Answer: B, C, E
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The difference between consecutive terms (numbers that come after each other) in arithmetic sequences is the same. That means you add the same number every time to get the next number. To figure out which choices are arithmetic sequences, just see if the differences are the same.
Choice A) 1, -2, 3, -4, 5, ...
-2 - 1 = -3
3 - (-2) = 5
The difference is not constant, so it is not an arithmetic sequence.
Choice B) 12,345, 12,346, 12,347, 12,348, 12,349, ...
12,346 - 12,345 = 1
12,347 - 12,346 = 1
The difference is constant, so it is an arithmetic sequence.
Choice C) <span>154, 171, 188, 205, 222, ...
171 - 154 = 17
188 - 171 = 17
The difference is constant, so it is an arithmetic sequence.
Choice D) </span><span>1, 8, 16, 24, 32, ...
8 - 1 = 7
16 - 8 = 8
</span>The difference is not constant, so it is not an arithmetic sequence.
Choice E) <span>-3, -10, -17, -24, -31, ...
-10 - (-3) = -7
-17 - (-10) = -7
</span>The difference is constant, so it is an arithmetic sequence.
Answer:
a
Step-by-step explanation:
-x=-12-4y
x=12+4y
2(12+4y)-4y=12
24+8y-4y=12
4y=-12
y=-3
x=12-12=0
A proportion says: (one fraction) is equal to (another fraction)
or (one ratio) is equal to (another ratio).
In this question, the ratio is (the area of a piece of carpet) to (the time it takes to manufacture it.
And we know we can write the ratio as (1 square yard) / (10 minutes).
The other ratio is (25.5 square yards) / (how long THOSE take).
The carpet factory works at a constant rate, so we know that those two ratios are equal. So we can write:
(1 yd²) / (10 min) = (25.5 yd²) / (how long that piece takes) .
To solve a proportion, you "cross multiply". That means
(left top) x (right bottom) = (left bottom) x (right top)
(1 yd²) x (how long the big piece takes) = (25.5 yd²) x (10 min)
There's an equation to solve.
Divide each side by (yd²):
(how long the big piece takes) = (25.5) x (10 min)
How long the big piece takes = 255 minutes
BUT ... the question wants to know "How many hours ..." , so you have to convert the 255 minutes into hours. You should be able to do that, because you certainly know that 60 minutes = 1 hour.
Big piece = (255 minutes) x (1 hour / 60 minutes)
Big piece = (255/60) hours
<em>Big piece = 4.25 hours </em> (that's 4 hours 15 minutes)