Which set of numbers does -5 belong

determine if the quadratic equation has 2 solutions, one, or 2 imaginary solutions by using the descriminant

Maurinko [17]

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

7 0

3 years ago

In a math class, 12 out of 15 girls are freshmen and 11 out of 15 boys are freshmen. What is the probability that in a randomly

SashulF [63]

Answer:

$P(2FG|3FB) = \frac{605}{7917}$

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:

$nCr = \frac{n!}{r!(n-r)!}$

where $n$ represents the total number of items and $r$ 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.

$2FG = 12C2 = \frac{12!}{2!(12-2)!} = \frac{12!}{2!(10)!} = 66$

$3FB = 11C3 = \frac{11!}{3!(11-3)!} = \frac{11!}{3!(8)!} = 165$

$5S = 30C5 = \frac{30!}{5!(30-5)!} = \frac{30!}{5!(25)!} = 142506$

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

$P(2FG|3FB) = \frac{2FG*3FB}{5S} = \frac{66*165}{142506} = \frac{605}{7917}$

4 0

3 years ago

Honey's blueberry muffin recipe calls for 3 1/4 pounds of blueberries and 2 1/2 cups of muffin mix. How many cups of muffin mix

astra-53 [7]

For this case we convert the mixed numbers to improper fractions: $3 \frac {1} {4} = \frac {4 * 3 + 1} {4} = \frac {12 + 1} {4} = \frac {13} {4}\\2 \frac {1} {2} = \frac {2 * 2 + 1} {2} = \frac {4 + 1} {2} = \frac {5} {2}$

Now, we propose a rule of three:

$\frac {13} {4}$ pounds of blueberries -------------> $\frac {5} {2}$ 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.

$x = \frac {7 * \frac {5} {2}} {\frac {13} {4}}\\x = \frac {\frac {35} {2}} {\frac {13} {4}}\\x = \frac {35 * 4} {2 * 13}\\x = \frac {140} {26}\\x = \frac {70} {13}\\x = 5.38$

So approximately Honey should use $5 \frac {5} {13}$ cups of muffin mix

Answer:

Approximately Honey should use $5 \frac {5} {13}$ cups of muffin mix

7 0

2 years ago

2/5of a number is 80. What is 34of the same number?

Masja [62]

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.

3 0

3 years ago

Which of the following is in the solution set of y< 8 x− 3? Select one: (7, 46) (7, 60) (10, 89) (9, 82)

navik [9.2K]

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.

3 0

3 years ago

Which set of numbers does -5 belong ​

Which set of numbers does -5 belong