Answer:
48+23(6)½
Step-by-step explanation:
A = l × w
A =[(8-(6)^½) × (9+4(6)^½)]
A =8(9+4(6)^½) + [-(6)^½(9+4(6)^½]
A =(72 + 32(6)^½ - 9(6)^½ - 24)
A =(72 - 24 + 32(6)^½ - 9(6)^½)
A =(48 + 23(6)^½)
Answer:
True!
Step-by-step explanation:
If an object travels at a constant speed, then the distance traveled is directly proportional to the time spent traveling, with the speed being the constant of proportionality. The circumference of a circle is directly proportional to its diameter, with the constant of proportionality equal to π.
Answer:
A. 45.7
Step-by-step explanation:
Side a = 8
Side b = 7.8
Side c = 11.17318
Angle ∠A = 45.725° = 45°43'31" = 0.79806 rad
Angle ∠B = 44.275° = 44°16'29" = 0.77274 rad
Angle ∠C = 90° = 1.5708 rad = π/2
Answer:
Step-by-step explanation:
we know that
The <u><em>conjugate root theorem</em></u> states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial
In this problem we have that
The polynomial has roots 1 and (1+i)
so
by the conjugate root theorem
(1-i) is also a root of the polynomial
therefore
The lowest degree of the polynomial is 3
so
Remember that
The leading coefficient is 1
so
a=1
![f(x)=(x-1)(x-(1+i))(x-(1-i))\\\\f(x)=(x-1)[x^{2} -(1-i)x-(1+i)x+(1-i^2)]\\\\f(x)=(x-1)[x^{2} -x+xi-x-xi+2]\\\\f(x)=(x-1)[x^{2} -2x+2]\\\\f(x)=x^{3}-2x^{2} +2x-x^{2} +2x-2\\\\f(x)=x^{3}-3x^{2} +4x-2](https://tex.z-dn.net/?f=f%28x%29%3D%28x-1%29%28x-%281%2Bi%29%29%28x-%281-i%29%29%5C%5C%5C%5Cf%28x%29%3D%28x-1%29%5Bx%5E%7B2%7D%20-%281-i%29x-%281%2Bi%29x%2B%281-i%5E2%29%5D%5C%5C%5C%5Cf%28x%29%3D%28x-1%29%5Bx%5E%7B2%7D%20-x%2Bxi-x-xi%2B2%5D%5C%5C%5C%5Cf%28x%29%3D%28x-1%29%5Bx%5E%7B2%7D%20-2x%2B2%5D%5C%5C%5C%5Cf%28x%29%3Dx%5E%7B3%7D-2x%5E%7B2%7D%20%2B2x-x%5E%7B2%7D%20%2B2x-2%5C%5C%5C%5Cf%28x%29%3Dx%5E%7B3%7D-3x%5E%7B2%7D%20%2B4x-2)
Answer: Option D is correct.
Step-by-step explanation: An exponential function is in the form of where a is the initial value and b≠ 0 , b >1 .
Given: The function f(x) = y = ......[1]
The domain is all real numbers and the range is y > 0.
y-intercept defined as the graph crosses the y-axis.
Substitute the value of x= 0 in [1] to solve for y;
y = = 4
y-intercept = (0, 4)
End behavior:
when b =3 >1
then;
as ,
as ,
therefore, the only graph which represents the function y = is Option D
