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olga nikolaevna [1]
3 years ago
14

Daniel is printing out copies of a presentation. It takes 3 minutes to print a color copy and 1 minute to print a black-and-whit

e copy. He needs to print at least 6 copies and must have the copies completed in no more than 12 minutes.
If the solution region represents the number of color copies and black-and-white copies that Daniel can print, determine which graph represents the solution set to the system of inequalities representing this situation.

Mathematics
1 answer:
Effectus [21]3 years ago
6 0
Work the information to set inequalities that represent each condition or restriction.

2) Name the variables. 

c: number of color copies
b: number of black-and-white copies

3) Model each restriction:

i) <span>It takes 3 minutes to print a color copy and 1 minute to print a black-and-white copy.
</span><span>
</span><span>3c + b
</span><span>
</span><span>
</span><span>ii) He needs to print at least 6 copies ⇒ c + b ≥ 6
</span><span>
</span><span>
</span><span>iv) And must have the copies completed in no more than 12 minutes ⇒</span>

3c + b ≤ 12
<span />

4) Additional restrictions are c ≥ 0, and b ≥ 0 (i.e. only positive values for the number of each kind of copies are acceptable)

5) This is how you graph that:

i) 3c + b ≤ 12: draw the line 3c + b = 12 and shade the region up and to the right of the line.

ii) c + b ≥ 6: draw the line c + b = 6 and shade the region down and to the left of the line.

iii) since c ≥ 0 and b ≥ 0, the region is in the first quadrant.

iv) The final region is the intersection of the above mentioned shaded regions.

v) You can see such graph in the attached figure.

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Round 0.578 to the nearest tenth
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In order to finish the order on time the factory was supposed to produce 70 items daily. After hiring three more people they wer
maria [59]

Answer:

  40 days

Step-by-step explanation:

Let x represent the original production time. Then 70x is the order quantity involved.

When the same order quantity is produced at a rate of 80 items per day for x-5 days, we have the equation ...

  70x = 80(x -5)

  70x = 80x -400

  0 = 10x -400 . . . . . subtract 70x

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The original schedule was for production to take 40 days.

8 0
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A ratio is?
Rama09 [41]
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Find the distance between the two points in simplest radical form.
Jlenok [28]

Answer:

d=\sqrt{58}\approx7.6

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2

Our first point, A, is at (1, 1) and our second point, B, is at (-2, 8).

Let's let A(1, 1) be (x₁, y₁) and B(-2, 8) be (x₂, y₂). Substitute this into the distance formula:

d=\sqrt{(-2-1)^2+(8-1)^2

Subtract:

d=\sqrt{(-3)^2+(7)^2

Square:

d=\sqrt{9+49}

Add:

d=\sqrt{58}

This cannot be simplified.

So, the distance between the two points is √58 or about 7.6 units.

And we're done!

So... where's my cookie :)?

6 0
3 years ago
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