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3 years ago

11

Eric practiced piano and guitar for a total of 8 hours this week. he practiced the piano for 1/4 or that time. how many hours di

d Eric practiced the piano this week

2 answers:

AlexFokin [52]3 years ago

5 0

2 because if 1/2 of 8 is 4 and 1/4 of 8 is = to 1/2 of 4, then 1/4 of 8 must be 2.

nika2105 [10]3 years ago

3 0

2 hours because if you count by 2's: 2, 4, 6, 8, you can see that a 1/4 of 8 is 2.
you can also just divide 8 by 2.

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vlabodo [156]

Steps to solve:

c - 12 = 3

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Answer:

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Step-by-step explanation:

We are given system of equations

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

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Firs we find determinant of system of equations

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

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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.

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Step-by-step explanation:

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