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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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20 is 40% of what number
pantera1 [17]

it depends what the number is

6 0
3 years ago
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Which phrase best describes the translation from the graph y=(x-5)^2+7 to the graph of y=(x+1)^2-2
Helga [31]

Start from the parent function f(x)=x^2


In the first case, you are computing


f(x-5)+7


In the second case, you are computing


f(x+1)-2 /tex] There are two translation going on: when you transform [tex] f(x) \to f(x+k), you translate the function horizontally, k units left if k>0 and k units right if k.


On the other hand, when you transform f(x) \to f(x)+k, you translate the function vertically, k units up if k>0 and k units down if k.


So, the first function is the "original" parabola f(x)=x^2, translated 5 units right and 7 units up. Likewise, the second function is the "original" parabola f(x)=x^2, translated 1 units left and 2 units down.


So, the transformation from (x-5)^2+7 to (x+1)^2-2 is: go 6 units to the left and 2 units down

8 0
3 years ago
Read 2 more answers
D=<img src="https://tex.z-dn.net/?f=d%3D%5Csqrt%7Bx%7D%20%281-%28-5%29x%5E%7B2%7D%20%2B%20%28-5-3%29x%5E%7B2%7D" id="TexFormula1
aleksandr82 [10.1K]
Bro i don’t know either
3 0
3 years ago
Can someone please explain?
AlladinOne [14]
<h2>Hello!</h2>

The answer is:

The correct option is the first option:  

y=-4x+64

<h2>Why?</h2>

To write the equation of the line in slope-interception  form we need to extract all the information that we need from the graphic.

We must remember that the slope-interception form of the lines is:

y=mx+b

Where,

y, is the function

m, is the slope of the line

x, is the variable

b, is the y-axis intercept

We can find the slope using the following formula:

m=\frac{ChangeInY}{ChangeInX}

Which is for this case:

m=\frac{64}{16}=4

As we can see from the graphic, the line is decresing, so the sign of the slope "m" will be negative, so:

m=-4

We can find the value of "b" seeing where the line intercepts the y-axis.

As we can see it intercept the y-axis at:  y=64

Then, now that we already know the value of "m" and "b", we can write the equation of the line:

y=mx+b=-4x+64\\y=-4x+64

So, the correct option is the first option:

y=-4x+64

Have a nice day!

4 0
3 years ago
Please help- I am very confused-
shusha [124]

Answer:

5÷9

Step-by-step explanation:

5/9 is a fraction where the numerator is divided by the denominator

5 divide by 9

5÷9

4 0
3 years ago
Read 2 more answers
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