$\qquad \qquad \textit{direct joint variation} \\\\ \textit{\underline{y} varies directly with \underline{x} and \underline{z}}~\hspace{8.5em} \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}xz~\hfill } \\\\ \textit{\underline{y} varies directly with \underline{x}, }w^2\textit{ and }z^5~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}xw^2z^5~\hfill } \\\\[-0.35em] ~\dotfill$

$y = kxz\qquad \textit{we know that} \begin{cases} x=2\\ y=12\\ z=5 \end{cases}\implies 12=k(2)(5) \\\\\\ \cfrac{12}{(2)(5)}=k\implies \cfrac{6}{5}=k~\hspace{10em}\boxed{y=\cfrac{6}{5}xz}$

6 0

2 years ago

Which point is on the perpendicular bisector of the segment with endpoints (-2,5) and (-2,-3)

Kryger [21]

(-2,0)

Lies on the X axis makes it perpendicular with the other points

3 0

2 years ago

A car uses 1 gallon of gasoline for every 25 miles driven. At the start of a trip the tank was full of gasoline. After driving 5

dezoksy [38]

Answer:

d = 22 - x / 25

Step-by-step explanation:

The first thing is to calculate the tank capacity, we know that per gallon 25 miles are traveled and at 500 miles there were still two gallons, therefore:

500 miles / 25 miles / gallon = 20

and how there were still 2

20 + 2 = 22

the tank has a 22 gallon capacity

Therefore the equation would be:

d = 22 - x / 25

where x is the number of miles traveled.

for example, if they have traveled 500 miles it would be:

d = 22 - 500/25 = 22 - 20

d = 2 gallons

we can verify that it is correct because it is what the statement says

8 0

3 years ago