Write the equation and then solve the equation
2 answers:
Step-by-step explanation: I have attached the equation in the image provided.
Don't be intimidated by the fraction that appears on the left side of this equation. We start this problem by distributing or multiplying through the parentheses on both sides.
So as we distribute the 1/5 through the parentheses on the left side of the equation, we get 1/5 × y which is y/5 and 1/5 × -1 which is -1/5. On the right, let's change the -2 to + and negative 2 so we know that we're distributing a -2 through the parentheses. When we do that, the right side of the equation simplifies to 6 - 8 + 2y.
Now we have y/5 - 1/5 = 6 - 8 + 2y. Notice that we can go one step further with the right side of the equation as it simplifies to -2 + 2y.
Now we have y/5 - 1/5 = -2 + 2y.
Now we are ready to get rid of the fractions.
Since both fractions have a denominator of 5, we can get rid of the fractions by multiplying both sides of the equation by 5. Make sure you distribute the 5 through both terms on both sides of the equation.
On the left our 5's cancel and we're left with y - 1. On the right, 5 × -2 is -10 and 5 × 2y is 10y.
Now we have y - 1 = -10 + 10y.
From here, we add 1 to both sides of the equation and then we get the following equation. y = -9 + 10y
Now we subtract 10y from both sides of the equation and we get -9y = -9. From here, we divide both sides of the equation by -9 and we get y = 1.
In the image provided, I have only attached steps up to y - 1 = -10 + 10y but the rest of the work is explained above.
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Answer:
(A) y= -1.026x^2 + 1016.402x - 162075
Step-by-step explanation:
Here is the options to the question
Which equation best represents the data?
A) y= -1.026x^2 + 1016.402x - 162075
B) y= -1.036x^2 + 1024.771x - 163710
C) y= 298.214x - 66317.667
D) y= 196.2x – 18710
(A) y= -1.026x^2 + 1016.402x - 162075
The data above represents the company's profit based on number of items produced.
To get the equation which best represents the data, we have to substitute the value of x into the given equations
By substituting x=100 in first equation, we have:
y = -1.02x² + 1016.402x – 162075
y = -1.026(100)² + 1016.402(100) – 162075
y = -70500
y = -70500
Option A satisfies.
Using the second equation
When x = 100
y = -1.036x^2 + 1024.771x - 163710
y = -1.036(100)² + 1024.771(100) - 163710
y = -10360 + 102477.1 – 163710
y = -71592.9
Option B doesn’t satisfies
We can also replace the various values of x in the equations to check whether or not they satisfy.
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