What is the unit rate for $1.25 every half hour?
1 answer:
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Answer:
a)Domain is all positive integers.
b)C(2000)=$7600
c) For C(x)<10000, less than 3846 items should be manufactured.
Step-by-step explanation:
Given that cost function is C(x)=5000+1.3x, where x is the number of manufactured items.
a) The domain of C(x) means the range of values x can take. Since x is the number of manufactured items, it cannot be negative and fraction.
Hence domain is all positive integers.
b)To find the cost of 2000 items, we should plugin x=2000 in C(x).
That is cost of 2000 items, C(2000)=5000+1.3(2000)=5000+2600=$7600
c) We are asked to find the number of items such that cost is kept below 10,000 that is C(x)<10000
5000+1.3x<10000
Subtract 5000 from both sides
1.3x<5000
Divide with 1.3 on both sides
x<3846.2
Hence number of items must be less than 3846 for C(x)<10000
Answer:
The slope of a line that is perpendicular to the line y = 2x – 6 is -1/2.
Step-by-step explanation:
The slope-intercept form of the line equation
where
is the slope
is the y-intercept
Step 1:
Finding the slope of the given equation
The given equation is
comparing with the slope-intercept form of the line equation
The slope of the equation is: m = 2
Step 2:
Determining the slope of the perpendicular line
In Mathematics, a line perpendicular to another line has a slope that is the negative reciprocal of the slope of the other line.
- As the slope of the equation is: m = 2
Therefore, the slope of the new perpendicular line:
Hence, the slope of a line that is perpendicular to the line y = 2x – 6 is -1/2.
Important Tip:
- The product of the slopes of perpendicular lines is -1.
<u>Verification:</u>
The slope of the given line:
The slope of the perpendicular line:
The product of the slopes is:
As the product of the slopes of perpendicular lines is -1, therefore, the lines are perpendicular.
Thus, the slope of a line that is perpendicular to the line y = 2x – 6 is -1/2.