A triangle has sides with lengths of 13 kilometers, 18 kilometers, and 20 kilometers. Is it a right triangle?

No, it is not a right triangle

Step-by-step explanation:

Lets explain how to check the sides lengths which formed a  right angled triangle

In triangle ABC :

The lengths of the sides of the triangle are 13 km, 18 km, 20 km

∵ The length of the longest sides is 20 km

- Find its square

∵ (20)² = 400

∴ The square of the length of the longest side is 400

∵ The length of the shortest sides are 13 km and 18 km

- Find the sum of their squares

∵ (13)² + (18)² = 169 + 324 = 493

∴ The sum of the squares of the lengths of the shortest sides is 493

∵ 400 ≠ 493

∴ The sides of 13 km, 18 km and 20 km CAN NOT be sides of

   a right triangle

No, it is not a right triangle

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:

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c