Michelle has $8 and wants to buy a combination of dog food to feed at least two dogs at the animal shelter. A serving of dry food costs $1, and a serving of wet food costs $3. This system of inequalities models the scenario:

x + 3y ≤ 8
x + y ≥ 2

Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set.

Part B: Is the point (8, 2) included in the solution area for the system? Justify your answer mathematically.

Part C: Choose a point in the solution set and interpret what it means in terms of the real-world context.

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x + 3y ≤ 8

x + y ≥ 2

write both of them like linear relationships in the slope-intercept

y ≤ -(1/3)*x + 8/3

y  ≥ 2 - x

a.

the graph of y ≤ -(1/3)*x + 8/3 is a solid line

y = -(1/3)*x + 8/3

(not sure how to add a graph but use desmos to help you graph)

b.

see if (8, 2) is a solution

so replace x by 8 and y by 2 in both inequalities

first inequality:

8 + 3*2 ≤ 8

8 + 6  ≤ 8

14  ≤ 8

False, 14 is not smaller than or equal to 8, then we already can see that (8, 2) is not a solution.

c.

We can see that one possible solution is (2, 1)

first inequality:

2  + 3*1 ≤ 8

5 ≤ 8

True.

Second inequality:

1 + 2 ≥ 2

3 ≥ 2

True.

(2, 1) is the solution

x = 2

y = 1

She can buy 2 dry food servings and 1 wet food serving.

hope this helped :)

plants store their excess carbohydrate in the form of starch so that it could be used as energy source later on. the excess carbohydrate is converted into starch in the plastid i.e. chloroplast & this process occurs in the presence of sunlight. it is an insoluble polymer of glucose which gets stored in cell organelles named as amyloplasts. in some plants, starch is also stored in roots and embryos.

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: