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Butoxors [25]
3 years ago
11

Write a function to represent the set of ordered pairs. {(2, -2), (3, 8), (4, 22), (5, 40)}

Mathematics
1 answer:
natali 33 [55]3 years ago
4 0

Answer:

y = 2x² - 10

Step-by-step explanation:

We must find a pattern in the numbers. Set out the numbers in a table (Columns 1 and 2 in the table).

<u>x</u>    <u> y</u>    <u>y/2</u>    <u>y/2 + 5 </u>

2   -2      -1           4

3    8       4           9

4  22      11          16

5  40    20         25

It looks like all y-values are multiples of 2.

Let's divide them by 2 (Column 3).

The numbers don't increase evenly. We may have a quadratic function.

If we add 5 to each quotient, we get a set of values equal to x² (Column 4).

y/2 +   5 = x²

y     + 10 = 2x²

y            = 2x² - 10

The function is y = 2x² - 10.

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3 years ago
If f(x)=e^2x(x^3+1) then f'(2)=
qaws [65]

Answer:

See below

Step-by-step explanation:

f(x)=e^2x(x^3+1) = e^2x^4+x

Considering

f'(x)=\dfrac{d}{dx}f(x)=\dfrac{d}{dx}e^2x^4+\dfrac{d}{dx}x

Once the derivative of a constant is 1 and  e^x = \dfrac{d}{dx} e^x

Then,

\dfrac{d}{dx}f(x)=\dfrac{d}{dx}e^2x^4+\dfrac{d}{dx}x =\boxed{ e^2 4x^3+1}

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3 years ago
Rewrite the equation by completing the square. x^2+10x+24 = 0
ser-zykov [4K]

Answer:

(x+5)^2 = 1

Step-by-step explanation:

x^2+10x+24 = 0

Subtract 24 from each side

x^2+10x+24 -24 = 0-24

x^2+10x = -24

Take the coefficient of x

10

Divide by 2

10/2 =5

Square it

5^2 = 25

Add it to each side

x^2+10x+25 = -24+25

Take the coefficient divided by 2 inside the factor

(x+10/2) ^2 = -24+25

(x+5)^2 = 1

3 0
3 years ago
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