Mathematics, 09.12.2019 07:31 hanny13

You are buying plants and soil for your garden. the soil cost 4.00 dollars per bag and the plants cost $10.00 each. you want to buy at least 5 plants and can spend no more than $100.

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Answer from: arigar

Part a) The system of linear inequalities is

$y\geq 5$

$4x+10y\leq 100$

Part b) The graph in the attached figure

Part c) A solution could be (5,7) (see the explanation)

Step-by-step explanation:

The complete question is

You are buying plants and soil for your garden. The soil cost 4.00 dollars per bag and the plants cost $10.00 each. You want to buy at least 5 plants and can spend no more than $100

a) write a system of linear inequalities to model the situation

b) Graph the system of linear inequalities

c) Identify and interpret a solution to the system

Part a) write a system of linear inequalities to model the situation

Let

x -----> the number of bags of soil

y ----> number of plants

we know that

The word "at least" means "greater than or equal"

$y\geq 5$ ----> inequality A

The word "no more" means "less than or equal"

$4x+10y\leq 100$ ----> inequality B

Part b) Graph the system of linear inequalities

we have

$y\geq 5$ ----> inequality A

$4x+10y\leq 100$ ----> inequality B

using a graphing tool

the solution is the triangular shaded area

see the attached figure

Part c) Identify and interpret a solution to the system

we know that

If a ordered pair is a solution to the system, then the ordered pair must lie on the shaded area of the solution

i take the point (5,7)

the point (5,7) lie on the shaded area of the solution

is a solution of the system

That means ----> You are buying 5 bags of soil and 7 plants for your garden

Verify the solution

Remember

If a ordered pair is a solution to the system, then the ordered pair must satisfy both inequalities

Verify inequality A

$7\geq 5$ ----> is true

The ordered pair (5,7) satisfy inequality A

Verify inequality B

$4(5)+10(7)\leq 100$

$90\leq 100$ ---> is true

The ordered pair (5,7) satisfy inequality B

therefore

The ordered pair (5,7) is a solution to the system

You are buying plants and soil for your garden. the soil cost 4.00 dollars per bag and the plants co

Answer from: Quest

Welp life just is hard

Answer from: Quest

so the perpendicular line goes through the given pointyou would get a perpendicular line at some random location

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.

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