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2 years ago

Identify the domain of the following rational expression:

Mathematics

1 answer:

dangina [55]2 years ago

6 0

Answer: D

Step-by-step explanation:

The domain of a function is the allowed 'x' values that the function can take on and produce a defined 'y' value. We can ignore the numerator since it will never be undefined. The denominator on the other hand has a singularity when it equals zero. The reason for this is because we cannot divide by zero. Therefore, lets set the denominator to zero and find which 'x' value makes the function undefined:

$3x+15=0$

$3x=-15$

$x=-5$

Every single real 'x' value will work besides when x = -5. Therefore the answer is D

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If x is a positive integer, which is equivalent to (root(4, x ^ 3))/(root(5, x ^ 2)) ? Assume x>0

Fittoniya [83]

Answer:

For sure the answer is not B

4 0

3 years ago

Consider the polynomials p(x) = 3x + 27x^2 and q(x)= 2 . Find the x -coordinate(s) of the point(s) of intersection of these two

Tom [10]

Answer:

The x -coordinate(s) of the point(s) of intersection of these two polynomials are $x=\frac{2}{9}\approx0.2222,\:x=-\frac{1}{3}\approx-0.3333$

The sum of these x -coordinates is $\frac{2}{9}+\left(-\frac{1}{3}\right)=-\frac{1}{9}$

Step-by-step explanation:

The intersections of the two polynomials, p(x) and q(x), are the roots of the equation p(x) = q(x).

Thus, $3x + 27x^2=2$ and we solve for x

$3x+27x^2-2=2-2\\27x^2+3x-2=0\\\left(27x^2-6x\right)+\left(9x-2\right)\\3x\left(9x-2\right)+\left(9x-2\right)\\\left(9x-2\right)\left(3x+1\right)=0$

Using Zero Factor Theorem: = 0 if and only if = 0 or = 0

$9x-2=0\\9x=2\\x=\frac{2}{9}$

$3x+1=0\\3x=-1\\x=-\frac{1}{3}$

The solutions are:

$x=\frac{2}{9}\approx0.2222,\:x=-\frac{1}{3}\approx-0.3333$

The sum of these x -coordinates is

$\frac{2}{9}+\left(-\frac{1}{3}\right)=-\frac{1}{9}$

We can check our work with the graph of the two polynomials.

4 0

4 years ago

Imagine your friend is writing an argument to convince adults that they should allow teens to own and use smartphones. Read her

Blababa [14]

I think it is the 2nd one

5 0

3 years ago

Sarah hiked a path that took her from 34 feet below sea level to 52 feet above sea level . What was the change in her elevation?

Ugo [173]

Answer:

86 ft

Step-by-step explanation:

<em>First method: Logical thinking</em>

Think of the position 34 ft below sea level as -34.

The position above sea level is 52.

You need to find the distance between -34 and 52.

You go from 34 ft below sea level, -34 to 0. That is 34 ft.

Then you go from sea level, 0 ft, to 52 ft above sea level. That is 52 ft.

The total is 34 ft + 52 ft = 86 ft

Answer: 86 ft

<em>Second method: Calculate a distance in math</em>

The distance between two points on a number line is the absolute value of the difference of their coordinates. The coordinates are -34 and 52. Subtract the numbers in either order, and take the absolute value of the difference.

|-34 - 52| = |-86| = 86

If you did it in the other order, you'd get the same answer.

|52 - (-34)| = |52 + 34| = |86| = 86

Answer: 86 ft

4 0

3 years ago

(19, 18), (-11, -14)

Readme [11.4K]

Answer:16/15

Step-by-step explanation:

slope= $\frac{y_{2}- y_{1} }{x_{2}-x_{1} }$