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1 year ago

What is the equation of the line that is used to show the reflection of a relation and its inverse?

Mathematics

1 answer:

Artyom0805 [142]1 year ago

5 0

The graph and inverse of a function are reflections of each other along the line y = x.

A relation made up of ordered pairs (x, y) has as its inverse the set of all ordered pairs (y, x).

When a point is mirrored over the line y = x, the x- and y-coordinates swap places. Similarly, when a point is mirrored over the line y = -x, the x- and y-coordinates swap places and become negated.

Therefore,

The point (x, y)'s reflection over the line y = x is (y, x).

The point (x, y)'s reflection over the line y = - x is (-y, -x).

Thus, the graph and inverse of a function are reflections of each other along the line y = x.

Learn more about reflections for inverse of a function at

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Lauren says that -3.5 is greater than -3 1/3. Do you agree? Explain.

kirza4 [7]

Answer:

$-3\frac{1}{2}$

Step-by-step explanation:

-3.5 means -(3 + $\frac{1}{2}$ )

In other words, -3.5 = $-3\frac{1}{2}$

When we draw two numbers $-3\frac{1}{3}$ and $-3\frac{1}{2}$ on a number line, $-3\frac{1}{2}$ comes first from left to right.

We know that all the numbers on a number line from left to right are in increasing order.

Therefore, $-3\frac{1}{2}$ is smaller than $-3\frac{1}{3}$ .

$-3\frac{1}{2}$

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3 years ago

Simplify 3a^2b^3c^5 __________________ 8x^4y^3z

Jobisdone [24]

We have to rewrite the expression so that it has no denominator.
For example:
1 / x = x^(-1)
1/8 = 8^(-1); 1/x^(4) = x^(-4); 1/y^(3) = y^(-3); 1/z = z^(-1).
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3 years ago

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Can someone please help me on this problem

Dafna1 [17]

Answer:

Step-by-step explanation:

Perimeter is all sides added together.

l is length, w is width, and P is perimeter.

$2l + 2w = P\\2(5x) + 2(x - 3) = 42\\10x + 2x - 6 = 42\\12x - 6 = 42\\12x = 48\\x = 4$

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45% of the population of a city are men

leonid [27]

Answer:

$\boxed{\textsf{ The number of children is \textbf{24150}.}}$

Step-by-step explanation:

Given that the 45% of the population of a city are men and 15% are children . The number of women is 64,400 . And we need to find the number of children . Here ,

$\sf\implies Percentage_{(men)}= 45/% .\\\\\sf\implies Percentage_{(children)}= 15\% .$

So the percentage of women will be equal to [ 100 - ( 45 -15) ]% = [ 100 - 60 ]% = 40% .

So let us take the total number of people be x . So ,

$\purple{\bigstar}\underline{\underline{\boldsymbol{ According\ to \ Question :- }}}$

$\sf\implies 40\% \ of \ x \ = \ 64,400 \\\\\sf\implies \dfrac{40x}{100}= 64,400 \\\\\sf\implies x =\dfrac{64,400\times 100}{40}\\\\\sf\implies \boxed{\pink{\sf x = 161,000 }}$

$\rule{200}2$

The percentage of children = 15% :-

$\sf\implies Number_{(children)}= 15\% \ of 161,000\\\\\sf\implies Number_{(children)}= \dfrac{15}{100}\times 161,000 \\\\\sf\implies \boxed{\pink{\frak {Number_{(children)}= 24150 }}}$

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3 years ago

Line RS bisects PQ at point R, Find RQ if PQ = 14 cm

Dovator [93]

If PQ is 14, each segment, PR and RQ will be 7.
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