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2 years ago

Find the domain and range

Mathematics

1 answer:

almond37 [142]2 years ago

6 0

Answer:

See answer above.

Step-by-step explanation:

These are the ordered pairs on the graph: (-2, 5), (2, 3), (-3, -2), (0, -5), (3, -6)

The domain is the first point in teach ordered pair and the range is the second number in the ordered pair.

So the domain is {-2, 2 , -3, 0, 3}

Range is {5, 3, -2, -5, -6}

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The sum of the squares of two consecutive positive even integers is 52.Find the integers

ankoles [38]

Answer:

The two consecutive positive integers are $4$ and $6$ .

Step-by-step explanation:

Let $x$ be an even integer, then the next even integer is $(x+2)$ .

The sum of the squares of these even integers is $52$ .

We can write the following equation and solve for $x$ .

$x^2+(x+2)^2=52$ .

We expand to get,

$x^2+x^2+4x+4=52$ .

We simplify to get,

$2x^2+4x+4-52=0$ .

This gives us,

$2x^2+4x-48=0$

We divide through by 2 to get,

$x^2+2x-24=0$ .

This is now a quadratic trinomial

We split the middle term to get,

$x^2+6x-4x-24=0$ .

We factor to obtain,

$x(x+6)-4(x+6)=0$

$\Rightarrow (x+6)(x-4)=0$

$\Rightarrow (x+6)=0 or (x-4)=0$

$\Rightarrow x=-6 or x=4$

We discard $x=-6$ since it is not a positive integer.

$\therefore x=4$

Hence the two consecutive positive even integers are,

$4$

and

$4+2=6$

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