6x^2 - 2x + 1 is a quadratic formula from the form ax^2 + bx + c. This form of equation represents a parabola.
Finding 6x^2 - 2x + 1 = 0, means that you need to find the zeroes of the equation.
Δ = b^2 - 4ac
If Δ>0, the equation admits 2 zeroes and 6x^2 - 2x + 1 = 0 exists for 2 values of x.
If Δ<0, the equation doesn't admit any zero, and 6x^2 - 2x + 1 = 0 doesn't exist since the parabola doesn't intersect with the axe X'X
If Δ=0, the equation admits 1 zero, which means that the peak of the parabola is touching the axe X'X.
In 6x^2 - 2x + 1, a=6, b=-2, and c =1.
Δ= b^2 - 4ac
Δ=(-2)^2 - 4(6)(1)
Δ= 4 - 24
Δ= -20
Δ<0 so the parabola doesn't intersect with the Axe X'X, which means there's no solution for 6x^2 - 2x + 1 = 0.
I've added a picture of the parabola represented by this equation under the answer.
Hope this Helps! :)
For the first, simply plug in the value of x given (x = 2) into the equation:
So, 8 would be your answer.
For the second, the sum of x and 2 would be expressed as x + 2. Twice this sum would be written as 2(x+2). Finally, 8 less than twice that sum would be written as 2(x+2) - 8, which would be your expression.
For the last question, the coefficient refers to the number directly in front of the variable, x. So you need only to check what the x would simplify to in each equation and look for the expression where x has no coefficient (i.e., its coefficient is 1). For Hunter, the coefficient would be 15 (5 × 3x = 15x); for Michael, the coefficient would be 11 (6x + 5x = 11x); for Nate, the coefficient would be 1 (x = 1x); and for Spencer, the coefficient would be 2 (2x = 2x). Thus, Nate's expression has a coefficient of 1 when simplified.
Answer:
2x - 5
Step-by-step explanation:
Step 1: distribute the 1/5, or divide by 5
1/5 ( 10x-25)
2x - 5
Done
3x - y = 0 . . . (1)
5x + 2y = 22 . . . (2)
From (1), y = 3x . . . (3)
Putting (3) into (2) gives:
5x + 2(3x) = 22
5x + 6x = 22
11x = 22
x = 2
From (3), y = 3(11) = 33
x = 11, y = 33.