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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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The area of a room is 600 square feet. The length is (x + 5) feet and the width is (x + 4) feet. Find the dimensions of the room
tangare [24]
I'm going to assume that the room is a rectangle.

The area of a rectangle is A = lw, where l=length of the rectangle and w=width of the rectangle. 

You're given that the length, l = (x+5)ft and the width, w = (x+4)ft. You're also told that the area, A = 600 sq. ft. Plug these values into the equation for the area of a rectangle and FOIL to multiply the two factors:
A = lw\\
600 = (x+5)(x+4)\\
600 =  x^{2} + 9x + 20


Now subtract 600 from both sides to get a quadratic equation that's equal to zero. That way you can factor the quadratic to find the roots/solutions of your equation. One of the solutions is the value of x that you would use to find the dimensions of the room:
600 = x^{2} + 9x + 20\\
x^{2} + 9x - 580 = 0\\
(x + 29)(x - 20) = 0\\
x + 29 = 0, \:\: x - 20 = 0\\
x = -29, x = 20

Now you know that x could be -29 or 20. For dimensions, the value of x must give you a positive value for length and width. That means x can only be 20. Plugging x=20 into your equations for the length and width, you get:
Length = x + 5 = 20 + 5 = 25 ft.
Width = x + 4 = 20 + 4 = 24 ft.

The dimensions of your room are 25ft (length) by 24ft (width).
8 0
3 years ago
Read 2 more answers
What 2 numbers that are the same multiply to be 36 and add up to be 15?
marysya [2.9K]
The only way to have two numbers that are the same and add up to be 15
is if they're both 7.5 , but those don't multiply to be 36.  So I guess there's
no answer that satisfies all the conditions of this question.
8 0
3 years ago
What is one whole and three fourths plus five sixths plus one whole and one fourth
Naddika [18.5K]

Answer:

First of all  cant give u the anssswer i am srry but i can give u a hint u need to find eqivelent fractions for the denominators then u can add them

Step-by-step explanation:

8 0
3 years ago
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7-^3<br> Simplify this expression. Use 7 as the base.
katen-ka-za [31]
Hopefully this photo helps

7 0
2 years ago
Estimate the solution to the system of equations. You can use the interactive graph below to find the solution.
Murrr4er [49]

Answer: x= 3/2 and y= 1/2

Step-by-step explanation:

Since both equations are equated to y, you just need to use substitution to create the equation below:

-x+2 = 3x-4

Solve the equation for x:

4x=6

x=6/4=3/2

Plug in x into any one of the given equations to find the value of y:

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Hope this helps!

4 0
3 years ago
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