The first option is your answer.
Sigma notation is just a fancy way to shorten a sum of a series of numbers using a set equation. The "n =" tells you where to start in the sequence and the top number tells you where to stop.
Answer:
x= -2, y = -3
Step-by-step explanation:
1. substitute x = 4+2y in the first equation: 
simplify it : 
2. isolate y in 8 + 5y = -7 --> 5y = -7 - 8 -->
3. solve for y: 5y = -15 --> y = -15/5 --> y= -3
4. solve for x: x = 4 + 2y
x = 4 + 2(-3)
x = 4 + (-6)
x = -2
1. 130°
I don't remember too many specifics from my past math classes, but I always remembered this because that is an upside-down mirror of the 130° angle.
2. 50°
A straight line is 180°, and 180 - 130 = 50.
Answer:
D) (x, y) → (1/3x , 1/3 y)
Step-by-step explanation:
A dilation is a change of size, if the dilation factor is greater than 1, then the figure is enlarged. If the dilation factor is smaller than 1, the figure is shrinked. In both cases, the coordinates are MULTIPLIED by the dilation factor.
Among the 4 choices, only 2 are dilations. One is with a dilation factor of 3 (A), which means the shape was enlarged. And the other is with dilation factor of 1/3, meaning the shape was shrinked.
Since we went from MNOP (LARGE one) to M'N'O'P' (small one), the dilation factor was < 1... so 1/3 is the answer.
Answers B and C show a translation/movement of the shape, not a dilation.
Answer:
Absolute minimum = 1.414
Absolute maximum = 2.828
Step-by-step explanation:
For absolute minimum we take the minimum values of 
and 
.
Plugging in the minimum values in the function.
Absolute minimum value will be always positive.
∴ Absolute minimum = 1.414
For absolute maximum we take the maximum values of and .
Plugging in the maximum values in the function.
Absolute maximum value will be always positive.
∴ Absolute maximum = 2.828
