The answer is d.2. hope it helps
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.
Answer:
36
Step-by-step explanation:
Note that if there are two of the same number multiplied within a root, it becomes a whole number
√18 x √18 = 18
Next, simplify √4. Factor the number:
√4 = √(2 x 2) = 2
Multiply: 18 x 2 = 36
36 is your answer
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Volume of Solids
The volume of the solid is 758.83 in³
Step-by-step explanation:
Given that the cone and half sphere is hollow
The volume of the cone = 
The Volume of the sphere = 
So the Volume of the half sphere =
The volume of solid = volume of cone + volume of the half sphere
Given
height h = 19 in
radius r = 5 in
= 
= 1/3 × 3.14 × 5 × 5 × 19
= 497.16 in³
= 2/3 × 3.14 × 5 × 5 × 5
= 261.67 in³
V = 497.16 in³ + 261.67 in³
= 758.83 in³
Hence the volume of the solid is 758.83 in³
The answer is 0.5 because 0.5 is 1/2 in fraction form.
