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)!!!
To solve the absolute value equation you first need to get everything not in the absolute value bars to the other side of the equation.
Step 1) Divide by 4
|n+8| = 14
*Remember: when solving absolute value equations, you make what the expression (n+8) is equal to negative and positive. Not the other way around.
Step 2) Make two equations
n+8 = 14
n+8 = -14
Solve and you'll see that n= 6 and -22
He would be spending less time because 2/3 is not a full number. Let's make an equation out of the: 2/3(m). Note: 3(2) means 3 times 2 and the m is the amount of miles biked last week. We could insert the number 3 to our equation. 2/3(3). Now if you do it the proper way, it is 2/3(3/1) and if you do the math it is 6/3 aka 2. And 2 is less than 3. So it is less time spent
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The answer is $4.85;$81.85<span> which is B. </span>