Hello from MrBillDoesMath!
Answer:
31a. 2 real roots
31b 2 complex roots
Discussion:
31a.
2x^2 + 3x - 6 = 0
Using standard quadratic notation, the above equation has a = 2, b = 3 and c = -6. The discriminant is given by b^2 - 4ac, which is
3^2 - 4*2*(-6) = 9 + 48 = 57 > 0, so the quadratic has 2 real roots
31b.
The equation is equivalent to 16x^2 + 10x +3 = 0. Its discriminant is
10^2 - 4 * (16) * (3) = 100 - 192 = -92 so this equation has two complex roots
Regards,
MrB
Answer:

Step-by-step explanation:
Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.To calculate combinations the below formula is used:

where
represents the total number of items and
represent the number of items being chosen at a time. The '!' represents factorial function which is the product of all integers equal to and less than the given integer. This can be calculated manually using the formula or by using the nCr function on a scientific calculator.
Thus, the number of ways to select 2 freshmen girls (2FG) and 3 freshmen boys (3FB) can be determined. The number of ways to select 5 students (5S) can be determined in the same way.



The probability of selecting 2 freshmen girls (2FG) and 3 freshmen boys (3FB) when selecting 5 students out of 30 is given as below:

For this case we convert the mixed numbers to improper fractions:
Now, we propose a rule of three:
pounds of blueberries ------------->
cups of muffin mix
7 pounds of blueberries -----------------------------> x
Where the variable "x" represents the number of cups of muffin mix that Honey should use.

So approximately Honey should use
cups of muffin mix
Answer:
Approximately Honey should use
cups of muffin mix
Answer:
150
Step-by-step explanation:
First you have to find what number 80 is 2/5 of, to do this do the reciprocal of 2/5 which would be 5/2. Multiply 80 by 5/2 and you'll get 200, then find what 3/4 of 200. Multiply 200 by 3, then divide by 4 to get the answer of 150.
Answer:
(7, 46)
Step-by-step explanation:
The offered answer choices have x-values of 7, 9, 10. The corresponding upper limit of y-value is ...
x=7 : y < 8·7 -3 = 53 . . . . . 46 is in the solution set, 60 is not
x=9 : y < 8·9 -3 = 69 . . . . 82 is not in the solution set
x=10 : y < 8·10 -3 = 77 . . . . 89 is not in the solution set
Of the choices offered, only (7, 46) is in the solution set.