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3 years ago

Find the p(2) for each of the following functions 1.p(x) = -2x³ + 4x - 1 ?

Mathematics

1 answer:

Sever21 [200]3 years ago

7 0

Answer:

p(2) = -9

General Formulas and Concepts:

Order of Operations: BPEMDAS

Step-by-step explanation:

<u>Step 1: Define</u>

p(x) = -2x³ + 4x - 1

p(2) is x = 2

<u>Step 2: Solve</u>

Substitute: p(2) = -2(2)³ + 4(2) - 1
Evaluate: p(2) = -2(8) + 4(2) - 1
Multiply: p(2) = -16 + 8 - 1
Add: p(2) = -8 - 1
Subtract: p(2) = -9

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AysviL [449]

You can take x = a, 2y = b and then can apply the binomial theorem.

The expansion of given expression is given by:

Option D: $x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$ is

<h3>What is binomial theorem?</h3>

It provides algebraic expansion of exponentiated(integer) binomial.

According to binomial theorem,

$(a+b)^n = \sum_{i=0}^n ^nC_i a^ib^{n-i}$

<h3>How to use binomial theorem for given expression?</h3>

Taking a = x, and b =2y, we have n = 7, thus:

$(x+2y)^7 = \: ^7C_0x^0(2y)^7 + \: ^7C_1x^1(2y)^6 + \: ^7C_2x^2(2y)^5 + \: ^7C_3x^3(2y)^4 + \:^7C_4x^4(2y)^3 + \:^7C_5x^5(2y)^2 + \:^7C_6x^6y^1 + \: ^7C_0x^7y^0\\\\
(x+2y)^7 = 128y^7 + 448xy^6 + 672x^2y^5 + 560x^3y^4 + 280x^4y^3 + 84x^5y^2 + 14x^6y + x^7\\\\
(x+2y)^7 = x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$

Thus, Option D: $x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$ is correct.

Learn more about binomial theorem here:

brainly.com/question/86555

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3 years ago

Which is the equation of a line that passes through the points (1,4) and (-1,1)

horsena [70]

Answer:

The equation of the line is y = 3/2x + 5/2

Step-by-step explanation:

To find the equation of this line, start by using the two points with the slope formula to find the slope.

m(slope) = (y2 - y1)/(x2 - x1)

m = (4 - 1)/(1 - -1)

m = 3/(1 + 1)

m = 3/2

Now that we have the slope, we can use that and either point in point-slope form to find the equation.

y - y1 = m(x - x1)

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y - 4 = 3/2x - 3/2

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Anna007 [38]

Answer:

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Step-by-step explanation:

to get it into y- intercept form we need to write it in the form y = mx + b

-8x = 2 - 2y, move 2y to the other side and -8x to the other side they both become positive.

2y = 8x + 2, dividing each by 2

yields y = 4x + 1

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Find the p(2) for each of the following functions 1.p(x) = -2x³ + 4x - 1 ?​

Find the p(2) for each of the following functions 1.p(x) = -2x³ + 4x - 1 ?