Answer: Raymond is correct
The DJ charges $75 an hour.
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Explanation:
x = number of hours
y = total cost
The DJ does a 3-hour event for $275. This means one point is (x,y) = (3,275)
Another point is (5,425) because a 5-hour event costs $425.
Let's find the slope of the line through these two points.
The slope is 75, meaning that each time y goes up by 75, x goes up by 1.
Flipped around it means each time x goes up by 1, y goes up by 75.
This means each time we add on an extra hour, the cost goes up by $75.
The DJ charges $75 an hour. Raymond is correct.
Answer:
x = 57/28
y = -95/84
z = 97/168
Step-by-step explanation:
Use the application in the next link: https://www.zweigmedia.com/RealWorld/tutorialsf1/scriptpivotold.html
Start with the expanded array:
![\left[\begin{array}{cccc}1&5&8&1\\3&2&2&5\\-2&-7&2&5\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%265%268%261%5C%5C3%262%262%265%5C%5C-2%26-7%262%265%5C%5C%5Cend%7Barray%7D%5Cright%5D)
then using the tool provided, make row operations until you find the solution:
r2 = r2-3r1
![\left[\begin{array}{cccc}1&5&8&1\\0&-13&-22&2\\-2&-7&2&5\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%265%268%261%5C%5C0%26-13%26-22%262%5C%5C-2%26-7%262%265%5C%5C%5Cend%7Barray%7D%5Cright%5D)
r3 = r3+2r1
![\left[\begin{array}{cccc}1&5&8&1\\0&-13&-22&2\\0&3&18&7\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%265%268%261%5C%5C0%26-13%26-22%262%5C%5C0%263%2618%267%5C%5C%5Cend%7Barray%7D%5Cright%5D)
r2 = r2*(-1/13)
![\left[\begin{array}{cccc}1&5&8&1\\0&1&22/13&-2/13\\0&3&18&7\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%265%268%261%5C%5C0%261%2622%2F13%26-2%2F13%5C%5C0%263%2618%267%5C%5C%5Cend%7Barray%7D%5Cright%5D)
r1 = r1- r2*5
![\left[\begin{array}{cccc}1&0&-6/13&23/13\\0&1&22/13&-2/13\\0&3&18&7\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26-6%2F13%2623%2F13%5C%5C0%261%2622%2F13%26-2%2F13%5C%5C0%263%2618%267%5C%5C%5Cend%7Barray%7D%5Cright%5D)
r3 = r3+ r2*-3
![\left[\begin{array}{cccc}1&0&-6/13&23/13\\0&1&22/13&-2/13\\0&0&168/13&97/13\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26-6%2F13%2623%2F13%5C%5C0%261%2622%2F13%26-2%2F13%5C%5C0%260%26168%2F13%2697%2F13%5C%5C%5Cend%7Barray%7D%5Cright%5D)
r3 = r3*13/168
![\left[\begin{array}{cccc}1&0&-6/13&23/13\\0&1&22/13&-2/13\\0&0&1&97/168\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26-6%2F13%2623%2F13%5C%5C0%261%2622%2F13%26-2%2F13%5C%5C0%260%261%2697%2F168%5C%5C%5Cend%7Barray%7D%5Cright%5D)
r2 = r2- r3*22/13
![\left[\begin{array}{cccc}1&0&-6/13&23/13\\0&1&0&-95/84\\0&0&1&97/168\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26-6%2F13%2623%2F13%5C%5C0%261%260%26-95%2F84%5C%5C0%260%261%2697%2F168%5C%5C%5Cend%7Barray%7D%5Cright%5D)
r2 = r2+ r3*6/13
![\left[\begin{array}{cccc}1&0&0&57/28\\0&1&0&-95/84\\0&0&1&97/168\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%260%2657%2F28%5C%5C0%261%260%26-95%2F84%5C%5C0%260%261%2697%2F168%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Here you have a reduced array an therefore the answers to each variable are on each row:
![\left[\begin{array}{c}x\\y\\z\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D)
C-Cost because it the most reasonableness one
Answer:
12600 g
Step-by-step explanation:
a kilogram is a thousand grams
(don't forget to include units)
Answer:
k=4
Step-by-step explanation:
-The constant of proportionality is defined as the ratio between two directly proportional variables.
-Given that B=4f
#The constant of proportionality is calculated as:
- the equation can be written in the form y=kx,
where y varies directly with x and k is the constant of variation:
Hence, B varies directly with f with a constant of proportionality k=4
