ANSWER:}------> <u><em>line b</em></u>
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)
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3 2
9 6
12 8
18 12
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2
2x
2
+5x−12
1 Split the second term in
2
x
2
+
5
x
−
1
2
2x
2
+5x−12 into two terms.
2
x
2
+
8
x
−
3
x
−
1
2
2x
2
+8x−3x−12
2 Factor out common terms in the first two terms, then in the last two terms.
2
x
(
x
+
4
)
−
3
(
x
+
4
)
2x(x+4)−3(x+4)
3 Factor out the common term
x
+
4
x+4.
(
x
+
4
)
(
2
x
−
3
)
(x+4)(2x−3)
