I added a screenshot with the complete question.
Answer:5 hours
Explanation:We are given that:
Revenue equation:
y = 420 + 72x
Overhead equation:
24x² + 180
We are asked to get the break-even point which is calculated by equating the revenue to the overhead cost.
This can be done as follows:
revenue = overhead cost
420 + 72x = 24x² + 180
24x² + 180 - 420 - 72x = 0
24x² - 72x -240 = 0
(x-5)(x+2) = 0
either: x-5=0 ..........> x = 5 hours (accepted value)
or: x+2=0 .......> x = -2 hours (rejected value as time cannot be negative)
Based on the above:
break-even occurs at 5 hours
Hope this helps :)
Answer:
11.55
Step-by-step explanation:
SOH CAH TOA reminds you ...
Tan = Opposite/Adjacent
The angle at lower left is the complement of 60°, so is 30°. Then the side x satisfies the equation ...
tan(30°) = x/20
Multiplying by 20 gives ...
20·tan(30°) = x ≈ 11.55
Answer: There is not a good prediction for the height of the tree when it is 100 years old because the prediction given by the trend line produced by the regression calculator probably is not valid that far in the future.
Step-by-step explanation:
Years since tree was planted (x) - - - - height (y)
2 - - - - 17
3 - - - - 25
5 - - - 42
6 - - - - 47
7 - - - 54
9 - - - 69
Using a regression calculator :
The height of tree can be modeled by the equation : ŷ = 7.36X + 3.08
With y being the predicted variable; 7.36 being the slope and 3.08 as the intercept.
X is the independent variable which is used in calculating the value of y.
Predicted height when years since tree was planted(x) = 100
ŷ = 7.36X + 3.08
ŷ = 7.36(100) + 3.08
y = 736 + 3.08
y = 739.08
Forward prediction of 100 years produced by the trendline would probably give an invalid value because the trendline only models a range of 9 years prediction. However, a linear regression equation isn't the best for making prediction that far in into the future.
Answer:
Long sides are 1.4 and short sides are 0.7
Step-by-step explanation:
Number the tables as follows:
1 2
3 4
Eliminate 3 and 4 immediately, because for x = 2 the y values are wrong (3 and 1).
In tables 1 and 2, the input (1) produces the correct output (-1).
So we have to determine which table agrees 100% with the system of equations given.
Comparing tables 1 and 2, row by row, we see that their contents are the same EXCEPT for the first rows. So focus on determing which of those 2 rows displays values that satisfy both given equations.
First I looked at y=2x-5, and subst. -1 for x. I got -7, which is correct in table 1 but not in table 2 (where the value would be -13).
Thus, table 1 correct represents the solution of the system of equations.
