Answer:
im sorry i do not know
Step-by-step explanation:
Answer:
A: This polynomial has a degree of 2 , so the equation 12x2+5x−2=0 has two or fewer roots.
B: The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots.
Step-by-step explanation:
f(x) = 12x^2 + 5x - 2.
Since this is a quadratic equation, or a polynomial of second degree, one can easily conclude that this equation will have at most 2 roots. At most 2 roots mean that the function can have either 2 roots at maximum or less than 2 roots. Therefore, in the A category, 2nd option is the correct answer (This polynomial has a degree of 2 , so the equation 12x^2 + 5x − 2 = 0 has two or fewer roots).
To find the roots of f(x), set f(x) = 0. Therefore:
12x^2 + 5x - 2 = 0. Solving the question using the mid term breaking method shows that 12*2=24. The factors of 24 whose difference is 5 are 8 and 3. Therefore:
12x^2 + 8x - 3x - 2 = 0.
4x(3x + 2) -1(3x+2) = 0.
(4x-1)(3x+2) = 0.
4x-1 = 0 or 3x+2 = 0.
x = 1/4 or x = -2/3.
It can be seen that f(x) has two distinct real roots. Therefore, in the B category, 1st Option is the correct answer (The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots)!!!
Answer:
Cabrina's time = 5 hours
Dabney's time = 6.5 hours
Step-by-step explanation:
The data of the exercise are:
Cabrina speed = 75 mph
Daney speed = 60 mph
The sum of their distance is 765 miles, therefore
Cabrina's distance Dabney's distance = 765
Cabrina's distance = x
Dabney's distance = 765-x
The sum of their times is 11.5 hours, therefore
Cabrina's time Dabneys time = 11.5
Cabrina's time = x / 75
Dabney's time = (765-x) / 60
x / 75 (765-x) / 60 = 11.5
Lowest common denominator of 75 and 60 is 300, therefore we have:
330 * x / 75 300 * (765-x) / 60 = 300 * 11.5
4 * x 5 * (- x 765) = 3450
4 * x - 5 * x 3825 = 3450
x = 375
Replacing:
Cabrina's time = 375/75 = 5 hours took
Dabney's time = (765-375) / 60 = 6.5 hours took
