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Artemon [7]
3 years ago
12

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
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