In circle l, arc mnop is 120° and the radius is 5 units. which statement best describes the length of arc mnop?
circle m with radii lm, ln, lo, and lp so that arc mnop is created
one half the area of circle l
one third the area of circle l
one half the circumference of circle l
one third the circumference of circle l

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:

this is a good question! i'll do some research and come back when i have the answer!

explanation:

the loan estimate encourages consumers to shop. since it is the lenders who are required to issue a standardized loan estimate in a specific time frame, this way consumers are provided an opportunity to compare lenders and their products. otherwise consumer wouldn't know the benefits offered by other lenders.  

if a loan originator does not provide a loan estimate within 3 business days of receiving a completed loan application, that lender is in violation. lenders are required to issue a loan estimate within 3 days of applying for a loan or within 7 days prior to closing. having a loan estimate has following information.

not having loan estimate won't give you an idea of money to be borrowed.

you get to know your interest rates.

you also get to know if your interest rate can or may vary.

not having a good faith estimate can keep you unaware of aforementioned points.