Answer:
C. x = 6
Step-by-step explanation:
6 + 4 = 10
This question is quite simple really. They are basically asking you to combine like terms. You have two different figures with the variable y, so you just combine the them. It would then be 3x + 2y. You cannot simplify this equation any further since there is nothing to solve for or anymore like terms to combine.
Across the y axis. This question becomes easier if you graph it out in your head. Let's say the bank is at (2,2). Because the grocery store has an opposite x coordinate, the bank would be at (-2,2). If you look at this in your head, they are not even on different sides of the x axis, and therefore must be reflected across the y axis.
When roots of polynomials occur in radical form, they occur as two conjugates.
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.
The first factor is x - (a + √b).
The second factor is x - (a - √b).
The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
= x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
= x² - 2ax + x√b - x√b + a² - b
= x² - 2ax + a² - b
This is a quadratic polynomial, as expected.
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
= a +/- (1/2)*√(4b)
= a +/- √b
x = a + √b, or x = a - √b, as expected.
