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2 years ago

Fill in the common equivalents. 1.) 662/3% = ?/?

Mathematics

1 answer:

baherus [9]2 years ago

5 0

3% is the same as 0.03
Therefore, 662/3% = 662/0.03

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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.

7 0

3 years ago

What is the quotient? startfraction n 3 over 2 n minus 6 endfraction divided by startfraction n 3 over 3 n minus 9 endfraction

bazaltina [42]

The quotient of the fraction n³ / (2n - 6) ÷ n³ / (3n - 9) is 2/3

<h3 /><h3>How to solve fraction</h3><h3 />

n³ / (2n - 6) ÷ n³ / (3n - 9)

multiply by the reciprocal of n³ / (3n - 9)

= n³ / (2n - 6) × 1 / n³ / (3n - 9)

= 2n - 6 / 3n - 9

= 2(n - 3) / 3(n - 3)

= 2/3

Therefore, quotient of the fraction n³ / (2n - 6) ÷ n³ / (3n - 9) is 2/3

Learn more about fraction:

brainly.com/question/1622425

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7 0

1 year ago

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Solve issuing Pythagorean theorem

Anna35 [415]

Step-by-step explanation:

(8x8) + (16x16) = 64+256 = 320

√320 = 17.9

8 0

2 years ago

Luigi is an urban planner. as an independent contractor, he charges $140 fee plus $ 25 per hour for each contract with the city.

yaroslaw [1]

x = hours 25 per hour = 25x

y = total

so y = 25x +140

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2 years ago

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Solve for y: 5x-3y<75

Arada [10]

y<-5/3x+25 Is your answer. To get it you subtract the 5x to both sides and then you divide the 3 on both sides

answer : y < -5/3x +25

4 0

2 years ago