Answer:
For x=7 and y=9 Caleb and Eva will meet again. That is, Caleb will have made 7 labs and Eva 9 labs.
Step-by-step explanation:
In order to find the number of labs that Caleb and Eva must complete, to meet again at the start, you can use the following equation:
(1)
where x is the number of labs made by Caleb and y the number of labs made by Eva. The equation (1) means that for the specific values of x and y, Caleb and Eva will spend the same amount of minutes on the labs.
Then, you need to find the least integers values of x and y.
First, you solve the equation (1) for y:
(2)
By inspection you can find that the least value of x that makes possible that y is an integer, is 7
In fact, you have:
Hence, for x=7 and y=9 Caleb and Eva will meet again. That is, Caleb will have made 7 labs and Eva 9 labs.
Answer: 20%.
Step-by-step explanation:
Given, The price of a shirt is marked down from $12.50 to $10.00.
Previous price = $12.50
New price = $10.00
Change in price = Previous price - New price
= $12.50 - $10.00
= $2.50
Now, the percent decrease of the shirt =
Hence, the percent decrease of the shirt = 20%.
Answer:
Step-by-step explanation:
<u>Inequalities</u>
They relate one or more variables with comparison operators other than the equality.
We must find the set of values for x that make the expression stand
The roots of numerator can be found by trial and error. The only real roots are x=1 and x=-1/2.
The roots of the denominator are easy to find since it's a second-degree polynomial: x=1, x=1/2. Hence, the given expression can be factored as
Simplifying by x-1 and taking x=1 out of the possible solutions:
We need to find the values of x that make the expression less or equal to 0, i.e. negative or zero. The expressions
is always positive and doesn't affect the result. It can be neglected. The expression
can be 0 or positive. We exclude the value x=1/2 from the solution and neglect the expression as being always positive. This leads to analyze the remaining expression
For the expression to be negative, both signs must be opposite, that is
Or
Note we have excluded x=1 from the solution.
The first inequality gives us the solution
The second inequality gives no solution because it's impossible to comply with both conditions.
Thus, the solution for the given inequality is