Answer:
Elizabeth spent 17.5 hours and her sister spent 12.5 hours.
Step-by-step explanation:
Let x be the number of hours that Elizabeth shoveled and y be the number of hours that her sister shoveled.
Number of hours they shoveled = 30
So, x + y = 30 or
y = 30 - x
Jenna charged $12 per sidewalk.
So, her total earnings = 12x
Her sister charged $11 per sidewalk.
So, her total earnings = 11y.
Their total income = $347.50.
So, 12x + 11y = 347.5
Substitute y = 30 - x,
12x + 11(30 - x) = 347.5
12x + 330 - 11x = 347.5
x + 330 = 347.5
x = 347.5 - 330
x = 17.5 and
y = 30 - x = 30 - 17.5 = 12.5.
Hence, Elizabeth spent 17.5 hours and her sister spent 12.5 hours.
Answer:
x+y
Step-by-step explanation:
Let's pretend the value of the crayon's is 'y'. The value of the markers is 'x'. If we add them together, we get x+y. This is because we do not know the value of each variable.
Hope this helps! Have a nice day <3
Answer:
7x + 6 = 6x - 3
Step-by-step explanation:
2(x+3) + 5x = 3(2x-1)
Distribute
2x + 6 + 5x = 6x - 3
Combine like terms
7x + 6 = 6x - 3
hope this helps
General Idea:
Domain of a function means the values of x which will give a DEFINED output for the function.
Applying the concept:
Given that the x represent the time in seconds, f(x) represent the height of food packet.
Time cannot be a negative value, so
The height of the food packet cannot be a negative value, so
We need to replace 
for f(x) in the above inequality to find the domain.
![-15x^2+6000\geq 0 \; \; [Divide \; by\; -15\; on\; both\; sides]\\ \\ \frac{-15x^2}{-15} +\frac{6000}{-15} \leq \frac{0}{-15} \\ \\ x^2-400\leq 0\;[Factoring\;on\;left\;side]\\ \\ (x+200)(x-200)\leq 0](https://tex.z-dn.net/?f=%20-15x%5E2%2B6000%5Cgeq%200%20%5C%3B%20%5C%3B%20%20%5BDivide%20%5C%3B%20by%5C%3B%20-15%5C%3B%20on%5C%3B%20both%5C%3B%20sides%5D%5C%5C%20%5C%5C%20%5Cfrac%7B-15x%5E2%7D%7B-15%7D%20%2B%5Cfrac%7B6000%7D%7B-15%7D%20%5Cleq%20%5Cfrac%7B0%7D%7B-15%7D%20%5C%5C%20%5C%5C%20x%5E2-400%5Cleq%200%5C%3B%5BFactoring%5C%3Bon%5C%3Bleft%5C%3Bside%5D%5C%5C%20%5C%5C%20%28x%2B200%29%28x-200%29%5Cleq%200%20)
The possible solutions of the above inequality are given by the intervals ![(-\infty , -2], [-2,2], [2,\infty )](https://tex.z-dn.net/?f=%20%28-%5Cinfty%20%2C%20-2%5D%2C%20%5B-2%2C2%5D%2C%20%5B2%2C%5Cinfty%20%29%20)
. We need to pick test point from each possible solution interval and check whether that test point make the inequality 
true. Only the test point from the solution interval [-200, 200] make the inequality true.
The values of x which will make the above inequality TRUE is 
But we already know x should be positive, because time cannot be negative.
Conclusion:
Domain of the given function is 
