Answer:
Every week, the mass of the sample is multiplied by a factor of 0.81
Step-by-step explanation:
Let's rewrite the base and find the expression whose exponent is just ttt.
(0.97)7t+5=(0.97)7t⋅(0.97)5=(0.977)t⋅(0.97)5
Therefore, we can rewrite the modeling function as follows.
M(t)=(0.97)5⋅(0.977)t
According to this model, the mass of the sample is multiplied by 0.977 every week. Rounding this to two decimal places, we get 0.977≈0.81.
Answer: it will take 40 rides to break even.
Step-by-step explanation:
Profit = Revenue - total cost
At the point of break even, there is no profit. It means that
revenue = total cost
The cost c (in dollars) for the fuel and maintenance of a go-cart is given by
c = 10x + 1200
where x is the number of rides. It costs $40 per ride. This means that the revenue gotten from x rides is 40x.
In order to break even, it means that
40x = 10x + 1200
40x - 10x = 1200
30x = 1200
x = 1200/30
x = 40
X=29 and y=10
You would isolate one of the variables and then plug the expression into the other equation to find the value of one variable. Then you would plug this value into the other equation to determine the value of the remaining variable.
Answer:
x = 5
Step-by-step explanation:
Step 1: Write equation
-(1 + 7x) - 6(-7 - x) = 36
Step 2: Solve for <em>x</em>
- Distribute: -1 - 7x + 42 + 6x = 36
- Combine like terms: -x + 41 = 36
- Subtract 41 on both sides: -x = -5
- Divide both sides: x = 5
Step 3: Check
<em>Plug in x to verify it's a solution.</em>
-(1 + 7(5)) - 6(-7 - 5) = 36
-(1 + 35) - 6(-12) = 36
-(36) + 72 = 36
-36 + 72 = 36
36 = 36
