Find the circumference of this circle. 47cm 3.14 30cm 15cm

The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the ge

Leno4ka [110]

Answer:

Infinite number of solutions.

Step-by-step explanation:

We are given system of equations

$5x+4y+5z=-1$

$x+y+2z=1$

$2x+y-z=-3$

Firs we find determinant of system of equations

Let a matrix A= $\left[\begin{array}{ccc}5&4&5\\1&1&2\\2&1&-1\end{array}\right]$ and B= $\left[\begin{array}{ccc}-1\\1\\-3\end{array}\right]$

$\mid A\mid=\begin{vmatrix}5&4&5\\1&1&2\\2&1&-1\end{vmatrix}$

$\mid A\mid=5(-1-2)-4(-1-4)+5(1-2)=-15+20-5=0$

Determinant of given system of equation is zero therefore, the general solution of system of equation is many solution or no solution.

We are finding rank of matrix

Apply $R_1\rightarrow R_1-4R_2$ and $R_3\rightarrow R_3-2R_2$

$\left[\begin{array}{ccc}1&0&1\\1&1&2\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\1\\-5\end{array}\right]$

Apply $R_2\rightarrow R_2-R_1$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\-5\end{array}\right]$

Apply $R_3\rightarrow R_3+R_2$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&0&-2\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\1\end{array}\right]$

Apply $R_3\rightarrow- \frac{1}{2}$ and $R_2\rightarrow R_2-R_3$

$\left[\begin{array}{ccc}1&0&1\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Apply $R_1\rightarrow R_1-R_3$

$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-\frac{9}{2}\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Rank of matrix A and B are equal.Therefore, matrix A has infinite number of solutions.

Therefore, rank of matrix is equal to rank of B.

4 0

3 years ago

1 in/2.54 cm = 90 in/? cm

nirvana33 [79]

1/2.54 = 90/x

Cross multiply
(1)x = (2.54)(90)

x would equal 228.6

The answer would be 90 in/ 228.6 cm.

7 0

3 years ago

Please solve this quickly

adell [148]

Answer:

I Didn't see nothing

Step-by-step explanation:

So I can't help you

7 0

2 years ago

Read 2 more answers

Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x) and express P(x) in the for

lilavasa [31]

Answer:

$P(x)=(x+9)(x^2-7x+52)+3$

Step-by-step explanation:

We are given that

$P(x)=x^3+2x^2-11x+471$

$d(x)=x+9$

We have to find the value of Q(x) and Remainder R(x).

Quotient, $Q(x)=x^2-7x+52$

Remainder, $R(x)=3$

We know that

$Dividend=Divisor\times Quotient+Remainder$

$P(x)=(x+9)(x^2-7x+52)+3$

4 0

3 years ago

M/n=p-6 what is n how to solve

madreJ [45]

M/n=p-6
n= m/(p-6)
i swapped the n and p-6

4 0

3 years ago