Answer:
Step-by-step explanation:
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21) Total number of cups: 26
6) Solution of the equation: x = -12
7) Father's age: 40
4) Distance driven: 400 miles
Step-by-step explanation:
21)
Let's call:
the height of each cup
the total height available in the dispenser
We are told that each cup added to the stack add a height of
We can therefore solve the problem by writing the following equation:
which means that the total height available (H) is filled by the height of one cup (h) + the number of additional cup multiplied by 0.8.
Solving for N:
And including the first cup, the total number of cups is
6)
The equation that we have to solve is
We proceed as follows:
First of all, we add +1 on both sides of the equation,
Now we multiply by 2 on both sides:
And now we divide both sides by 5:
7)
Let's call:
k = Karma's age
f = father's age
We are told that Karma is 13 years old, so
k = 13
Also, Karma's age is 2 years less than 3/8 of the father's age, so we can write
By combining the two equations,
And solving for f, we find:
So, the father's age is 40.
4)
Let's call:
T = 16 the total volume of the tank (16 gallons)
We also know that the car burns 0.03 gallons per mile, so the amount of fuel consumed after x miles is
This means that the amount of fuel left after x miles is
We also know that the amount of fuel left is 4 gallons, therefore:
So, 400 miles.
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Answer:
(x, y) = (3, 5/2)
Step-by-step explanation:
I'll solve by elimination here. If you invert the second equation and add it to the first, 2y and -2y would cancel out.
Now just add those from top to bottom.
Nothing else needs to be done for that part. Now, you can pick either equation and use the known value of x to solve for y.
(x, y) = (3, 5/2)