Answer:
The complex number is 0+i/3.
Step-by-step explanation:
Let the imaginary part be x.
The complex number will be a+xi
Given:
real part =a
(a+xi)*3=i...............(i)
To find:
imaginary part
Solution:
3a + 3xi=i.............(ii)
Comparing real and imaginary parts of eq(ii).
3a=0 and 3x=1
a=0
x=1/3.
Let's compare the given function with the model for a quadratic equation:

Since the value of a is positive, the parabola has its concavity upwards, and the function has a minimum value.
The minimum value can be found calculating the y-coordinate of the vertex:

Therefore the minimum value is -24.
Answer:The claim is correct
Explanation:Assume the given triangle ABCperimeter of triangle ABC = AB + BC + CA ............> I
Now, we have:D is the midpoint of AB, this means that:
AD = DB = (1/2) AB ..........> 1E is the midpoint of AC, this means that:
AE = EC = (1/2) AC ...........> 2DE is the midsegment in triangle ABC, this means that:
DE = (1/2) BC ...........> 3perimeter of triangle ADE = AD + DE + EA
Substitute in this equation with the corresponding lengths in 1,2 and 3:perimeter of triangle ADE = (1/2) AB + (1/2) BC = (1/2) AC
perimeter of triangle ADE = (1/2)(AB+BC+AC) .........> IIFrom I and II, we can prove that:perimeter of triangle ADE = (1/2) perimeter of triangle ABC
Which means that:perimeter of midsegment triangle is half the perimeter of the original triangle.
Hope this helps :)
First find all possible rational roots. To do this, find all the factors of the lowest order coefficient and the highest order coefficient. For #1, the highest order coefficient is 1 because the x^3 doesn't have a number in front of it. The lowest order coefficient is 30.
Here are all the factors:
Factors of 1 are: 1
Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
Now divide each factor of 30 (positive and negative), and divide them by each factor of 1.
All possible rational roots are:
-1, 1, -2, 2, -3, 3, -5, 5, -5, 6, -10, 10, -15, 15, -30, 30
Now we perform synthetic division like you have started to do. Try dividing the polynomial by each possible root. If the result has a remainder, that possible root does NOT work. Try another possible root. If there is not a remainder, you have found one of the roots.
For example, when dividing x^3 - 4x^2 -11x + 30 by the possible root 2, we get x^2 - 2x - 15 without a remainder. That means 2 is a root. From here we can factor the result to (x-5)(x+3).
So the roots for #1 are x = -3, 2, and 5.
Let me know if you need help with the others :)
Answer: Should be 6x+10
Step-by-step explanation: