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Verifying that and are Not Perpendicular
To determine whether the lines and are perpendicular, convert both equations to slope-intercept form to compare their slopes.
First equation: Solve for . Subtract from both sides: Divide by : The slope is .
Second equation: Solve for . Subtract from both sides: Divide by : The slope is .
Check for negative reciprocals: The slopes and are reciprocals, but they share the same negative sign. For lines to be perpendicular, their slopes must be negative reciprocals with opposite signs. Since their product is \left(-\frac{5}{4} ight)\left(-\frac{4}{5} ight) = 1 instead of , the lines are not perpendicular.
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A site surveyor is checking the alignment of two property boundaries defined by the equations 7x + 2y = 3 and 2x + 7y = 5. After converting to slope-intercept form, the surveyor identifies the slopes as -7/2 and -2/7. According to the mathematical rule for perpendicularity, why are these boundaries NOT perpendicular?
A maintenance technician is checking the intersection of two support cables defined by the equations 7x + 2y = 3 and 2x + 7y = 5. The slopes are calculated as -7/2 and -2/7. In the process of verifying that these cables are NOT perpendicular, the technician identifies that the product of the slopes is ____.
A construction inspector is evaluating the intersection of two structural supports defined by the equations 7x + 2y = 3 and 2x + 7y = 5. To verify that the supports are NOT perpendicular, the inspector must identify the slopes and their product. Match each description with its corresponding numerical value.
A site inspector is reviewing a CAD drawing where two intersecting beams are represented by the equations and . A junior drafter claims that because the slopes of these lines (- rac{7}{2} and - rac{2}{7}) are reciprocals, the beams are perpendicular. True or False: The drafter's claim is mathematically correct.
Slope Sign Requirement for Perpendicularity
A project site inspector is following a standard verification procedure to confirm that two layout lines, represented by the equations and , are not perpendicular. Arrange the following steps of the verification process in the correct chronological order.
Telecommunications Infrastructure Layout Verification
Verification of Layout Line Alignment
A maintenance technician is converting the boundary equation $7x + 2y = 3y = mx + b$) to identify its slope. Which of the following represents the correct equation for this line?
A site planning coordinator is verifying the coordinates of a utility easement represented by the linear equation . To calculate the easement's orientation, the coordinator must first identify the slope of the line. What is the slope () of the line ?
Verifying that and are Not Perpendicular
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An electrical technician is verifying if two conduits, modeled by the lines and , are perpendicular. Match each part of the verification process with its correct value or description.
A structural inspector is verifying the angle between two support cables modeled by the equations and . Arrange the steps of the verification process in the correct order to conclude that these cables are NOT perpendicular.
A landscape architect is designing two walking paths modeled by the linear equations and . After determining that the slopes of these paths are and - rac{4}{5}, the architect verifies if the paths meet at a right angle. Which of the following statements correctly recalls the product of these slopes and explains why the paths are NOT perpendicular?
A design engineer is verifying the alignment of two layout lines modeled by the equations and . The engineer determines that the product of the slopes of these two lines is 1, which confirms that the lines are NOT perpendicular.
Recalling Slopes and Perpendicularity Rules for Linear Boundaries