Answer:
Step-by-step explanation:
It's y = x^2, not y = x2. The graph of y = x^2 is a parabola with vertex (0, 0) and which opens up.
The graph of y = (x + 5)^2 has the same shape as that of y = x^2, but has been translated 5 units to the left.
Answer:
5 rooms
Step-by-step explanation:
4 rooms = 9 hours
9 hours = 540 minutes
1 room = 540 ÷ 4 = 135 minutes
60 x 12 = 720 minutes (12 hours)
720 ÷ 135 = 5.33333
5.3333 estimated to nearest whole number = 5
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.
Commercial jet's speed = 2x-162 (plug this in the equation below)
Private jet's speed = x
Equation:
10(x) = 8(2x-162)
10x = 16x - 1296
6x = 1296
x = 216 (Private jet's speed)
Take the first equation and plug x value in;
2x-162
2(216) - 162 = 270 ( Commercial jet's speed)
Answer:
Some.
Terms that include a number and a letter are expressions.
