The nature of roots of a quadratic equation can be determined from its discriminant.
Discriminant = b² - 4ac
b = coefficient of x term = 2
a = coefficient of squared term = 2
c = constant = 4
So,
Discriminant = 4 - 4(2)(4) = -28
Since the discriminant is negative, the two roots of the given equation will be complex .
Therefore, the answer to this question is option B
Answer: The running speed of Elena is 5 miles/hour and this can be determined by using the formula of speed.
Step-by-step explanation:
A circular running track 1/4 is a mile long.
Elena runs on this track, completing each lap in 1/20 of an hour.
Speed formula is used to determine the speed of Elena. The formula of speed is given by:
----- (1)
where S is the speed, D is the distance and T is the time taken by Elena to run a circle.
Now, put the value of distance D and time T in the equation (1).
Speed = 5 miles/hour
Therefore, the running speed of Elena is 5 miles/hour.
For more information, refer to the link given below:
brainly.com/question/22610586
Answer:
a. – 4 or –3
b. –4 or –2
c. 4 or –3
d. 7 or 4
Step-by-step explanation:
To factorize the above expression, multiply the first and last term together, then find two factors of the result such that their sum will result to the middle term of the expression.
Now, we shall give the answers to the question.
a. x² + 7x + 12 = 0
x² + 3x + 4x + 12 = 0
Factorise
x(x + 3) + 4(x + 3) = 0
(x + 4)(x + 3) = 0
x + 4 = 0 or x + 3 = 0
x = 0 – 4 or x = 0 – 3
x = – 4 or –3
Therefore, the roots of the equation are – 4 or –3
b. t² + 6t + 8 = 0
t² + 2t + 4t + 8 = 0
Factorise
t(t + 2) + 4(t + 2) = 0
(t + 4)(t + 2) = 0
t + 4 = 0 or t + 2 = 0
t = 0 – 4 or t = 0 – 2
t = –4 or –2
Therefore, the roots of the equation are –4 or –2
c. 2n² – 2n – 24 = 0
Divide through by 2
n² – n – 12 = 0
n² + 3n – 4n – 12 = 0
Factorise
n(n + 3) – 4(n + 3) = 0
(n – 4)(n + 3) = 0
n – 4 = 0 or n + 3 = 0
n = 0 + 4 or n = 0 – 3
n = 4 or n = –3
Therefore, the roots of the equation are 4 or –3
d. y² – 11y + 28 = 0
y² – 4y – 7y + 28 = 0
Factorise
y(y – 4) – 7(y – 4) = 0
(y – 7)(y – 4) = 0
y – 7 = 0 or y – 4 = 0
y = 0 + 7 or y = 0 + 4
y = 7 or 4
Therefore, the roots of the equation are 7 or 4.
Answer:
17.325 liters
Step-by-step explanation:
Number of Apollo Spas Services= 105 hot tubs
Each hot tub needs Muriatic acid= 165 ml
We have to find the total liters of muriatic acid
Total number of liters required = Number of hots cups× 165 ml
Total number of liters required= 105×165 ml
Total number of liters required= 17,325 ml
1ml = 1/1000 liters
Total number of liters required= 17.325 liters
Hence, the correct answer is 17.325 liters
