point "b" has coordinates of -2,-5 after a translation 4 units down a reflection across the y axisand a translation 6 units up w
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Let's start by visualising this concept.
Number of grains on square:
1 2 4 8 16 ...
We can see that it starts to form a geometric sequence, with the common ratio being 2.
For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
Thus, there are 16, 384 grains on the fifteenth square.
The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.
Number of grains on square:
1 2 4 8 16 ...
We can see that it starts to form a geometric sequence, with the common ratio being 2.
For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
Thus, there are 16, 384 grains on the fifteenth square.
The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.
Answer:
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Step-by-step explanation:
Graph (-5,-3) and use the slope, -2, to find another point. -2 can also be written as
and
**
Use both. This works because either way, they will lie on the same line with the same slope. So, starting at (-5,-3), go down two points (-)* and to the left 1 (+)*, then, starting at (-5,-3) again, go up two points (+)* then to the right 1 point (-)*.
* If the number is negative, you either go down or to the right. If the number is positive, you go up and to the left.
**Rise over run refers to the change in the y-axis and the change in the x-axis: . Only one number is negative because, if both were negative, that would make a positive number, but the slope is -2, not 2.
Another way you could do this is by finding points first. All you need to do is turn the slope into a "point". Remember, 2 is the y and 1 is the x:
and
Then, using (-5,-3) and your new points, add them separately:
(-4,-5) is one point
(-6,-1) is another point. Connect the three points. You can check your work on the graph:
