taumulurtulkyoy
2022-10-12
Answered

If 12 friends want 1/3 of a sandwich each how many sandwiches would they need to order?

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Audrey Russell

Answered 2022-10-13
Author has **16** answers

$\frac{1}{3}\times \frac{12}{1}=\frac{12}{3}=4$

So, each friend wants a third of a sandwich and there are twelve friends. Twelve times one third is twelve thirds, or four.

So, each friend wants a third of a sandwich and there are twelve friends. Twelve times one third is twelve thirds, or four.

asked 2021-06-01

Find the linear approximation of the function

Use L(x) to approximate the numbers

asked 2022-07-10

we have a system of linear equations as such:

$x+2y+(a-1)z=1\phantom{\rule{0ex}{0ex}}-x-y+z=0\phantom{\rule{0ex}{0ex}}-ax-(a+3)y-az=-3\phantom{\rule{0ex}{0ex}}-ax-(a+2)y+0\cdot z={a}^{2}-5a-2$

and i have to find the solution in $\mathbb{R}$ and ${\mathbb{Z}}_{\mathbb{5}}$ so i have no problem for $\mathbb{R}$ i get the matrix

$\left(\begin{array}{cccc}1& 2& a-1& 1\\ 0& 1& a& 1\\ 0& 0& a& 0\\ 0& 0& a& {a}^{2}-5\cdot a\end{array}\right)$

but the questions i have are as follows:

1. Can i use what i found for the augmented matrix and the discussion by parameter a in $\mathbb{R}$ to deduce ${\mathbb{Z}}_{\mathbb{5}}$?

2. Or is there some other way i must reduce to row echelon form for ${\mathbb{Z}}_{\mathbb{5}}$ and then have the discussion for parameter a?

3. If i had an 3x3 or 4x4 system to solve over a low prime ${\mathbb{Z}}_{{\mathbb{p}}_{\mathbb{1}}}$ and ${\mathbb{Z}}_{{\mathbb{p}}_{\mathbb{2}}}$ (eg 5 and 7) how would i go about doing it with the matrix gauss elimination?could i use the same augmented matrix and reduce it to row echelon over $\mathbb{R}$ and then use that augmented matrix for the rest like above or not?

4. If i recall correctly there was a theorem about the rank of the original matrix and augmented that says something about the number of solutions but i do not recall how that would help me find solutions just eliminate the a's where there is none?

$x+2y+(a-1)z=1\phantom{\rule{0ex}{0ex}}-x-y+z=0\phantom{\rule{0ex}{0ex}}-ax-(a+3)y-az=-3\phantom{\rule{0ex}{0ex}}-ax-(a+2)y+0\cdot z={a}^{2}-5a-2$

and i have to find the solution in $\mathbb{R}$ and ${\mathbb{Z}}_{\mathbb{5}}$ so i have no problem for $\mathbb{R}$ i get the matrix

$\left(\begin{array}{cccc}1& 2& a-1& 1\\ 0& 1& a& 1\\ 0& 0& a& 0\\ 0& 0& a& {a}^{2}-5\cdot a\end{array}\right)$

but the questions i have are as follows:

1. Can i use what i found for the augmented matrix and the discussion by parameter a in $\mathbb{R}$ to deduce ${\mathbb{Z}}_{\mathbb{5}}$?

2. Or is there some other way i must reduce to row echelon form for ${\mathbb{Z}}_{\mathbb{5}}$ and then have the discussion for parameter a?

3. If i had an 3x3 or 4x4 system to solve over a low prime ${\mathbb{Z}}_{{\mathbb{p}}_{\mathbb{1}}}$ and ${\mathbb{Z}}_{{\mathbb{p}}_{\mathbb{2}}}$ (eg 5 and 7) how would i go about doing it with the matrix gauss elimination?could i use the same augmented matrix and reduce it to row echelon over $\mathbb{R}$ and then use that augmented matrix for the rest like above or not?

4. If i recall correctly there was a theorem about the rank of the original matrix and augmented that says something about the number of solutions but i do not recall how that would help me find solutions just eliminate the a's where there is none?

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2n +2 = 16

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Find the augmented matrix for the following system of linear equations:

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Define what linear first-order equation forms?

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The Bagel Factory has 12 employees. Eight of them are paid $8.00 an hour, three are paid $10.00 an hour, and the foreman is paid $12.00 an hour. What are the total earnings for one hour?

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Write an equation of a line through (5 -2), perpendicular to x=0