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bezimeni [28]
3 years ago
9

In the inverse variation function, what happens to the output when the

Mathematics
1 answer:
Nookie1986 [14]3 years ago
7 0

Answer:

Option D.

Step-by-step explanation:

An inverse variation function is defined as

y\propto \dfrac{1}{x}

y=\dfrac{k}{x}

where, k is constant of proportionality.

In the above equation x represents input and y represents output.

If the function's input value is multiplied by 4, then

y_1=\dfrac{k}{x_1}

y_1=\dfrac{k}{4x}

y_1=\dfrac{1}{4}\cdot \dfrac{k}{x}

y_1=\dfrac{1}{4}y

The output is divided by 4​.

Therefore, the correct option is D.

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What is the domain and range of the function y = 2x2 - 4x - 10?
11111nata11111 [884]

Answer:

Step-by-step explanation:

The domain of all polynomials is all real numbers.  To find the range, let's solve that quadratic for its vertex.  We will do this by completing the square.  To begin, set the quadratic equal to 0 and then move the -10 over by addition. The first rule is that the leading coefficient has to be a 1; ours is a 2 so we factor it out.  That gives us:

2(x^2-2x)=10

The second rule is to take half the linear term, square it, and add it to both sides.  Our linear term is 2 (from the -2x).  Half of 2 is 1, and 1 squared is 1.  So we add 1 into the parenthesis on the left.  BUT we cannot ignore the 2 sitting out front of the parenthesis.  It is a multiplier.  That means that we didn't just add in a 1, we added in a 2 * 1 = 2.  So we add 2 to the right as well, giving us now:

2(x^2-2x+1)=10+2

The reason we complete the square (other than as a means of factoring) is to get a quadratic into vertex form.  Completing the square gives us a perfect square binomial on the left.

x^2-2x+1=(x-1)^2 and on the right we will just add 10 and 2:

2(x-1)^2=12

Now we move the 12 back over by subtracting and set the quadratic back to equal y:

2(x-1)^2-12=y

From this vertex form we can see that the vertex of the parabola sits at (1,-12).  This tells us that the absolute lowest point of the parabola (since it is positive it opens upwards) is -12.  Therefore, the range is R={y|y ≥ -12}

4 0
3 years ago
Learning Task 3: In your answer sheet, write the letter of the correct answe
miss Akunina [59]

Answer:

a.) May or may not a polynomial function ( depends on c)

b.) Not a polynomial function.

c.) Not a polynomial function.

d.) It is a polynomial function.

Step-by-step explanation:

A polynomial function is of the form - a_{n}x^{n} + a_{n-1} x^{n-1} + a_{n-2} x^{n-2} + .....+ a_{1}x + a_{0}

where n is positive integer and n\neq 0

a.)

P(x) = 2x³ + 32 - 4x + 4c

It may or may not a polynomial function because we did not know about the constant c.

b.)

H(x) = 4x^{\frac{1}{2} } - 3x⁴

It is not a polynomial function because \frac{1}{2} is not integer.

c.)

G(x) = 2x^{-3} + 5

It is not a polynomial function because -5 is not a positive integer.

d.)

F(x) = 2x³ - 5x + 33x²

It is a polynomial function.

8 0
3 years ago
Zoe had a board 5 1/4 feet long she cut off a piece now the board is 3 5/6 feet long how long was the piece she cut off
11Alexandr11 [23.1K]

5 1/4-3 5/6=1 5/12

Hope this helped!!! :P

7 0
3 years ago
Please help i have a 15 percent in math please ill give brainliest
dusya [7]
32.92 next is 27 last is 230
7 0
3 years ago
100 points!! Brainliest if correct!!
Elena-2011 [213]

surface area (S) of a right rectangular solid is:

S = 2*L*W + 2*L*H + 2*W*H (equation 1)

where:

L = length

W = width

H = height

-----

you have:

L = 7

W = a

H = 4

-----

formula becomes:

S = 2*7*a + 2*7*4 + 2*a*4

simplify:

S = 14*a + 56 + 8*a

combine like terms:

S = 22*a + 56

-----

answer is:

S = 22*a + 56 (equation 2)

-----

to prove, substitute any value for a in equation 2:

let a = 15

S = 22*a + 56 (equation 2)

S = 22*15 + 56

S = 330 + 56

S = 386

-----

since a = 15, then W = 15 because W = a

go back to equation 1 and substitute 15 for W:

S = 2*L*W + 2*L*H + 2*W*H (equation 1)

where:

L = length

W = width

H = height

-----

you have:

L = 7

W = 15

H = 4

-----

equation 1 becomes:

S = 2*7*15 + 2*7*4 + 2*15*4

perform indicated operations:

S = 210 + 56 + 120

S = 386

-----

surface area is the same using both equations so:

equations are good.

formula for surface area of right rectangle in terms of a is:

S = 22*a + 56

-----

8 0
3 years ago
Read 2 more answers
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