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3 years ago

Simply 2p(p+2)-3p(2p-3) =

Mathematics

1 answer:

nadezda [96]3 years ago

4 0

Answer:

p (13 - 4 p)

Step-by-step explanation:

Simplify the following:

2 p (p + 2) - 3 p (2 p - 3)

Hint: | Pull a common factor out of 2 p (p + 2) - 3 p (2 p - 3).

Factor p out of 2 p (p + 2) - 3 p (2 p - 3), resulting in p (2 (p + 2) - 3 (2 p - 3)):

p (2 (p + 2) - 3 (2 p - 3))

Hint: | Distribute 2 over p + 2.

2 (p + 2) = 2 p + 4:

p (2 p + 4 - 3 (2 p - 3))

Hint: | Distribute -3 over 2 p - 3.

-3 (2 p - 3) = 9 - 6 p:

p (2 p + 9 - 6 p + 4)

Hint: | Group like terms in 2 p - 6 p + 4 + 9.

Grouping like terms, 2 p - 6 p + 4 + 9 = (4 + 9) + (2 p - 6 p):

p (4 + 9) + (2 p - 6 p)

Hint: | Combine like terms in 2 p - 6 p.

2 p - 6 p = -4 p:

p (-4 p + (4 + 9))

Hint: | Evaluate 4 + 9.

4 + 9 = 13:

Answer: p (13 - 4 p)

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Given: A, B, and C What is the value of X in the matrix equation AX + B = C?

Ksju [112]

Answer:

Option (2)

Step-by-step explanation:

Given expression is, AX + B = C

$A=\begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}$

$B=\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix}$

$C=\begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}$

AX + B = C

AX = C - B

C - B = $\begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}-\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix}$ = $\begin{bmatrix}-42+7 & -20+9\\ 5-4 & 4+1\end{bmatrix}$

C - B = $\begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}$

Let $X=\begin{bmatrix}a & b\\ c & d\end{bmatrix}$

AX = $\begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}\times \begin{bmatrix}a & b\\ c & d\end{bmatrix}$

= $\begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}$

Since AX = C - B

$\begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}=\begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}$

Therefore, a = 1, b = 5

(-3a - 4c) = -35

3(1) + 4c = 35

3 + 4c = 35

4c = 32

c = 8

And (-3b - 4d) = -11

3(5) + 4d = 11

4d = -4

d = -1

Therefore, Option (2). X = $\begin{bmatrix}1 & 5\\ 8 & -1\end{bmatrix}$ will be the answer.

7 0

3 years ago

What is 4% of 75 please

Paul [167]

4% Of 75 is 3 so yeah the answer to your question is 3

8 0

3 years ago

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Rotate the figure 90 degrees about vertex A.

ziro4ka [17]

Answer:

A' is (1,1) B is (4,1) C is (1,-1)

Step-by-step explanation:

Since we rotating the figure about point a, we know a is the center of the rotation meaning no matter how far we rotate point a new image will stay on where point a pre image was which in this case is (1,1). Also since we know the rules of rotating a angle 90 degrees About the origin we are going to translate the figure to have the one point we are rotating about at the orgin. Since translations are a rigid transformations, the figure will stay the same A. Move the figure 1 to the left and 1 down so A becomes 0,0 B becomes 0,3 and C becomes 2,0. Then apply the rules of 90 degree clockwise rotation rules. (x,y) goes to (y,-x) . A stays (0,0) B becomes (3,0) and C becomes (0,-2). Then translate the figure 1 to the right and 1 down since we rotating about point a which is 1,1 and it at 0,0 rn. A' is 1,1. B' becomes (4,1). C' becomes (1,-1).

5 0

3 years ago

Find a polynomial f(x) of degree 4 that has the following zeros. 0, -5, 8, -2

Roman55 [17]

Answer:

The polynomial of the function degree '4'

x⁴ - x³ -46 x² -80x =0

Step-by-step explanation:

Explanation:-

Given zeros are 0 ,-5,8,-2

x =0 , x=-5 ,x=8 and x=-2

(x-0) , ( x+5) , (x-8) and (x+2)

The polynomial function with degree '4'

(x-0)(x-(-5)(x-8)(x-(-2) =0

x ( x+5) (x-8) (x+2) =0

(x² +5x)(x-8)(x+2) =0

(x³ -8 x²+5x² -40 x)(x+2) =0

( x³ -3 x² - 40 x) (x +2) =0

x⁴ + 2 x³ - 3 x³- 6 x²-40 x²- 80 x =0

x⁴ - x³ -46 x² -80x =0

Final answer:-

The polynomial of the function degree '4'

x⁴ - x³ -46 x² -80x =0

3 0

3 years ago

Solve the following for the variable x. 3x - 16 = 38

shusha [124]

Answer: x= 18

Step-by-step explanation:

3x - 16 = 38

38 + 16 = 54

3x/3 = 54/3

X= 18

3 0

3 years ago

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