Write a system of equations to describe the situation below, solve using substitution, and fillin the blanks.Nora, an office manager, needs to find a courier to deliver a package. The first courier she isconsidering charges a fee of $14 plus $5 per kilogram. The second charges $15 plus $4 perkilogram. Nora determines that, given her package's weight, the two courier services areequivalent in terms of cost. What is the weight? How much will it cost?
Answers
The first courier service cost is;
Where, x is the number of kilograms delivered;
The second courier service cost is;
Equating it, we have;
Thus, the weight that will result in equal cost is 1 kilogram.
And the cost is 5( 1 )+14 = $19
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6. How many solutions does the given system have?y = 3x - 16x - 2y = -2A. one solutionB. two solutionsC. infinite solutionsD. no solution
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a. How much wire must be used for the square in order to maximize the total area?
b. How much wire must be used for the square in order to minimize the total area?
Answers
Answer:
wire for square to maximize total area = 23 m
Wire to minimize total area = 2.019 m
Step-by-step explanation:
For the square, let's say the total length of the square is "y" m.
Thus, length of one side is = y/4
And area of the square = (y/4) = y²/16
Since the wire is 23 m, then total length of equilateral triangle is; 23 - y.
Thus, length of one side of equilateral triangle = (23 - y)/3
Using trigonometric ratio, we can find the height of the triangle and thus area.
Area of triangle = (√3)/4) × ((23 - y)/3)²
Area of triangle = (√3)/36)(23 - y)²
So, total area of square and triangle is;
A_total = (y²/16) + (√3)/36)(23 - y)²
Now, extremizing this function by derivatives, we have;
dA/dy = (y/8) - (√3)/18)(23 - y)
d²A/dy² = ⅛ + (√3)/18)
So, d²A/dy² > 0
Now,let's find the maximum or minimum of the function.
So, we equate dA/dy to zero.
Thus;
(y/8) - (√3)/18)(23 - y) = 0
y/8 = (√3)/18)(23 - y)
(y/8) + (√3)/18)y = 23((√3)/18)
Multiply through by 8 to give;
y + 0.0962y = 2.2132
1.0962y = 2.2132
y = 2.2132/1.0962
y = 2.019 m
2.019 will be a minimum because d²A/dy² > 0
The maximum will occur at a boundary of the allowed values. Thus, the absolute maximum is for y = 23.
Note that a square has more area than a triangle and as such it is normal for the square to get the largest area over the triangle and therefore we will have to use all of the wire to construct the square.
Answers
Look at the millions place. 1 is in the millions place.
Now look at the number to the right of 1.
Since it is 5 or greater, round 1 up to 2.
Change all the numbers after 1 to 0.
1,563,385 rounded to the nearest million is 2,000,000.
Answers
Answer:
((2^(-2))÷(3^3))^4=
Step-by-step explanation: expand
Which is the function represented by the table?
Answers
Answer:
f(x) = 4x
Step-by-step explanation:
-2 x 4 = -8
-1 x 4 = -4
0 x 4 = 0
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Answers
Answer: 7a+3
Step-by-step explanation:
9a and 2a are two like terms that we can combine. Because there is a minus sign in front of the 2a, we should subtract 9a from 2a to get
7a. Then because the 3 has plus sign in front of it, we add 7a to 3. BUT because 3 a is NOT a like term, you don’t actually add it, so it looks like this: 7a+3. Hope this helped!
Answers
Answer:
8 cups
Step-by-step explanation:
Let the total batch of salsa be x.
x = 5.2
x =
× 5.2
x = 8