Johnathan ran 5 days this week. The most he ran in one day was 3.5 miles. Write an inequality that shows the distance johnathan
1 answer:
<em><u>An inequality that shows the distance Johnathan could of ran any day this week is:</u></em>
<em><u>Solution:</u></em>
Let "x" be the distance Johnathan can run any day of this week
Given that,
Johnathan ran 5 days this week. The most he ran in one day was 3.5 miles
Therefore,
Number of days ran = 5
The most he ran in 1 day = 3.5 miles
Thus, the maximum distance he ran in a week is given as:
The maximum distance he ran in a week is 17.5 miles
If we let x be the distance he can run any day of this week then, we get a inequality as:
If we let y be the total distance he can travel in a week then, we may express it as,
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I am somehow confused with the given matrix. Because usually, when the system of equations is given as:
ax + by = c
dx + ey = f
the matrix would be written in this manner:
![\left[\begin{array}{ccc}a&b&c\\d&e&f\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%26c%5C%5Cd%26e%26f%5Cend%7Barray%7D%5Cright%5D%20)
Let me just assume that the arrangement of the given corresponds to this system of equations:
4x + 8y = 0
2x + 5y = 6
So you write it as
![\left[\begin{array}{ccc}4&8&0\\2&5&6\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%268%260%5C%5C2%265%266%5Cend%7Barray%7D%5Cright%5D%20)
In order to solve this, the matrix should look like this where x and y are the answers
![\left[\begin{array}{ccc}1&0&x\\0&1&y\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26x%5C%5C0%261%26y%5Cend%7Barray%7D%5Cright%5D%20)
So, the first thing to do is apply this pattern: Row 2 = Row 1 - 2*Row 2. The result will be
![\left[\begin{array}{ccc}4&8&0\\0&-2&-12\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%268%260%5C%5C0%26-2%26-12%5Cend%7Barray%7D%5Cright%5D%20)
Next, Row 1 = (Row 1/4) + R2:
![\left[\begin{array}{ccc}1&0&-12\\0&-2&-12\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26-12%5C%5C0%26-2%26-12%5Cend%7Barray%7D%5Cright%5D%20)
Lastly, Row 2 = Row 2 / -2:
![\left[\begin{array}{ccc}1&0&-12\\0&1&6\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26-12%5C%5C0%261%266%5Cend%7Barray%7D%5Cright%5D%20)
Thus, the answer is x=-12 and y=6.
ax + by = c
dx + ey = f
the matrix would be written in this manner:
Let me just assume that the arrangement of the given corresponds to this system of equations:
4x + 8y = 0
2x + 5y = 6
So you write it as
In order to solve this, the matrix should look like this where x and y are the answers
So, the first thing to do is apply this pattern: Row 2 = Row 1 - 2*Row 2. The result will be
Next, Row 1 = (Row 1/4) + R2:
Lastly, Row 2 = Row 2 / -2:
Thus, the answer is x=-12 and y=6.