Answer:
<h3>36 and 12</h3>
Step-by-step explanation:
Let the two positive integers be x and y.
If their product is 432, then
xy = 432 ......... 1
Also if the sum of the first plus three times the second is a minimum, then;
p(x) = x + 3y
From 1;
y = 432/x ..... 3
Substitute 3 into 2;
p(x) = x+3y
p(x)= x + 3(432/x)
p(x) = x + 1296/x
Since the expression is at minimum when dp(x)/dx = 0
dp/dx = 1 + (-1296)/x²
dp/dx = 1 -1296/x²
0 = 1 -1296/x²
0 = (x²-1296)/x²
cross multiply
0 = x²-1296
x² = 1296
x = √1296
x = 36
Since xy = 432
36y = 432
y = 432/36
y = 12
Hence the two positive numbers are 36 and 12
The decagon can be divided in 10 equal parts, so if a full rotation is of 360º, a one tenth rotations will be of 360º/10= 36º
So if you rotate the decagon by a multiple of 36º the rotation will be onto itself, i.e. the figure will look as if it wasn't moved.
From the choices given, the angle that will rotate the angle counterclockwise onto himself will be multiple of 36º, the only one is 72º
This figure has 5 lines of symmetry that cross each vertex and 5 lines of symmetry that cross form the midpoint of one side to the midpoint of the oposite side. This is a total of 10 lines of symetry.
So you can reflect the decagon 10 different ways.
The correct choice is C: 36º, 72º, 10, 5
right answer is a.
The lender benefits, because the interest compounded increases further interest calculations.
Answer:
C.
Step-by-step explanation:
For an angle to be supplementary to another angle, they must be equal to 180. Angles 6, 10, 13, and 9 are all supplementary to angle 16. Although there are more choices in different answers it wouldn't work with question, so C is the right answer.
Angle 16 is supplementary to angle 9 by the Same Side Interior Angles Theorem, which makes it supplementary to angle 10 by the Alternate Exterior Angles Theorem, which is also congruent to angle 13 by the Vertical Angles Theorem, which is also supplementary to angle 6 by the Alternate Exterior Angles Theorem.