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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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Answer:

B

Step-by-step explanation:

Because all whole numbers are integers, but not all integers are whole numbers.

Hope this helps! :)

4 0
3 years ago
Read 2 more answers
Use the given conditional statement to determine the converse and inverse statements. If a line is vertical, then it has undefin
Georgia [21]
1) Definitions:

1.1) Inverse statement: negating the hypothesis and the conclusion of the original statement, i.e.:

conditional statement: p → q

inverse: ~p → ~q (the symbol ~ means the negation)

1.2) Converse statement: switching the hypothesis and the conclusion of the conditional statement, i.e.:

conditional statement: p → q

converse: q → p

2)  converse of the given statement

conditional: <span>If a line is vertical, then it has undefined slope.

converse: switch the hypothesis and the conclusion

if a line has undefined slope, then it is vertical <------- answer

</span>3) Inverse of the given statement

conditional: if <span>a line is vertical, then it has undefined slope.

inverse: negate both hypothesis and conclusion.

 </span>if a line is not vertical, then it does not have an undefined slope <---answer

8 0
3 years ago
6.2×0.03= and tell me how you did it please ​
matrenka [14]

Answer:

0.186

Step-by-step explanation:

       6.2

<u>x    0.0</u><u>3</u>

           6

    1

       6.2

<u>x    0.0</u><u>3</u>     since 6*3=18, we have to carry the 1

        86

     1

       6.2

<u>x    0.0</u><u>3</u>

       186

       6.2

<u>x    0.</u><u>0</u><u>3</u>

        186

         0

       6.2

<u>x    0.</u><u>0</u><u>3</u>

       186

       00

       6.2

<u>x    </u><u>0</u><u>.03</u>

       186

       00

      0

       6.2

<u>x    </u><u>0</u><u>.03</u>

        186

+      00            add the partial products

<u>      0</u><u>0                   </u>

     00186

      6.2

<u>x    0.</u><u>03</u><u>     </u>                   count how many digits are after the decimal point      from each factor =3 and place in product

        186

+      00            

<u>      00                   </u>

     00.186=0.186

<em>answer=0.186</em>

8 0
3 years ago
Which expressions can be used to find the coordinates of the midpoint of PQ with endpoints P(3, –1) and Q(–7, –6)?
Tanzania [10]

Step-by-step explanation:

it is the ans of midpoint PQ

3 0
3 years ago
Write the next three terms of the following sequence 4,5,7,10,14
Law Incorporation [45]
4,5,7,10,14=19,25, 32
8 0
3 years ago
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