This is a linear relationship. The slope-intercept form of the linear equation is:
Where,
- m is the rate of change (positive if increasing rate and negative if decreasing rate)
- c is the y intercept, or the initial value
<u><em>Rate of change is 2.5 quarts per minute (it is decreasing so m is -2.5)</em></u>
<u><em>Initial value is 50 quarts, so c is 50.</em></u>
Plugging in the values we get 
.
Changing variables to w instead of y and t instead of x, gives us,
. Where w is warts of water left in the tub and t is the time in minutes.
There is no viable solution when t=30 because at t=20, w=0 (
). It means after 20 minutes, there is no water left. So t=30 minutes doesn't make sense.
ANSWER:
Modelling equation:
When 
, there is no VIABLE solution
Answer:
you just have to check the first and the third box
Step-by-step explanation:
put each into slop intercept form
y+6=-5(x-2) is the same as y=-5x+4
y-2=-5(x+6) is the same as y=-5x-28
y=-5x+4
y=-5x-28
all of them have a slope of -5, but you need to plug in (2,-6) to see which on is true
Answer:
32. ∛((x-7)/4) = f^(-1)(x)
33. -10x - 9
Step-by-step explanation:
32. We want to switch f(x) and x, and then solve for f(x) to get the inverse.
x = 4f(x)³ + 7
subtract 7 from both sides
x -7 = 4f(x)³
divide both sides by 4
(x-7)/4 = f(x)³
cube root both sides
∛((x-7)/4) = f(x)
make f(x) f^(-1)(x) because this is now the inverse
∛((x-7)/4) = f^(-1)(x)
the second answer is correct
33. for composition, we can treat (f · g) (x) as attached picture (content filter!), so we plug g(x) into f(x). This results in
2(-5x-7) + 5
expand
-10x - 14 + 5
add
-10x - 9
the second answer is correct
So we already drew two cards and both of them are spades. So that means there are 50 cards and 11 spades left.
Then third card being spades would be 11 / 50
Now there are 10 spades and 49 cards left.
So the probability for fourth card would be 10 / 49
Fifth card would be 9 / 48.
So the probability of next three cards being spades would be
Hope this helps.
