Justin and Amy are trying to prove the Triangle Angle Sum Theorem. Justin draws a triangle on a piece of paper, tears off the corners, and arranges them to form a line. Amy constructs a line through one vertex that is parallel to the opposite side and uses the Alternate Interior Angles Theorem to show that the interior angles add up to 180°. Who proved the theorem? Explain. Please Help A.) Both Amy and Justin proved the theorem. Amy used postulates and theorems, while Justin used a demonstration. B.) Only Justin proved the theorem because he demonstrated that the angles formed a line. C.) Neither Amy nor Justin proved the theorem. D.) Only Amy proved the theorem because she used postulates and theorems to construct a logical argument to show that the interior angles in a triangle add up to 180°.

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range:

57.09 minus 7.0435 equals

step-by-step explanation:

just subtrach them both and u get the answer of 50.0465

answer: 12/52

step-by-step explanation: my reasoning is that there are 12 face cards in a deck and a total of 52 cards in all.