One ring in the Stonehenge Monument was originally made of 30 Stones, each about six and a half feet wide, 3 ft thick, and 13 ft
1 answer:
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Answer:
12 pencils in each package.
Step-by-step explanation:
Given:
Ethan bought 4 packages of pencils.
No of Packages = 4
No of pencils given to friend = 8 pencils
No of pencils left over =40 pencils
∴Total Number of Pencils = No of pencils given to friend + No of pencils left over =
Total Number of pencils in each package =
F(x) = {(8, 3), (4, 1), (0, -1), (-4, -3)}
f(x) = ¹/₂x - 1
f(x) = ¹/₂x - 1
y = ¹/₂x - 1
x = ¹/₂y - 1
+ 1 + 1
x + 1 = ¹/₂y
2(x + 1) = 2(¹/₂y)
2(x) + 2(1) = y
2x + 2 = y
2x + 2 = f⁻¹(x)
2x + 2 = g(x)
g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}
g(x) = 2x + 2
f(x) = ¹/₂x - 1
f(x) = ¹/₂x - 1
y = ¹/₂x - 1
x = ¹/₂y - 1
+ 1 + 1
x + 1 = ¹/₂y
2(x + 1) = 2(¹/₂y)
2(x) + 2(1) = y
2x + 2 = y
2x + 2 = f⁻¹(x)
2x + 2 = g(x)
g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}
g(x) = 2x + 2
Answer:
2, 2, 4, 6, 4
Step-by-step explanation:
Fundamental Theorem of Algebra states that 'An 'n' degree polynomial will have n number of real roots'.
1. The polynomial is given by
So, on simplifying we get that, .
Since, degree of polynomial is 5, it will have 5 roots.
This gives us that the roots of the equation are x = 0, -2, 2, 4i and -4i
So, the number of complex roots are 2.
2. The polynomial is given by
Since, degree of polynomial is 4, it will have 4 roots.
Equating them both by zero, and
gives that the roots of the polynomial are x = 2i, -2i, -5, -5.
So, the number of complex roots are 2.
3. The polynomial is given by
Since, degree of polynomial is 6, it will have 6 roots.
On simplifying, we get that the real roots of the polynomial are x = -1.75 and x = 4.28.
So, the number of complex roots are 6-2 = 4.
4. The polynomial is given by
Since, degree of polynomial is 7, it will have 7 roots.
On simplifying, we get that the only real root of the polynomial is x = -2.
So, the number of complex roots are 7-1 = 6.
5. The polynomial is given by
Since, degree of polynomial is 5, it will have 5 roots.
Simplifying the equation gives
Equating each to 0, we get the real roots of the polynomial is
So, the number of complex roots are 5-1 = 4