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3 years ago

What is the coefficient of x4y4 in the expansion of (x + y)8?

Mathematics

2 answers:

dimulka [17.4K]3 years ago

5 0

Answer:

Step-by-step explanation:

If you use Pascal's Triangle, you will need 9 lines, since there are 9 terms in a binomial raised to the 8th power. Those 9 terms are:

1, 8, 28, 56, 70, 56, 28, 8, 1

The first expansion through the one we need are below (I hope you know how to use Pascal's Triangle!):

$1(x^8)(y^0)+8(x^7)(y^1)+28(x^6)(y^2)+56(x^5)(y^3)+70(x^4)(y^4)+...$

Korolek [52]3 years ago

5 0

Answer:

Step-by-step explanation:

apex

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Can I get help with this

Hunter-Best [27]

Answer:

The correct option is;

B) -6

Step-by-step explanation:

The given parameters are;

The line of symmetry of f(x) = The line of the reflection of g(x) over the y-axis

f(x) = 3·x² + b·x + c

From the given graph of g(x), we have;

The vertex point of g(x) = (-1, 8)

The line of symmetry is the line x = -1

The image of the reflection of (x, y) over the y-axis is (-x, y)

The image of the vertex of g(x) following a reflection across the y-axis is (1, 8)

Therefore;

The line of symmetry of the image of g(x) following a reflection over the x-axis is the line x = 1

The line (axis) of symmetry of a quadratic function is the line x = -b/(2·a), which is a line that always go through the vertex of the parabola

Where;

a = The coefficient of x²

b = The coefficient of 'x'

For f(x) = 3·x² + b·x + c, a = 3, and b = b

Given that f(x) and the image of g(x) have the same line of symmetry, we have;

The line of symmetry of f(x) is x = 1

Therefore, from the formula for the line of symmetry, we have;

x = -b/(2·a)

x = 1

By substitution, we have;

1 = -b/(2·a)

∴ -2·a = b

Given that a = 3, we get;

-2 × 3 = -6 = b

b = -6

3 0

3 years ago

What two factors that can be multiply by 19

Vsevolod [243]

19 is a prime number so 1, 19
hope this helps!

5 0

3 years ago

Read 2 more answers

Rewrite this standard form quadratic equation into vertex form by completing the square. Upload your work here to show your thin

Alex787 [66]

Solution :

Given the equation :

$y = x^2 - 6x+3$

$y=1(x^2 - 6x +n)+3$

$n = \left(\frac{b}{2}\right)^2$

$n = \left(\frac{6}{2}\right)^2$

n = 9

$y=1(x^2 - 6x +9-9)+3$

$y=1(x^2 - 6x +9)-9+3$

$y=1(x-3)^2- 6$

Therefore the vertex form of $y = x^2 - 6x+3$ is $y=1(x-3)^2- 6$ .

3 0

3 years ago

The roots of a quadratic equation ax2+bx+c=0 are 1+i 5 and 1−i 5 . Find possible values of a, b and c.

Anarel [89]

Answer:

Step-by-step explanation:

If the roots are 1 + 5i and 1 - 5i, then you need the factors that result from those roots. They are (x - 1 + 5i) and (x - 1 - 5i). Now what you do with those is FOIL them out. Doing that gives you the following:

$x^2-x+5ix-x+1-5i-5ix+5i-25i^2$ (what a mess, huh?)

The good thing is that several of those terms cancel each other out. +5ix cancels out the -5ix; -5i cancels out the 5i; and the 2 -x terms combine to -2x. That leaves you with:

$x^2-2x-25i^2$

Obviously you're in the section in math that deals with complex (imaginary) numbers so you should know that i-squared is equal to -1. Making that replacement:

$x^2-2x+25$

a = 1, b = -2, c = 25

6 0

4 years ago

Read 2 more answers

62 is divisible by which of the following numbers

SVEN [57.7K]

Answer:

Step-by-step explanation:

4 0

3 years ago