For the rectangle with given area of 10x^2+11x+3 determine the binomial factors that describes the dimensions. PLEASE HELP

Explanation:

We could use the AC factoring method here. Multiply the first coefficient (10) with the last term (3) to get 10*3 = 30.

We need to find factors of 30 that add to 11

1+30 = 31

2+15 = 17

3+10 = 13

5+6 = 11

we have found the pair of factors that add to 11. So we'll break the 11x into 5x+6x and then use factor by grouping method

10x^2 + 11x + 3

10x^2 + 5x + 6x + 3

(10x^2 + 5x) + (6x + 3)

5x(2x + 1) + 3(2x + 1)

(5x+3)(2x+1)

We see the two factors are 5x+3 and 2x+1.

To check the answer, use either the box method, distribution, or FOIL rule to expand out (5x+3)(2x+1) and you should get 10x^2+11x+3 again.

As an alternative, you can solve 10x^2+11x+3 = 0 through any method you prefer (graphing, completing the square, quadratic formula). The quadratic formula is the best option as it works for any quadratic. The two solutions you should get are x = -3/5 and x = -1/2

Using x = -3/5 and x = -1/2, we can do the following

Note how we have the 5x+3 and 2x+1 as found in the section above. At this point we can stop as we found the factors needed. I'm using the zero product property which says that if A*B = 0, then either A = 0 or B = 0.

step-by-step explanation:

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: