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denis23 [38]
3 years ago
8

Match each binomial expression with the set of coefficients of the terms obtained by expanding the expression.

Mathematics
2 answers:
user100 [1]3 years ago
8 0

 explanation:

(A) (2x+y)^3=8 x^3 + 12 x^2 y + 6 x y^2 + y^3

Answer option C)  8, 12, 6, 1

B) (2x+3y)^4 = 16 x^4 + 96 x^3 y + 216 x^2 y^2 + 216 x y^3 + 81 y^4

Answer option D) 16, 96, 216, 216, 81

C) (3x+2y)^3 = 27 x^3 + 54 x^2 y + 36 x y^2 + 8 y^3

Answer option B) 27, 54, 36, 8

D)(x+y)^4 = x^4 + 4 x^3 y + 6 x^2 y^2 + 4 x y^3 + y^4

Answer option A) 1, 4, 6, 4, 1

andreev551 [17]3 years ago
3 0
(A) (2x+y)^3 = (C) 8, 12, 6, 1
(B) (2x+3y)^4 = (D) 16, 19, 216, 216, 81
(C) (3x+2y)^3 = (B) 27, 54, 36, 8
(D) (x+y)^4 = (A) 1, 4, 6, 41
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natka813 [3]

The interpretation of the given question is as follows:

Use the given inverse to solve the system of equations

x- y - z = -6  \\ \\ 2y + z = -6 \\ \\  3x -8 y = - \dfrac{1}{2}

The inverse of  \left[\begin{array}{ccc}1&-1&1\\0&2&1\\3&-8&0\end{array}\right]   is \left[\begin{array}{ccc}-8&8&3\\-3&3&1\\6&-5&-2\end{array}\right]

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Answer:

x = - 1.5

y = - 0.5

z =  - 5

Step-by-step explanation:

Using the correlation  of inverse of matrix AX = B to solve the question above;

AX = B

⇒ A⁻¹(AX)  = A⁻¹ B

X =  A⁻¹ B

So ;

X         =        A⁻¹                             B

\left[\begin{array}{c}x\\y\\z\end{array}\right] =     \left[\begin{array}{ccc}-8&8&3\\-3&3&1\\6&-5&-2\end{array}\right] =   \left[\begin{array}{ccc}-6\\ -6\\- \dfrac{1}{2}\end{array}\right]

   

 \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}(-8*-6)+(8*-6)+(3*-\dfrac{1}{2})\\(-3*-6)+(3*-6)+(1*-\dfrac{1}{2})\\(6*-6)+(5*-6)+(-2* - \dfrac{1}{2})\end{array}\right]

\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}(48)+(-48)+(\dfrac{-3}{2})\\(18)+(-18)+(\dfrac{-1}{2})\\(-36)+(30)+(1)\end{array}\right]

\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}(\dfrac{-3}{2})\\(\dfrac{-1}{2})\\(-5)\end{array}\right]

\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}-1.5\\-0.5\\ -5\end{array}\right]

5 0
3 years ago
(48. PERSEVERE Wha
katrin2010 [14]

Answer: 4

Step-by-step explanation:

We know that a plane is 2 dimensional surface that extends infinitely far.

The number of points required to define a plane = 3

Here , we have 4 points A, B, C, and D.

So, the number of possible combinations of 3 points to make a plane from 4 points = C(4,3)

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Hence, the greatest number of planes determined using any three of the points A, B, C, and D if no three points are collinear = 4.

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Leni [432]
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