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I am Lyosha [343]
3 years ago
7

A hardware store orders at most $2,500 worth of concrete and sand. The store needs to make a profit of at least $2,750 on the or

der. The possible combinations of concrete and sand for this order are given by this system of inequalities, where c = pounds of concrete and s = pounds of sand: 6c + 2s ≤ 2,500 4.50c + 3s ≥ 2,750 Which graph's shaded region represents the possible combinations of concrete and sand for this order?

Mathematics
1 answer:
yaroslaw [1]3 years ago
5 0

Answer: The below graph's shaded region represents the possible combinations of concrete and sand for this order

Step-by-step explanation:

Here, the system of inequality that represents the given situation is,

6c + 2s ≤ 2,500 --------(1)

4.50c + 3s ≥ 2,750 -------(2)

Where c = pounds of concrete,

s = pounds of sand

Now, The related equation of the above inequalities are,

6c + 2s = 2500

4.50c + 3s = 2750

By solving the above equations,

We get, c =222.\bar{2}, s = 583.\bar{3}

Thus, the intersection point of the inequalities = (222.\bar{2}, 583.\bar{3})

Now, At (0,0) ,

inequality (1), 6×0 + 2×0≤ 2500 ⇒ 0 ≤ 2500 ( true)

Hence, the shaded region of inequality contains the origin.

Similarly, At (0,0), inequality (2) is false,

⇒ The shaded region of inequality (2) does not contain the origin.

Thus, By the above explanation we can plot the shaded region of the system of the given inequalities.

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Can someone help me out please
Tju [1.3M]

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PLEASE HELP, THANK YOU! :)
elena-s [515]

Steps to solve:

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~Subtract 4 to both sides

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~Divide 8 to both sides

0 = 0

All real numbers are solutions.

Set builder notation: {x | R}

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Best of Luck!

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If y varies directly as x and y-21 when x<br> is 7, find x when y = -5.
klasskru [66]

Step-by-step explanation:

Since, y varies directly as x:

\therefore \: y = kx..(1) \\ (k = constant \: of \: proportionality) \\ at \: y = 21 \: and \: x = 7 \\ 21 = k \times 7 \\ k =  \frac{21}{7}  = 3 \\ plugging \: k = 3 \: in \: equation \: (1) \\ y = 3x..(2) \\ plugging \:  \: y =  - 5  \: in \: (2)\\  - 5 = 3x \\ x =  \frac{ - 5}{3}  \\   \:  \:  \:  \:  \:  \: \huge \red{ \boxed{x =  -  \frac{5}{3} }}

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