Problem 1
Question
Find the distance between each pair of points. If necessary, round answers to two decimals places. $$(2,3) \text { and }(14,8)$$
Step-by-Step Solution
Verified Answer
The distance between points (2,3) and (14,8) is 13 units.
1Step 1: Identify the Coordinates
Identify the coordinates of the two points. For our case, the first point is (2,3) and the second point is (14,8). Therefore, \(x_1 = 2\), \(y_1 = 3\), \(x_2 = 14\), and \(y_2 = 8\).
2Step 2: Substitute into Formula
Substitute the values of \(x_1\), \(y_1\), \(x_2\), and \(y_2\) into the distance formula. This will give:\[d = \sqrt{(14 - 2)^2 +(8 - 3)^2}\]
3Step 3: Simplify
Simplify the equation for easier calculation. This gives:\[d = \sqrt{(12)^2 +(5)^2}\]\[d = \sqrt{144 + 25}\]\[d = \sqrt{169}\]
4Step 4: Calculate Distance
Calculate the square root of 169 to find the distance. That is:\[d = 13\]
Other exercises in this chapter
Problem 1
If \(f(x)=2 x^{2}-5\) and \(g(x)=3 x+7,\) find: a. \((f+g)(x)\) b. \((f+g)(4)\)
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In Exercises \(1-8,\) determine whether each relation is a function. Give the domain and range for each relation. $$\\{(1,2),(3,4),(5,5)\\}$$
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Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)=x^{2}-1 $$
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Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, fa
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