A bank loaned out $10,000, part of it at the rate of 6% per year and the rest at 16% per year. If the interest received in one year totaled $1000, how much was loaned at 6%? How much of the $10,000 did the bank loan out at 6%?

  $6,000 was loaned at 6%

Step-by-step explanation:

Let 'a' represent the amount loaned at 6%. Then the amount of interest from the loans was ...

  a·6% + (10000 -a)·16% = 1000

  -0.10a +1600 = 1000 . . . . . simplify

  600 = 0.10a . . . . . . . . . . . . add 0.10a-1000

  6000 = a . . . . . . . . . . . . . . divide by 0.10

The bank loaned $6000 at 6%.

not solvable

step-by-step explanation:

we need more information, or at least an

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: