For this case we have that the following function complies with the given conditions:
To prove it, let's find the roots of the polynomial:
By doing common factor 3 we have:
Factoring the second degree polynomial we have:
Then, the solutions are:
Solution 1:
Solution 2:
Answer:
A second degree polynomial function f (x) that has a lead coefficient of 3 and roots 4 and 1 is:
Answer:
7 quarts = 28 cups
10 cups = 2.5 quarts
Step-by-step explanation:
In order to solve the two different questions in the problem, starting with a ratio of the number of quarts to the number of cups would be helpful:
So, for every 1 quart of milk, she can pour 4 cups. Using this ratio, we can set up equivalent ratios, or proportions, to solve for the missing value. For the first question, we need to know that amount of cups in 7 quarts:
We can solve for 'x' by multiplying the numerator and denominator by the same factor, in this case '7'. So, 4 x 7 = 28 cups.
Next, we need to solve for the amount of quarts needed for 10 cups:
4 x 2.5 = 10, so we need to multiply the numerator by 2.5: 1 x 2.5 = 2.5 quarts.