A set of angles has a ratio of 5 to 2. If the larger angle is 105 degrees then what is the measure of the smaller angle?

5:2

5:105

2:x

=105*2=5x

=210/5x

=smaller angle is euqals to 42 degree's

Step-by-step explanation:

we first note down the ratio

since we given the degree of the larger ratio we write 5 is equal to 105 and 2 is equals to x. we looking for x which is the degree of the smaller angle

after that we cross multiple, when we cross multiple therefore it gives us 105 multiplied by 2 and 5 multiplied x

it will give us 210 and 5x remember we a looking for the value of x

in order for us to remain juss x we divide 210 by 5x

it will give us x= 42

remember x here represent the value of the smaller angle

a negative exponent is translated as follows:

so, we have

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: