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3 years ago

Help me please..........

Mathematics

1 answer:

natali 33 [55]3 years ago

4 0

9514 1404 393

Answer:

Step-by-step explanation:

You can reflect point x across the origin to find is is just above -1. Adding 3 to that value gives a point just above -1+3 = 2. That's where point C is located.

<em>Algebraic solution</em>

Algebraically, you can set y = -x +3, and solve for x. That gives you ...

x = 3 -y

Using the relation given at the start:

0 < x < 1

0 < 3 -y < 1 . . . . . substitute for x

Adding y gives ...

y < 3 < y+1

We can separate this into two inequalities:

y < 3, and

3 < y+1

2 < y . . . subtract 1

Now, we have ...

2 < y < 3 . . . . . the location of point C

As you can see, it is much easier to use the number line directly to find the desired point.

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A. What formula will be use to relate the data? Explain the part of the formula?

Alenkasestr [34]

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Answer:

2.5 miles

Step-by-step explanation:

1A. The formula that applies to time/speed/distance problems is ...

distance = speed × time

The units of the numbers involved need to be compatible, which is to say the speed units need to be the ratio of distance units to time units.

The other applicable relationship is that the resultant speed in a body of water is the sum of the boat speed and the water speed. When they are in the same direction, the speeds add; when they are in the opposite direction, the net speed is their difference.

1B, C. Since Tom is traveling upstream, his net speed is the difference between his paddling speed (8 mph) and the current (3 mph). That is, he makes headway upstream at the rate of 8-3=5 mph. This difference is the "speed" in the formula.

Note that the time is given in minutes, but the units of speed have time units of hours. It is easiest in this problem to translate the time in minutes to a time in hours. (30 min = 1/2 h) This is the "time" in the formula.

We can "let 'distance' represent the distance we're being asked to find in the problem statement."

1D. Using the formula, we find ...

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This is the "formula" equation of part A with speed and time values filled in.

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<em>Additional comment</em>

You may see the above formula written a number of ways. Using single-letter variables, it is often written as ...

d = rt

where d represents distance, r represents speed, and t represents time. By using whole words for the variable names, I find less explanation is necessary.

By using units along with the numbers in the formula, the units of the answer "fall out". If they don't, then there has been a mistake. For example, if you use 30 minutes instead of 1/2 hour, your answer would be ...

(5 mi/h)(30 min) = 150 mi·min/h

These units are not distance units, so you know a mistake has been made. (The units multiply and/or cancel the same as any variable(s).)

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