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3 years ago

If the original function () = 22 − 1 is shifted to the left 3 units to make the

Mathematics

1 answer:

Rom4ik [11]3 years ago

4 0

A horizontal translation is expressed by transforming

$f(x)\mapsto f(x+k)$

If $k$ is positive, the function is translated to the left. If $k$ is negative, the function is translated to the right.

So, a 3-units left shift is given by $k=3$ . So you have

$f(x)=2x^2-1 \implies f(x+3)=2(x+3)^2-1$

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Help me with this question please.

Nadya [2.5K]

19:1 = 19:1

38:2 = 19:1

57:3 = 19:1

So, the constant is 19.

7 0

2 years ago

Here are two expressions whose product is a new expression, :

Vera_Pavlovna [14]

Answer:

1. Fill in the box with 1

2. Fill in the box with -2

Step-by-step explanation:

Expression:

$(-2x^3 + [\ ]x)(x^{[\ ]}+1.5) = A$

Solving (1): Fill in the box to make it a polynomial.

To make it a polynomial, we simply fill in the box with a positive integer (say 1)

Fill in the box with 1

$(-2x^3 + [1]x)(x^{[1]}+1.5) = A$

Remove the square brackets

$(-2x^3 + x)(x^1+1.5) = A$

$(-2x^3 + x)(x+1.5) = A$

Open bracket

$-2x^4 - 3x^3 + x^2 + 1.5x = A$

Reorder

$A = -2x^4 - 3x^3 + x^2 + 1.5x$

The above expression is a polynomial.

This will work for any positive integer filled in the box

Solving (2): Fill in the box to make it not a polynomial.

The powers of a polynomial are greater than or equal to 0.

So, when the boxes are filled with a negative integer (say -2), the expression will cease to be a polynomial

Fill in the box with -2

$(-2x^3 + [-2]x)(x^{[-2]}+1.5) = A$

Remove the square brackets

$(-2x^3 - 2x)(x^{-2}+1.5) = A$

Reorder

$A = (-2x^3 - 2x)(x^{-2}+1.5)$

Open brackets

$A = -2x-3x^3-2x^{-1}-3x$

Collect Like Terms

$A = -3x^3-2x-3x-2x^{-1}$

$A = -3x^3-5x-2x^{-1}$

Notice that the least power of x is -1.

Hence, this is not a polynomial.

3 0

3 years ago

(2,-6), (-4,-3)<br> What is the slope

mel-nik [20]

Step-by-step explanation:

the slope is -3

that is the answer

3 0

2 years ago

Read 2 more answers

Read the following statement.

nekit [7.7K]

Bro... ahahaha the answer is D DDDDDDDDDDDDDDD peace man

8 0

3 years ago

Read 2 more answers

A right rectangular prism has a length of 2 1/2 feet, a width of 3 feet,and a height of 1 1/2 feet. Unit cubes with side lengths

Illusion [34]

The statement "unit cubes with side lengths of 1/2 foot are added to fill the prism with no space remaining" is useless information so you can disregard that. All you need to know to calculate the volume is the length, width, and height.

Volume = length x width x height
Volume = (5/2) x 3 x 11/2
Volume = 15/2 x 11/2
Volume = 165/4
Volume = 41.25 ft cubed

7 0

3 years ago