Answer: $13
Step-by-step explanation:
To determine the solution arithmetically in two steps, first divide 68.25 by 3 and then subtract 9.75 from the result. To determine the solution algebraically, set up and solve the equation 3(x+9.75)=68.25. Each friend paid $13 for dinner.
Answer:
Step-by-step explanation:
A direct variation equation is of the form
y = kx,
where, in words, it reads "y varies directly with x" or "y varies directly as x". In order to use this as a model, we have to have enough information to solve for k, the constant of variation. The constant of variation is kind of like the slope in a straight line. It rises or falls at a steady level; it is the rate of change.
We have that a vet gives a dose of three-fifths mg to a 30 pound dog. If the dose varies directly with the weight of the dog, then our equation is
d = kw and we need to find k in order to have the model for dosing the animals.
Divide both sides by 1/30 to get k alone.
and
Our model then is
This means that for every pound of weight, the dog will get one-fiftieth of a mg of medicine.
To find the height, you would do the area divided by the base, or in this case,187.5 / 25 which equals 7.5 inches. Hope this helped!
Given:
4log1/2^w (2log1/2^u-3log1/2^v)
Req'd:
Single logarithm = ?
Sol'n:
First remove the parenthesis,
4 log 1/2 (w) + 2 log 1/2 (u) - 3 log 1/2 (v)
Simplify each term,
Simplify the 4 log 1/2 (w) by moving the constant 4 inside the logarithm;
Simplify the 2 log 1/2 (u) by moving the constant 2 inside the logarithm;
Simplify the -3 log 1/2 (v) by moving the constant -3 inside the logarithm:
log 1/2 (w^4) + 2 log 1/2 (u) - 3 log 1/2 (v)
log 1/2 (w^4) + log 1/2 (u^2) - log 1/2 (v^3)
We have to use the product property of logarithms which is log of b (x) + log of b (y) = log of b (xy):
Thus,
Log of 1/2 (w^4 u^2) - log of 1/2 (v^3)
then use the quotient property of logarithms which is log of b (x) - log of b (y) = log of b (x/y)
Therefore,
log of 1/2 (w^4 u^2 / v^3)
and for the final step and answer, reorder or rearrange w^4 and u^2:
log of 1/2 (u^2 w^4 / v^3)
