Concept explainers
a.
To write:
An equation describing the possible values of x and y .
a.
Answer to Problem 30E
The equation
Explanation of Solution
Given:
The rectangle shown has a perimeter of 16 inches.
Calculation:
We know that the perimeter of a rectangle is sum of two times length and two times width. Upon representing our given information in an equation, we will get:
Therefore, the equation
b.
To graph:
The equation from part (a) using intercepts.
b.
Answer to Problem 30E
x -intercept:
y -intercept:
Explanation of Solution
Given:
The rectangle shown has a perimeter of 16 inches.
Calculation:
To find x -intercept, we will substitute
Therefore, the x -intercept of our given equation is
To find y- intercept, we will substitute
Therefore, the y -intercept of our given equation is
Upon graphing our given equation, we will get our required graph as shown below:
c.
To give:
Three pairs of whole number values of x and y that could represent side lengths of rectangle.
c.
Answer to Problem 30E
Our required pairs would be
Explanation of Solution
Given:
The rectangle shown has a perimeter of 16 inches.
Calculation:
To get three possible pairs for side lengths, we need to identify 3 points on the line graphed in part (b).
We can see that the points
Therefore, the points
d.
To explain:
Does either the x -intercept or the y -intercept represent a possible side length of the rectangle.
d.
Answer to Problem 30E
Neither x -intercept nor the y -intercept represent a possible side length of the rectangle.
Explanation of Solution
Given:
The rectangle shown has a perimeter of 16 inches.
Calculation:
We know that the x -intercept is the point on x -axis, where the value of y is 0. The y -intercept is the point on y -axis, where the value of x is 0.
We also know that to form a rectangle we need two sides and both sides should be greater than 0. At the both intercepts, one side will be 0.
Therefore, neither x -intercept nor the y -intercept represent a possible side length of the rectangle.
Chapter 8 Solutions
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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