The florist can order roses bunches of one dozen and lilies in bunches of 8. Last month she ordered the same number of roses as lilies. If she ordered no
more than 100 roses, how many bunches of each could she have ordered?
What is the smallest number of bunches of each that she could have
ordered? Explain your reasoning.
2. Find the GCF from the two numbers, and rewrite the sum using the
distributive property.
A. 12.+18
B.42+14
C.36+27

9514 1404 393

  1. (rose bunches, lily bunches) ∈ {(2, 3), (4, 6), (6, 9), (8, 12)}. The least is (2, 3).

  2. 6(2+3); 14(3+1); 9(4+3)

Step-by-step explanation:

I like Euclid's algorithm for finding the greatest common factor (GCF): divide the larger number by the smaller, and note the remainder. If the remainder is zero, the smaller is the GCF; if not, use the remainder in place of the larger number and repeat.

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1. The GCF of 8 and 12 is 4, so the least common multiple is ...

  LCM(a, b) = ab/GCF(a, b)

  LCM(8, 12) = 8·12/4 = 24

24 roses is 2 bunches; 24 lilies is 3 bunches. Up to 8 bunches of roses can be ordered to keep the number less than 100.

The florist could have ordered these numbers of bunches (roses, lilies):

  (2, 3), (4, 6), (6, 9), (8, 12)

The least order is 2 bunches of roses and 3 bunches of lilies.

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2.

A. GCF = 6, so the factored form is 6(2+3)

B. GCF = 14, so the factored form is 14(3+1)

C. GCF = 9, so the factored form is 9(4+3)

14

step-by-step explanation:

14 x 3 = 42

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: