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3 years ago

Which of the following is equivalent to (p3)(2p2 - 4p)(3p2 - 1)?

Mathematics

2 answers:

aleksandrvk [35]3 years ago

7 0

(p³)(2p² - 4p)(3p² - 1) = (p³)(2p²*3p² - 4p*3p² - 1*2p² - 4p*(-1)) =
= (p³)(6p⁴ - 12p³ - 2p² + 4p)

Answer: A)

ser-zykov [4K]3 years ago

6 0

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

$(p^3)(2p^2-4p)(3p^2-1)$

Now, we will solve the last two terms using "Product of polynomials":

$\left(2p^2-4p\right)\left(3p^2-1\right)\\\\\text{Using this :}\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\\\\a=2p^2,\:b=-4p,\:c=3p^2,\:d=-1\\\\=2p^2\cdot \:3p^2+2p^2\left(-1\right)+\left(-4p\right)\cdot \:3p^2+\left(-4p\right)\left(-1\right)$

So, at last it becomes:

$\left(p^3\right)\left(6p^4-12p^3-2p^2+4p\right)$

Hence, Option 'A' is correct.

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Please answer the question above.

kenny6666 [7]

Answer:

5.3!

Step-by-step explanation:

( in case you need work ) the angles are congruent so you set them equal to each other!

6x+12=9x-4

you then get 16=3x then divided its 5.3!

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3 years ago

Solve these linear equations by Cramer's Rules Xj=det Bj / det A:

timurjin [86]

Answer:

(a) $x_1=-2,x_2=1$

(b) $x_1=\frac{3}{4} ,x_2=-\frac{1}{2} ,x_3=\frac{1}{4}$

Step-by-step explanation:

(a) For using Cramer's rule you need to find matrix $A$ and the matrix $B_j$ for each variable. The matrix $A$ is formed with the coefficients of the variables in the system. The first step is to accommodate the equations, one under the other, to get $A$ more easily.

$2x_1+5x_2=1\\x_1+4x_2=2$

$\therefore A=\left[\begin{array}{cc}2&5\\1&4\end{array}\right]$

To get $B_1$ , replace in the matrix A the 1st column with the results of the equations:

$B_1=\left[\begin{array}{cc}1&5\\2&4\end{array}\right]$

To get $B_2$ , replace in the matrix A the 2nd column with the results of the equations:

$B_2=\left[\begin{array}{cc}2&1\\1&2\end{array}\right]$

Apply the rule to solve $x_1$ :

$x_1=\frac{det\left(\begin{array}{cc}1&5\\2&4\end{array}\right)}{det\left(\begin{array}{cc}2&5\\1&4\end{array}\right)} =\frac{(1)(4)-(2)(5)}{(2)(4)-(1)(5)} =\frac{4-10}{8-5}=\frac{-6}{3}=-2\\x_1=-2$

In the case of B2, the determinant is going to be zero. Instead of using the rule, substitute the values of the variable $x_1$ in one of the equations and solve for $x_2$ :

$2x_1+5x_2=1\\2(-2)+5x_2=1\\-4+5x_2=1\\5x_2=1+4\\ 5x_2=5\\x_2=1$

(b) In this system, follow the same steps,ust remember $B_3$ is formed by replacing the 3rd column of A with the results of the equations:

$2x_1+x_2 =1\\x_1+2x_2+x_3=0\\x_2+2x_3=0$

$\therefore A=\left[\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right]$

$B_1=\left[\begin{array}{ccc}1&1&0\\0&2&1\\0&1&2\end{array}\right]$

$B_2=\left[\begin{array}{ccc}2&1&0\\1&0&1\\0&0&2\end{array}\right]$

$B_3=\left[\begin{array}{ccc}2&1&1\\1&2&0\\0&1&0\end{array}\right]$

$x_1=\frac{det\left(\begin{array}{ccc}1&1&0\\0&2&1\\0&1&2\end{array}\right)}{det\left(\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right)} =\frac{1(2)(2)+(0)(1)(0)+(0)(1)(1)-(1)(1)(1)-(0)(1)(2)-(0)(2)(0)}{(2)(2)(2)+(1)(1)(0)+(0)(1)(1)-(2)(1)(1)-(1)(1)(2)-(0)(2)(0)}\\ x_1=\frac{4+0+0-1-0-0}{8+0+0-2-2-0} =\frac{3}{4} \\x_1=\frac{3}{4}$

$x_2=\frac{det\left(\begin{array}{ccc}2&1&0\\1&0&1\\0&0&2\end{array}\right)}{det\left(\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right)} =\frac{(2)(0)(2)+(1)(0)(0)+(0)(1)(1)-(2)(0)(1)-(1)(1)(2)-(0)(0)(0)}{4} \\x_2=\frac{0+0+0-0-2-0}{4}=\frac{-2}{4}=-\frac{1}{2}\\x_2=-\frac{1}{2}$

$x_3=\frac{det\left(\begin{array}{ccc}2&1&1\\1&2&0\\0&1&0\end{array}\right)}{det\left(\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right)}=\frac{(2)(2)(0)+(1)(1)(1)+(0)(1)(0)-(2)(1)(0)-(1)(1)(0)-(0)(2)(1)}{4} \\x_3=\frac{0+1+0-0-0-0}{4}=\frac{1}{4}\\x_3=\frac{1}{4}$

6 0

3 years ago

The formula can be used to work outthe cost, in riyals, of hiring a helmet inQatar for a number of days.Kasun wants to hire a bi

Margaret [11]

Answer:

The answer is below

Step-by-step explanation:

a) Cost of hiring the bicycle for 14 days is:

Cost = 65 * 14 days + 44 = 954 riyals

b) The number of days the bicycle is hired is to be the same as the number of days the bicycle is to be hired. Let us assume that the bicycle and helmet is to be hired for x days, hence:

Cost of bicycle = 65 * x + 14 = 65x + 44

Cost of helmet = 12.5 * x = 12.5x

Total cost = 65x + 44 + 12.5x = 77.5x + 44

Since 750 riyals is available, hence:

750 = 77.5x + 44

77.5x = 706

x = 9.11

Therefore the maximum number of days is 11. The total cost for 11 days is:

Total cost = 77.5(9) + 44 = 741.5 riyals

Money not spent = 750 riyals - 741.5 riyals = 8.5 riyals

6 0

2 years ago

A radio station had 60 tickets to a concert. They gave away 2 times as many tickets to listeners as to employees. How many ticke

Nataly_w [17]

Answer:

they gave 20 to the employee trust me

5 0

2 years ago

The length of a room is 4 feet less than twice its width. The perimeter of

AlladinOne [14]

L=2W-4

PERIMETER=2L+2W

58=2(2W-4)+2W

58=4W-8+2W

58=6W-8

6W=58+8

6W=66

W=66/6

W=11 ANS. FOR THE WIDTH.

L=2*11-4

L=22-4

L=18 ANS. FOR THE LENGTH.

PROOF:

58=2*18=2*11

58=36+22

58=58

5 0

2 years ago