Answer:
The domain of a function is the complete set of possible values of the independent variable. The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Step-by-step explanation:
When finding the domain, remember:
The denominator (bottom) of a fraction cannot be zero
The number under a square root sign must be positive in this section
The range is the resulting y-values we get after substituting all the possible x-values.
Answer:
7
Step-by-step explanation:
We need to find the common number that goes into both numbers and thus we get 7
Answer:
It will take 2.8 minutes
Step-by-step explanation:
Given
See attachment for complete question
Required
Time to fill the tube with 46.2 gallons
The attached table is a represents a direct proportional relationship between x and y.
This relationship is:
Where k is the constant of proportionality.
When (x,y) = (1,16.5), we have:
So, we have:
To calculate the required time to fill 46.2 gallons, we make x the subject
Where
Answer: Here is the complete table, with the filled in values:
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Time (h) Distance (mi)
3 2
9 6
12 8
18 12
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Explanation:
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Let us begin by obtaining the "?" value; that is, the "distance" (in "mi.") ;
when the time (in "h") is "18" ;
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12/8 = 18/?
Note: "12/8 = (12÷4) / (8÷4) = 3/2 ;
Rewrite: 3/2 = 18/? ; cross-multiply: 3*? = 2 * 18 ;
3*? = 36 ;
Divide each side by "3" ;
The "?" = 36/3 = 12 ;
So, 12/8 = 18/12 ;
The value: "12" takes the place for the "?" in the table for "distance (in "mi.);
when the "time" (in "h") is "18".
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Now, let us obtain the "? " value for the "distance" (in "mi.");
when the "time" (in "h") is: "9" .
12/8 = 9/? ; Solve for "?" ;
We know (see aforementioned) that "12/8 = 3/2" ;
So, we can rewrite: 3/2 = 9/? ; Solve for "?" ;
Cross-multiply: 3* ? = 2* 9 ; 3* ? = 18 ;
Divide each side by "3" ;
to get: "6" for the "?" value.
When the time (in "h") is "9", the distance (in "mi.") is "6" .
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Now, to solve the final "?" value in the table given.
9/6 = ?/2 ; Note: We get the "6" from our "calculated value" (see above problem).
9/6 = (9÷3) / (6÷3) = 3/2 ;
So, we know that the "?" value is: "3" .
Alternately: 9/6 = ?/2 ;
Cross-multiply: 6*? = 2*9 ; 6 * ? = 18 ; Divide each side by "6" ;
to find the value for the "?" ;
"?" = 18/6 = "3" .
When the "distance" (in "mi.") is: "2" ; the time (in "h") is: "3" .
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Here is the complete table—with all the values filled in:
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<span>Time (h) Distance (mi)
____________________________________________________
3 2
9 6
12 8
18 12
____________________________________________________</span>
