Note: (f/g)(x) can be written as
f(x)/g(x). This simply means f(x) divided by g(x).
We know what f(x) and g(x) are because that information is given to us in the problem. See it?
Set up the rational function and factor.
(x^2 - 9)/(x^2 -4x + 3)
We now factor the top and bottom.
(x - 3)(x + 3)/(x - 3)(x - 1)
Cancel out common terms.
We now have (x + 3)/(x - 1) as the reduced rational function.
To find the domain, set the bottom to 0 and solve for x.
x - 1 = 0
x = 1
The domain is ALL REAL NUMBERS EXCEPT FOR 1. In the given function, x CANNOT BE 3 because this would create a zero in the denominator.
Answer in interval notation is
(-00, 1) U (1, 3) U (1, 00).
The interval notation reads as follows:
All negative numbers included but not 1 united with the open interval that does not include 1 and 3 united with the interval that excludes 1 but includes all positive numbers greater than 1. I hope this is clear.
Given:
Cost of dishwasher : 315 before sales tax
sales tax : 9.22%
Total cost = 315 * 1.0922 = 344.043
Average of 10 uses per week for the next 6 years before replacing it.
There are 52 weeks in a year.
10 uses per week * 52 weeks per year * 6 years = 3120 average uses
cost for water = 0.09 ; cost for electricity = 0.13 ; total cost per use = 0.22
0.22 * 3120 = 686.40 cost of use
purchase cost = 344.043
cost of use = <u>686.40</u>
lifetime cost 1,030.443
3/8 is equivalent to 0.375.
Answer: 6.403 miles; or, write as: 6.403 mi. .
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Explanation:
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5
--------------------------------------------
` right angle |_ |
` (right triangle ) |
` | 4
` |
`
"c" ` \
(hypotenuse) Starting point
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Since we have a "right triangle, we solve for "c"; using the
"Pythagorean theorem" ;
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→ a² + b² = c² ; Solve for "c" ; our answer (in "miles"; or, "mi.") ;
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Given : a = 4; b = 5 ;
____________________________
Plug these known values into our equation:
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→ 4² + 5² = c² ;
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→ 16 + 25 = c² ; ↔ c² = 16 + 25 ;
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→ c² = 41 ;
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→ Take the positive square root of each side of the equation (since the side of a "triangle" cannot be "negative";
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→ √(c²) = √(41) ;
_____________________________
→ c = √41 ; Use calculator;
________________________________
→ c = 6.40312423743 ; Round to:
→ c = 6.403 miles; or, 6.403 mi.
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Answer:
Salesman A made $569.1 more commission than salesman B
Step-by-step explanation:
(11/100)*67530= (amount made by salesperson A)
=7428.3
(8/100)*85740= (amount made by salesperson B)
=6859.2
A-B= 569.1
Hope this helps :D
