Apex Grocery wants to build a warehouse that is exactly five miles from each of the routes between stores L, M, and N. Which con
struction correctly finds the best location of the warehouse?
1 answer:
Answer: Option C - Construction Y because point E is the circumcentre of triangle LMN.
Point E is the best location for the warehouse as it is exactly equidistant from the three stores at L, M and N.
Step-by-step explanation:
Before solving an algebra problem, it sometimes helps to get a geometric picture of what's happening. Geometry says that three points determine a circle - in other words, given three points that are not
all on the same line, there is exactly one circle which passes through all 3. Finding the point equidistant from the 3 points is the same thing as finding the center of the circle that passes through all of them (since all points on a circle are equidistant from the center).
Our points are L, M and N. Draw the lines LM, LN and MN to form a triangle. Now construct the perpendicular bisectors of any two of the lines, and their intersection, point E, will be the center of this circle.
As shown in the Construction Y because E is the circumcentre of triangle LMN.
This is the best location for the warehouse as it is exactly equidistant from the three stores at L, M and N.
QED!
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Answer:
A) Pairs of sunglasses should be sold to maximize profits is 100 thousand.
B) The actual maximum profits that can be expected is 180 thousands dollars.
Step-by-step explanation:
Given : Suppose the Sunglasses Hut Company has a profit function given by
where, q is the number of thousands of pairs of sunglasses sold and produced and P(q) is the total profit, in thousands of dollars, from selling and producing q pairs of sunglasses.
To find :
A) How many pairs of sunglasses (in thousands) should be sold to maximize profits?
Profit is
Compare with general quadratic equation
a=-0.02, b=4, c=-20
The maximum value of quadratic function is at
So, maximum profit occur at q is given by,
i.e. 100 thousand pair of sunglasses.
Pairs of sunglasses should be sold to maximize profits is 100 thousand.
B) What are the actual maximum profits (in thousands) that can be expected?
Maximum profit occurs at q=100 thousand pairs is given by,
The actual maximum profits that can be expected is 180 thousands dollars.
The second leftover expression is not o(a+b). It is 6(a + b). I have attached the correct question to depict that.
Answer:
The equivalent expressions are;
8a + 2 and 6a + 6b
Step-by-step explanation:
The two leftover expressions are given as;
2(4x + 1) and 6(a + b)
In algebra, equivalent expressions are simply those expressions which when simplified, give the same resulting expression as the initial one.
Thus simply means expanding or collecting like times to make it clearer.
Now, in our question, like terms have already been collected. This means that to find an equivalent expression, we will just expand the bracket.
Thus;
2(4x + 1) will be expanded by using the 2 outside the bracket to multiply the terms inside the bracket. This gives;
8x + 2
Similarly,
6(a + b) will be expanded by using the 2 outside the bracket to multiply the terms inside the bracket. This gives;
6a + 6b
Thus;
The equivalent expressions are;
8a + 2 and 6a + 6b
