Answer:
The image of AB will be 15 cm long after dilation by a scale factor of 5.
Step-by-step explanation:
We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.
- If the scale factor > 1, the image is enlarged
- If the scale factor is between 0 and 1, it gets shrunk
- If the scale factor = 1, the object and the image are congruent
Rule to calculate the mage of the segment AB after dilation of the segment AB by a scale factor 5 centered at the origin
AB = length → A'B' = 5(length)
It means the length of the image of the segment AB can be determined by multiplying the length of the original segment AB by 5.
so
AB = 3 cm
Thus, the length of image A'B' will be:
A'B' = 5(3) = 15 cm
Therefore, the image of AB will be 15 cm long after dilation by a scale factor of 5.
Answer
The answer to this equation would be 64. '^' just means multiplied by. It has the same mathematical definition as the multiplication sign.
Step-by-step explanation:
USING PEMDAS (NO PARENTHESES)
4 x 2 x 2 x 4
8 x 2 x 4
16 x 4
64
USING PEMDAS (WITH PARENTHESES)
(4 x 2) x (2 x 4)
(8) x (2 x 4)
(8) x (8)
64
<span>y'' + 5y' + 6y = 2e^t is a second order differential equation with solution y = Ae^mt + Be^nt + p(t); where m and n are the roots of the quadratic equation x^2 + 5x + 6 = 0, and p(t) is the particular solution.
x = -2 and x = -3
y = Ae^-2t + Be^-3t + p(t)
For the particular solution, Ke^t + 5Ke^t + 6Ke^t = 2e^t
12K = 2
K = 1/6
Therefore, solution is </span>
<span>y = Ae^-2t + Be^-3t + 1/6 e^t
</span>
Answer:
the answer is 729.........