Is 2 rational ? And why

Mathematics

2 answers:

zubka84 [21]3 years ago

6 0

Yes, because it can be expressed as the quotient or fraction of two integers you

SVEN [57.7K]3 years ago

3 0

2 is a rational number because it has the ability to be expressed through fraction or quotient

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Find the 82nd term of the following sequence.<br><br> -32, -27, -22, ....

My name is Ann [436]

The 82nd term for the sequence would be -4

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2 years ago

In this composite function, (f◦g)(x) where f(x)=(X-3) and g(x)=X^2 what is (f◦g)(x) when x=1?

Alekssandra [29.7K]

Answer:

When x = 1, (f◦g)(x) is -2.

Step-by-step explanation:

Composite function:

The composite function of f and g is given by:

$(f \circ g)(x) = f(g(x))$

In this question:

$f(x) = x - 3, g(x) = x^2$

Composite function:

The composite function is:

$f(g(x)) = f(x^2) = x^2 - 3$

At x = 1

$(f \circ g)(1) = 1^2 - 3 = 1 - 3 = -2$

When x = 1, (f◦g)(x) is -2.

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3 years ago

Jacob transformed quadrilateral FGHJ to F'G'H'J'.

Rudik [331]

Answer:

A. Reflection across the line x = 1

Step-by-step explanation:

Please find the attachment.

We have been given that Jacob transformed quadrilateral FGHJ to F'G'H'J'. We are asked to find which transformation Jacob used to reflect FGHJ to F'G'H'J'.

Since we know that while reflecting a figure, the line of reflection will lie between the original figure and reflected figure. Each point of the reflected figure will have the same distance from the line of reflection as the corresponding point of the original figure.

Now let us see our given choices one by one.

A. Reflection across the line x = 1.

Upon looking at point G and G' we can see that both points are equidistant (2 units) from the line x=1. Other corresponding points of both quadrilaterals are also equidistant from line x=1, therefore, Jacob used the reflection across the line x=1 to transform quadrilateral FGHJ to F'G'H'J'.

B. Reflection across the line y = 1 .

If Jacob had reflected quadrilateral across line y=1, the points of quadrilateral F'G'H'J' will lie in second and third quadrant. We can see from our graph that F'G'H'J' lies in 1st quadrant, therefore, option B is not a correct choice.

C. Reflection across the line y-axis.

If Jacob had reflected quadrilateral across y-axis, the coordinates of points of quadrilateral F'G'H'J' will be G'(1,4), H'(1,2), J'(4,0) and F'(2,5). Therefore, option B is not a correct choice.

D. Reflection across the x -axis.

If Jacob had reflected quadrilateral across x-axis, the points of quadrilateral F'G'H'J' will lie in third quadrant. We can see from our graph that F'G'H'J' lies in 1st quadrant, therefore, option D is not a correct choice.