1, 1, 2, 6, 24, ... What are the next three numbers in the pattern?
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Answer:
a. The value of the constant k is 21
b. The equation is y = k * x, where k is the proportionality constant, "x" is the number of terraced houses and "y" is the width of a row of identical houses.
Step-by-step explanation:
a.
<em>A proportional relationship satisfies the equation y = k * x, where k is a positive constant and is called a proportionality constant. In this case "x" is the number of terraced houses and "y" is the width of a row of identical houses. </em>
The data you have is that the width of 5 townhouses are 105 feet. This means that the value of "x" is 5 houses and the value of "y" is 105 feet. By replacing in the equation y = k * x and isolating the constant k, you get:
<em>105=k*5 </em>
<em>k=21 </em>
<u><em>So the value of the constant k is 21.</em></u>
b.
<em>As mentioned, the equation is y = k * x, where k is the proportionality constant, "x" is the number of terraced houses and "y" is the width of a row of identical houses.</em>
This means that just as "x" increases, "y" increases. And that if "x" decreases, "y" will decrease. And this relationship between "x" e "and" will always be the same, determined by the value of the constant "k".