runs through (2,-5)
![\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-5})~\hspace{10em} \stackrel{slope}{m}\implies 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{1}(x-\stackrel{x_1}{2}) \\\\\\ y+5=x-2\implies y=x-7](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B2%7D~%2C~%5Cstackrel%7By_1%7D%7B-5%7D%29~%5Chspace%7B10em%7D%20%5Cstackrel%7Bslope%7D%7Bm%7D%5Cimplies%201%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20%5Ctextit%7Bpoint-slope%20form%7D%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y-y_1%3Dm%28x-x_1%29%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D%5Cimplies%20y-%5Cstackrel%7By_1%7D%7B%28-5%29%7D%3D%5Cstackrel%7Bm%7D%7B1%7D%28x-%5Cstackrel%7Bx_1%7D%7B2%7D%29%20%5C%5C%5C%5C%5C%5C%20y%2B5%3Dx-2%5Cimplies%20y%3Dx-7)
Answer:
A. f(-x) = f(x)
Step-by-step explanation:
When plugged into a graph, we can see that the y value of -x is equal to x.
This means, that if we compare the y value of x=3 and x=-3, they will be the same on the graph.
Answer:
2
Step-by-step explanation:
The intersection of A and B is basically how many black 6s there are in a deck. There are 2: the 6 of spades and the 6 of clubs so the answer is 2.