Arithmetic sequences use addition, so each term is a constant amount (common difference) more or less than the last.
Geometric sequences use multiplication, so each term is multiplied by a constant amount (common ratio) to get the next one.
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Answer:
Angle y measures 130 degrees
Step-by-step explanation:
Notice that the angles marked as "2x+18", and "4x-14" must be equal angles since they are generated on the same sector (top right) of the parallel lines by the transverse line "b".
Then by finding the value of "x" we can deduce the value of the actual angle these two angles measure:
![2x+18=4x-14\\18+14=4x-2x\\32=2x\\x=16^o](https://tex.z-dn.net/?f=2x%2B18%3D4x-14%5C%5C18%2B14%3D4x-2x%5C%5C32%3D2x%5C%5Cx%3D16%5Eo)
Now, we can find the actual value of these two angles, we use for example the first expression:
Top-right angle = ![2\,(16^o)+18^o=50^o](https://tex.z-dn.net/?f=2%5C%2C%2816%5Eo%29%2B18%5Eo%3D50%5Eo)
Now, if these two angles measure
, then angle "y" (which is the supplementary angle (angle which added renders
) for them, must equal ![180^o-50^o=130^o](https://tex.z-dn.net/?f=180%5Eo-50%5Eo%3D130%5Eo)
The line equation in slope-intercept form is given by
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where b is the y-intercept and m is the slope.
Then, we need to convert the given equation into the slope-intercept form. Then, by subtracting 10x to both sides, we have
![2y=-10x+3](https://tex.z-dn.net/?f=2y%3D-10x%2B3)
and by dividing both sides by 2, we get
![y=-5x+\frac{3}{2}](https://tex.z-dn.net/?f=y%3D-5x%2B%5Cfrac%7B3%7D%7B2%7D)
By comparing this result with the first equation, we can see that the slope is m= -5. So, the answer is: -5
Answer:
2 cups
Step-by-step explanation:
to find the extra cup of coffee
![3\frac{1}{2}-1\frac{1}{2}=\frac{7}{2}-\frac{3}{2}=\frac{4}{2}=2 cups](https://tex.z-dn.net/?f=3%5Cfrac%7B1%7D%7B2%7D-1%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B7%7D%7B2%7D-%5Cfrac%7B3%7D%7B2%7D%3D%5Cfrac%7B4%7D%7B2%7D%3D2%20cups)
Answer:
$90
Step-by-step explanation:
0.75*120