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Anon25 [30]
2 years ago
11

Let f(x) = x + 8 and g(x) = x2 − 6x − 7. Find f(g(2)). (1 point)

Mathematics
1 answer:
pantera1 [17]2 years ago
4 0
Hello,

f(x)=x+8
g(x)=x²-6x-7
f(g(x))=f(x²-6x-7)=x²-6x-7+8=x²-6x+1

f(g(2))=2²-6*2+1=4-12+1=-8+1=-7

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

Step-by-step explanation:

We are given system of equations

5x+4y+5z=-1

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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]

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\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]

ApplyR_2\rightarrow R_2-R_1

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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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