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3 years ago

Explain how Pascal’s triangle allows you to compute the coefficient of x2y3 when (x − y)5 is

Mathematics

1 answer:

nirvana33 [79]3 years ago

6 0

Answer:

-10

Step-by-step explanation:

Pascal’s triangle: It represents the binomial coefficients. If a binomial expression is (a+b)^n, then (n+1)th row of Pascal’s triangle represents the binomial coefficients or that binomial expression.

The given binomial expression is

$(x-y)^5$

The elements of 6th row are 1, 5, 10, 10, 5 and 1.

$(x-y)^5=1(x)^5+5(x)^4(-y)^1+10(x)^3(-y)^2+10(x)^2(-y)^3+5(x)^1(-y)^4+1(-y)^5$

$(x-y)^5=x^5 - 5 x^4 y + 10 x^3 y^2 - 10 x^2 y^3 + 5 x y^4 - y^5$

Therefore, the coefficient of x²y³ is -10.

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Select all expressions that are equivalent to 5x + (x+6) +3x.

zhuklara [117]

Answer:

9x + 6 and 6x + 6 + 3x

Step-by-step explanation:

6 0

2 years ago

A gallon of Moo Milk costs $5.12. What is the price, in dollars, of an 8 ounce glass of Moo Milk? There are 128 ounces in 1 gall

Trava [24]

<h2>Answer:</h2>

$0.32.

<h2>Explanation:</h2>

1 gallon = 128 fluid ounces.

So to find the price of an 8 ounce glass of Moo Milk we need to multiply (8/128) x 5.12.

That equals $0.32.

6 0

3 years ago

Read 2 more answers

An arched drainage culvert can be modelled by the function:

Zanzabum

Substitute 136.5 for y.

$136.5=\frac{x(191-x)}{60}$

$8190=x(191-x)$

$8190=191x-x^{2}$

$x^{2} -191x+8190=0$

Compare this equation with $ax^{2} +bx+c=0$

a = 1, b = - 191, c = 8190

$x=\frac{-b+\sqrt{b^{2}-4ac } }{2}$ or

$x=\frac{-b-\sqrt{b^{2}-4ac } }{2}$

$x=\frac{191+\sqrt{191^{2}-4(1)(8190) } }{2}$ or

$x=\frac{191-\sqrt{191^{2}-4(1)(8190) } }{2}$

$x=\frac{191+\sqrt{36481-32760 } }{2}$ or

$x=\frac{191-\sqrt{36481-32760 } }{2}$

$x=\frac{191+\sqrt{3721 } }{2}$ or

$x=\frac{191-\sqrt{3721 } }{2}$

$x=\frac{191+61}{2}$ or

$x=\frac{191-61}{2}$

$x=\frac{252}{2}$ or

$x=\frac{130}{2}$

x = 126 or x = 65

Hence, the points on the curve are (65, 136.5) and (126, 136.5).

The width of the air space is the distance between these points.

Width = $\sqrt{(x_{2}- x_{1})^{2} +( y_{2}- y_{1}) ^{2}$

= $\sqrt{(126- 65)^{2} +(136.5-136.5) ^{2}$

= 126 - 65

= 61

Hence, width of the air space is 61m.

5 0

3 years ago

Please solve these for 20 points : solving formulas for a variable

Digiron [165]

6. (A/pi = r^2)
7. [(P - 2l)/2 = w]
8. [C/(2pi)= r]
9. (2A/h = b)
10. (E/c^2 = m)

6 0

3 years ago

What is the slope of the line that passes through these two points?

Dmitry_Shevchenko [17]

Answer:

undefined

Step-by-step explanation:

We can use the slope formula to find the slope

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

= ( 9-3) / ( 2-2)

= 6/0

When we divide by zero, the result is undefined

This means the slope is undefined

7 0

2 years ago