What is 3 1/5 as an improper factor?
1 answer:
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Answer:
The solution x = 229.89 ≅ 230 (since we cannot have a decimal number of sweatshirts)implies that, the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.
Step-by-step explanation:
Here is the complete question
In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.
y=35x; y=-0.05(x-400)²+9,492
what does the solution of the system represent in this context?
Solution
The solution of the system is obtained when both equations are equal. That is y=35x = y=-0.05(x-400)²+9,492 .
So, 35x = -0.05(x-400)² + 9,492.
Expanding the right side, we have
35x = -0.05(x² - 800x + 160000) + 9492
35x = -0.05x² -800x × -0.05 + (-0.05) × 160000 + 9492
35x = -0.05x² +40x - 8000 + 9492
35x = -0.05x² +40x + 1492
Collecting all the terms to the left side, we have
0.05x² - 40x - 1492 + 35x = 0
0.05x² - 5x -1492 = 0
Using the quadratic formula,
We choose the positive answer x = 229.83. Since we cannot have a decimal number of sweatshirts, we approximate to the nearest whole number. So, x = 229.83 ≅ 230 sweatshirts.
The solution implies that the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.
We confirm that by plugging in x = 229.83 in both equations.
y = 35x = 35(229.83) = 8044.05 ≅ 8044.1
y=-0.05(x-400)²+9,492 = y=-0.05(229.83-400)²+9,492 = y=-0.05(-170.17)²+9,492 = y=-0.05(28,957.8289)+9,492 = -1447.8914 + 9492 = 8044.11 ≅ 8044.1
By using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.
<h3>What is a function?</h3>A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables.
<h3>The types of function.</h3>In Mathematics, there are different types of functions and these include the following;
- Periodic function
- Inverse function
- Modulus function
- Signum function
- Piece-wise defined function.
- Logarithm function
A logarithm function can be defined as a type of function that represents the inverse of an exponential function. Mathematically, a logarithm function is written as follows:
y = logₐₓ
y = log₁₀10
y = log₁₀10 = 1.
Therefore, if log₁₀x < 1, then, x < 10. Also, if log₁₀x > 1, then, x > 10.
For this exercise, you should take note of this deductive points:
- The upper left number can't be smaller than 1 but its log must be the smallest. Thus, if the exponent equals 0, the red box can assume any number.
- The fractions in the lower left and upper right should be as large as possible with their denominators being small while their numerators are large.
In conclusion, by using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.
Read more on logarithm function here: brainly.com/question/26788007
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