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3 years ago

Can a -150/10 be classified as both a rational number and a integer

1 answer:

6 0

Yes! This is because -150/10 can be simplified to be -15, which is a rational number.

The word “rational” sounds like another math word you’ve heard of before. Do you know what it is?

Well, it’s “ratio”!! Ratios can be seen in the forms x:y and x/y.

ANY RATIONAL NUMBER HAS THE ABILITY TO BE WRITTEN AS A RATIO!! This will completely exclude numbers with super long decimal points (ex: 1.2345678809928374737272828...)

This number also meets the requirements of being an integer. An integer is any whole number (this excludes decimals and fractions)

I know it’s written as a fraction. However, the fraction could be simplified, making it -15, which means this is both a rational number and an integer!!

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Which statement describes the inverse of m(x) = x^2 – 17x?

DochEvi [55]

Given:

The function is

$m(x)=x^2-17x$

To find:

The inverse of the given function.

Solution:

We have,

$m(x)=x^2-17x$

Substitute m(x)=y.

$y=x^2-17x$

Interchange x and y.

$x=y^2-17y$

Add square of half of coefficient of y , i.e., $\left(\dfrac{-17}{2}\right)^2$ on both sides,

$x+\left(\dfrac{-17}{2}\right)^2=y^2-17y+\left(\dfrac{-17}{2}\right)^2$

$x+\left(\dfrac{17}{2}\right)^2=y^2-17y+\left(\dfrac{17}{2}\right)^2$

$x+\left(\dfrac{17}{2}\right)^2=\left(y-\dfrac{17}{2}\right)^2$ $[\because (a-b)^2=a^2-2ab+b^2]$

Taking square root on both sides.

$\sqrt{x+\left(\dfrac{17}{2}\right)^2}=y-\dfrac{17}{2}$

Add $\dfrac{17}{2}$ on both sides.

$\sqrt{x+\left(\dfrac{17}{2}\right)^2}+\dfrac{17}{2}=y$

Substitute $y=m^{-1}(x)$ .

$m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}$

We know that, negative term inside the root is not real number. So,

$x+\left(\dfrac{17}{2}\right)^2\geq 0$

$x\geq -\left(\dfrac{17}{2}\right)^2$

Therefore, the restricted domain is $x\geq -\left(\dfrac{17}{2}\right)^2$ and the inverse function is $m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}$ .

Hence, option D is correct.

Note: In all the options square of $\dfrac{17}{2}$ is missing in restricted domain.

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3 years ago

A factory makes 1,200 shirts every 6 hours. The factory makes shirts for 9 hours each workday. Enter the fewest number of workda

eduard

<span>The factory makes shirts for 9 hours each workday. </span>

7 0

3 years ago

A football team loses 3 yards in 3 consecutive plays. What’s the total yardage gained?

Anni [7]

-3×3=-9 so gain is 0

4 0

3 years ago

What are the next two terms in the pattern 3,6,5,10,9,18,17..?

valkas [14]

34 68
becaiseits half of each!

5 0

3 years ago

Read 2 more answers

What are the domain and Range of f(x)=log(x+6)-4

erik [133]

The function $g(x)=\log x$ has domain $(0,\infty)$ and range $(-\infty, \infty )$ .

The function $f(x)=\log(x+6)-4$ is obtained from the function $g(x)$ by translating 6 units left and 4 units down.

So, the domain of $f(x)$ is $(-6,\infty)$ and range is $(-\infty, \infty )$ .

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3 years ago