To find the distance between the points \( A(-3, 5) \) and \( B(4, 14) \), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where:
- \( (x_1, y_1) = (-3, 5) \)
- \( (x_2, y_2) = (4, 14) \)
Now, substitute the coordinates into the formula:
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Calculate \( x_2 - x_1 \): \[ 4 - (-3) = 4 + 3 = 7 \]
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Calculate \( y_2 - y_1 \): \[ 14 - 5 = 9 \]
Now, plug these values into the distance formula:
\[ d = \sqrt{(7)^2 + (9)^2} \]
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Calculate \( (7)^2 \) and \( (9)^2 \): \[ 7^2 = 49 \] \[ 9^2 = 81 \]
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Now sum these values: \[ 49 + 81 = 130 \]
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Take the square root: \[ d = \sqrt{130} \approx 11.401754 \]
Finally, round this to the nearest tenth:
\[ d \approx 11.4 \]
Thus, the distance between points \( A(-3, 5) \) and \( B(4, 14) \) is approximately \( \boxed{11.4} \).