24. Every 12 minutes, Bus A completes a trip from P to X to S to X to P. Every 20 minutes, Bus B completes a
trip from Q to X to T to X to Q. Every 28 minutes,
Bus C completes a trip from R to X to U to X to
R. At 1:00 p. m., Buses A, B and C depart from P, Q e-
#T
and R, respectively, each driving at a constant speed,
and each turning around instantly at the endpoint of its
route. Each bus runs until 11:00 p. m. At how many times
R
S
between 5:00 p. m. and 10:00 p. m. will two or more buses
arrive at X at the same time?
(A) 18
(B) 19 (C) 20
(D) 21 (E) 22
25. A sequence of positive integers with 2020 terms is called an FT sequence if each term
after the second is the sum of the previous two terms. For example, if the first two
terms of an FT sequence are 8 and 7, the sequence would begin 8, 7, 15, 22, 37,
For some positive integer m, there are exactly 2415 FT sequences where the first two
terms are each less than 2m and the number of odd-valued terms is more than twice
the number of even-valued terms. What is the value of m?
(A) 21
(B) 69 (C) 115 (D) 35
(E) 105

in the attachment.   i didn't see your choices.   the word which means there is choices.

step-by-step explanation:

(x,y)

x tells you how much left or right you go from the origin

y tells you how much down or up you go from the origin

so for example (-3,2), you go left 3 and up twice. i denoted which of the ordered pairs is which in my graph.

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:

there is nothing below so i cannot

step-by-step explanation:

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct