What is the graph of the absolute value inequality?|x + 5| ≥ y – 2
2 answers:
Step-by-step explanation:
|x + 5| ≥ y – 2
First we replace the inequality sign by = sign
|x + 5| = y – 2
solve for y and then graph it
add 2 on both sides
y = |x + 5|+ 2
Equation is in the form of y=a|x-h|+k
where (h,k) is the vertex
h = -5 and k = 2
So vertex is (-5,2)
Now make a table
x y = |x + 5|+ 2
-10 y = |-10+5| + 2= 7
-5 y = |-5+5| + 2= 2
0 y = |0+5| + 2= 7
Now plot all the points we got the table and graph it
Now we do shading
Lets pick any point inside the V shaped graph and check with our inequality
LEts pick (-5,5)
|x+5| ≥ y – 2
plug in -5 for x and 5 for y
|-5+5| ≥ 5– 2
0 > = 3, its false
So we cannot shade the part containing (-5,5)
we shade the bottom part on graph
the graph is attached below
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A used book store buys a hardback book for $1.50 and then sells it for $5. Over time, the store sells the same number of books it buys. The store manager can use the equation P(x)=5x−1.5x to determine the store's profit, P(x), where x is the number of books that the store sells. Which statement about the book store is true based on the profit equation?
Cost Price of book, C.P.=$1.50
Selling Price of book, S.P.=$5
PROFIT=S.P. -C.P.
So, Profit=$5-$1.50=$3.50
So, Profit=$3.50 on each book
Or, we are given P(x)= 5x-1.50x
Or, P(x)=3.50x
For each book, we must divide the profit P(x) by x, that is, number of books
So, Profit for each book sold is $3.50
Answer:Option C