Step-by-step explanation: Let
Let
y
be the total fee, and
x
the number of months.
Equation 1:
y
=
50
+
55
x
Equation 2:
y
=
200
+
45
x
Solve the system for
x
and
y
:
50
+
55
x
=
200
+
45
x
10
x
=
150
x
=
15
y
=
200
+
45
(
15
)
y
=
875
∴
The total amount paid to both gyms is equal after
15
months and will be
$
875
.
Hopefully this helps!
Answer:
177 pounds
Step-by-step explanation:
Create an equation to represent the system.
Since it's 18% more than what was used last month an equation can be written such as the one below:
(118%)( last month's cheese ) = this month's cheese
Convert the percentages into decimals by moving the decimal place at the end of 118.00 two places to the left
118% = 1.18
( 1.18 )( last month's cheese ) = this month's cheese
Next, plug in the number for last month's cheese
( 1.18 )( 150 pounds) =
177 pounds
<span>The fact that Helen’s indifference curves touch the axes should immediately make you want to check for a corner point solution. To see the corner point optimum algebraically, notice if there was an interior solution, the tangency condition implies (S + 10)/(C +10) = 3, or S = 3C + 20. Combining this with the budget constraint, 9C + 3S = 30, we find that the optimal number of CDs would be given by 3018â’=Cwhich implies a negative number of CDs. Since it’s impossible to purchase a negative amount of something, our assumption that there was an interior solution must be false. Instead, the optimum will consist of C = 0 and Helen spending all her income on sandwiches: S = 10. Graphically, the corner optimum is reflected in the fact that the slope of the budget line is steeper than that of the indifference curve, even when C = 0. Specifically, note that at (C, S) = (0, 10) we have P C / P S = 3 > MRS C,S = 2. Thus, even at the corner point, the marginal utility per dollar spent on CDs is lower than on sandwiches. However, since she is already at a corner point with C = 0, she cannot give up any more CDs. Therefore the best Helen can do is to spend all her income on sandwiches: ( C , S ) = (0, 10). [Note: At the other corner with S = 0 and C = 3.3, P C / P S = 3 > MRS C,S = 0.75. Thus, Helen would prefer to buy more sandwiches and less CDs, which is of course entirely feasible at this corner point. Thus the S = 0 corner cannot be an optimum]</span>
Answer: -10x + 1y = 2
Step-by-step explanation:
The standard formula says that Ax + By = C where A is the coefficient of the x variable, B is the coefficient of the y variable, and C is the constant value.
y = 10x + 2 Subtract 10x from both sides of the equation .
-10x -10x
-10x + 1y = 2
We know that the lace is also what we would call the circumference of the circle.
And we also know that the circumference of a circle is represented by the equation:
.
We then can use the length of the lace (12.56 ft) to solve for the diameter (d) of the rug. Let us solve for that now:
We now know that the diameter of the rug is
4 ft.
