Answer:
Price of widget to break even= $37.9
Step-by-step explanation:
We are told that the equation representing the amount of profit, y, made by the company, in relation to the selling price of each widget, x is;
y = -8x² + 348x - 1705
Now, the company will break even when it has made no profit. That is when, y = 0
Thus;
0 = -8x² + 348x - 1705
Rearranging,
8x² - 348x + 1705 = 0
Using quadratic formula ;
x = [-b ± √(b² - 4ac)]/2a
x = [-8 ± √(-348² - 4•1•1705)]/(2 x 8)
x = $5.63 or $37.87
We'll use $37.87 because it is the highest price for which no profit is made, and higher price means that we could sell least number of products to earn a certain amount of money.
We are told to approximate to nearest cent. Thus,
Price of widget = $37.87 ≈ $37.9
Answer:
-3(4c-2) -2c = -14c+6
Step-by-step explanation:
We need to find the equivalent expression for -3(4c-2) -2c.
First we open the brackets as follows :
-3(4c-2) -2c
= -12c+6-2c
=-12c-2c+6
=-14c+6
So, the equivalent expression is -14c+6.
The letter 'C' has 2 lines of symmerty
the upper-case 'D' has 2 lines of symmetry
the uper -case 'E' has 2 lines of symmetry
the upper case 'H' has 2 lines of symmetry
the upper case 'I' has 2 lines of symmetry
the small case 'L' has 2 lines of symmmetry
the letter 'O' has infinite lines of symetry
the letter 'x' has 4 lines of symmetry
The approximate area that is within range of the motion sensor is 4975 square meters
<h3>How to determine the area of the range?</h3>
The figure is not given, however the area of the range can be calculated without the figure.
The given parameters are:
Angle, ⊕ = 135°
Radius, r = 65 meters
The area of the range is calculated using the following sector area
This gives
Evaluate
A = 4974.9375
Approximate
A = 4975
Hence, the approximate area that is within range of the motion sensor is 4975 square meters
Read more about sector areas at:
brainly.com/question/16736105
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Answer: the length of the field is 70 yards. The width of the field is 35 yards
Step-by-step explanation:
Let L represent the length of the rectangular athletic field.
Let W represent the width of the rectangular athletic field.
A rectangular athletic field is twice as long as it is wide. This means that
L = 2W
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + W)
If the perimeter of the athletic field is 210 yards, it means that
210 = 2(L + W)
L + W = 210/2 = 105
Substituting L = 2W into L + W = 105, it becomes
2W + W = 105
3W = 105
W = 105/3 = 35
L = 2W = 2 × 35
L = 70
