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SSSSS [86.1K]
3 years ago
5

graph and show points for 3x+6yless than or equal to 12, -x+y greater than or equal to 0, x is greater than or equal to 0, y is

greater than or equal to 0. Please show points and shading? Im confused bad

Mathematics
1 answer:
My name is Ann [436]3 years ago
8 0

Answer:

Step-by-step explanation:

Given equations are

3x+6y\leq 12

-x+y\geq 0

Now the inequalities intersect at x=\frac{4}{3}

y=\frac{4}{3}

and we have to satisfy this also

x\geq 0

y\geq 0

Above all conditions is shown in graph

and the shaded  area is the required area

For  3x+6y\leq 12 put (0,0)

it satisfy the point i.e. (0,0) lie on that side which satisfy the inequality similarly check for

-x+y\geq 0

put (4,0) it do not satisfy the inequality therefore it lies on the side which do not satisfy the inequality

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A scientist needs 10 L of a solution that is 60% acid. She has a 50% acid solution and a 90% acid solution she can mix together
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Answer:

<u>The equations system is:</u>

<u>x + y = 10</u>

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Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Liters of 60% acid solution needed = 10

x = Number of liters of the 50% solution

y = Number of liters of the 90% solution

2. Which equation represents the total liters of acid that are needed?

There are two equations needed:

The first one related to the total liters needed, 10 in this case:

x + y = 10

The second one related to the acid concentration of the 10 liters:

0.5x + 0.9y = 10 * 0.6

0.5x + 0.9y = 6

<u>The equations system is:</u>

<u>x + y = 10</u>

<u>0.5x + 0.9y = 6</u>

Solving for x and y in the 2nd equation, we have:

0.5 (10 - y) + 0.9y = 6

5 - 0.5y + 0.9y = 6

0.4y = 6 - 5

0.4y = 1

y = 1/0.4 = 2.5 ⇒ x = 7.5 (10 - 2.5)

The scientist can mix 7.5 liters of the 50% acid solution and 2.5 liters of the 90% acid solution to get the 10 liters of the 60% acid solution.

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