How do i Subtract and simplify: (11x2 + 7) – (6x2 + 3x – 3)
1 answer:
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Answer:
a) <em>t</em> ≥ 5
b) (see below)
Step-by-step explanation:
First, make note of the info you are given and what you're trying to do:
- at midnight, 5°C
- drops consistently 2°C per hour
- finding <em>t</em>
- <em>t </em>= # of hours past midnight when temp. was past -4°C
- put <em>t</em> on a number line
So, first, you need to find the first point at when the temperature goes past -4°C. Notice that the question is asking for past -4°C, not -4°C<em> and</em> past. This means we're not including -4°C.
Every hour, we're dropping by 2°C. You can draw a visual to better understand the situation. See the image below.
So we know that starting from 5 am, we are lower than -4°C.
This is 5 hours from midnight.
So <em>t</em> ≥ 5. This means that the number of hours past midnight when the temperature was colder than -4°C was 5 or more hours.
On the number line, draw a circle on 5 (between 4 and 6), but shade it in because it includes 5. Then, shade or highlight to the right of that circle to the end of the number line.
This shows that <em>t</em> is equal to or greater than 5.
So just by the question, we are aware that when we divide 4,005 ounces by 16, it is not going to be a pretty number - there are going to be some left over in the form of a fraction.
First we must find out how many of these bottles can be completely filled until there is only the small fraction left that is not able to fill up a bottle. So let's divide:
And now we know that 250 bottles will be filled completely. To find the amount of ounces left over, let's see how many ounces 250 bottles is:
There are 4,000 ounces in 250 bottles. So we need to subtract our initial amount from this known amount:
So there are only 5 ounces of water remaining after 250 bottles are completely filled. To put this into a fraction of the original amount, we just divide by the initial amount (4,005):
If the question is asking for the remainder in terms of a bottle, we just divide these 5 ounces by the 16 ounces it would take to fill this bottle: