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3 years ago

Determine algebraically whether the function is even, odd, or neither even nor odd.

Mathematics

1 answer:

svet-max [94.6K]3 years ago

4 0

Hello,

f(x)=-4x^3+4x

f(-x)=-4(-x)^3+4(-x)
=4x^3-4x
=-(-4x^3+4x)
=-f(x)

Function is ODD

Answer is C

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Select the correct answer.

DedPeter [7]

Answer: The correct option is (D) (4, -6).

Step-by-step explanation: Given that the areas of the triangles ADC and DCB are in the ratio 3 : 4.

We are to find the co-ordinates of point C.

From the diagram, we note that

the co-ordinates of point A and B are A(1, -9) and B(8,-2).

So, the length of the line segment AB, calculated by distance formula, is

$AB=\sqrt{(1-8)^2+(-9+2)^2}=\sqrt{49+49}=7\sqrt2.$

Now, area of ΔADC is

$A_{ABC}=\dfrac{1}{2}\times AC\times CD,$

and area of ΔDCB is

$A_{DCE}=\dfrac{1}{2}\times BC\times CD.$

According to the given information, we have

$A_{ADC}:A_{DCB}=3:4\\\\\\\Rightarrow \dfrac{A_{ADC}}{A_{DCE}}=\dfrac{3}{4}\\\\\\\Rightarrow \dfrac{\frac{1}{2}\times AC\times CD}{\frac{1}{2}\times BC\times CD}=\dfrac{3}{4}\\\\\\\Rightarrow \dfrac{AC}{BC}=3:4.$

So, the point C divides the line segment AB internally in the ratio 3 : 4.

We know that

if a point divides a line segment with end-points (a, b) and (c, d) internally in the ration m : n, then its co-ordinates are

$\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).$

Since point C divides the line segment AB with end-points A(1, -9) and B(8, -2) internally, so the co-ordinates of point C will be

$\left(\dfrac{3\times 8+4\times 1}{3+4},\dfrac{3\times (-2)+4\times (-9)}{3+4}\right)\\\\\\=\left(\dfrac{28}{7},\dfrac{-42}{7}\right)\\\\\\=(4, -6).$

Thus, the co-ordinates of point C are (4, -6).

Option (D) is correct.

3 0

3 years ago

Read 2 more answers

N Which equation represents a proportional relationship? Y=x+1/3 Y=3X+1/3 Y=1/3X

loris [4]

Which table shows a proportional relationship between x and y? x 2 4 5 6 y 6 12 18 21 x 1 3 4 5 y 50 150 200 250 x 3 5 7 8 y 1.5 2.5 3 4.5 x 1 2 3 6 y 1.5 3 6 9 the graph of a proportional relationship passes through (12,16) and (1,y) find y. can someone please walk me through this?

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3 years ago

I need help, it is a grade

Rudiy27

Viruses are site articles that contain either DNA or RNA protected by a protein coat. Which statement best susiests why viruses must have host cells to replicate their genetic materials and build new
article
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3 years ago

The population of Friendly City is 150% of what it was 10 years ago. If its population was 25,000 what is its population now?

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3 years ago

These are the first four terms of a sequence. 3 -1 -5 -9. Find the nth term.

podryga [215]

Answer:

4n-1

Step-by-step explanation:

Diffrence bweetween each number, 3 and -1, -1 and -5, -5 and -9 is 4

find the closest numbers

4*1=4

4*0=0

4*-1=-4

4*-2=-8

now we figure out how to make these numbers into our terms of this sequence

4n-1

4*1-1=3

4*0-1=-1

4*-1-1=-3

4*-2-1=-9

so the nth term is 4n-1

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2 years ago