Mathematics, 15.07.2019 19:00 broyochey1

:when two-thirds of an even number is added to one-quarter of the next consecutive even number, the result is 28. what are the numbers?

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The numbers are: "30" and "32" .

The two (2) consecutive even numbers are: "x" and "(x+2)" .
We are asked to find these numbers.
If we can solve for "x" (one of these numbers); we can solve for "(x+2)" by adding "2" to "x".

→ (⅔) x + (¼) (x + 2) = 28 ; Solve for "x" ;

Note the distributive property of multiplication:

a(b+c) = ab + ac ;

a(b − c) = ab − ac ;

As such: " + (¼) (x + 2) = (¼) x + (¼) (2) = (¼) x + ½ ;

Rewrite the equation: → (⅔) x + (¼) (x + 2) = 28 ;

as: " → (⅔) x + (¼) x + ½  = 28 ;

Multiply the entire equation by "12" ; to get rid of the fractions:

  → 12 * { (⅔) x + (¼) x + ½  = 28 } ;

→ (24/3) x + (12/4)x + (12/2) = 28*(12) ;

→ 8x + 3x + 6 = 336

  → 11x + 6 = 336 ;

Subtract "6" from each side of the equation:

→ 11x + 6 − 6 = 336 − 6 ;

→ 11x = 330 ;

Divide each side of the equation by "11" ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ 11x / 11 = 330 / 11 ;

→ x = 30 ;

The next consecutive even integer is:
"(x + 2)" ; which equals: "30 + 2 = 32" .

The numbers are: "30" and "32" .

Let us check our answer, by plugging the value for "x" in the original equation; to see if it holds true:

→ (⅔) x + (¼) (x + 2) = 28 ;

→ (⅔) (30) + (¼) (30 + 2) = ? 28 ? ;

→ (60/3) + (¼)*(32) = ? 28 ? ;

→ 20 + 8 = ? 28 ? ; Yes!

Answer from: Quest

the answer is a

step-by-step explanation:

Answer from: Quest

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: