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ahrayia [7]
3 years ago
13

Please help me with this

Mathematics
1 answer:
goldenfox [79]3 years ago
7 0
For part A, if P is the center of that triangle, then PR and PT have the same length; therefore, triangle RPT is isosceles.  For part B, by the definition of an incenter...if P is an incenter, then it is the place where all the angle bisectors meet.  Therefore, angles SRP and PRT are congruent, as are angles STP and PTR.  Since the vertex angle measures 64, then each of the base angles by the isosceles triangle theorem measure 58.  Half of 58 makes the base angles within the smaller triangle measure 29.  And if both of those measure 29, by the triangle angle-sum theorem, 180-29-29 = 122  And that's the measure of angle RPT.  Eek.
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Step-by-step explanation:

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Step-by-step explanation:

#1) We want a line that passes through (1, -3) and is parallel to y = 2-4(x-1).  First we simplify our equation using the distributive property:

y = 2-4(x-1) = 2-4(x) -4(-1) = 2-4x--4 = 2-4x + 4 = -4x + 6

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y-y_1=m(x-x_1)\\\\y--3=-4(x-1)\\\\y+3=-4(x)-4(-1)\\\\y+3=-4x+4\\\\y+3-3=-4x+4-3\\\\y=-4x+1

#2) We must first write our second equation in slope-intercept form by isolating the y term:

2x+y=7

Subtract 2x from each side"

2x+y-2x = 7-2x

y = -2x+7

This means the slope is -2; the slopes are the same, so the lines are parallel.

#3) The slope of our given equation is 2.  To be perpendicular, the second line must have a slope that is a negative reciprocal (flipped and opposite signs); this makes it -1/2.  Using point-slope form,

y-0=\frac{-1}{2}(x-5)\\\\y=\frac{-1}{2}(x)+\frac{-1}{2}(-5)\\\\y=\frac{-1}{2}x+\frac{5}{2}

#4) The slope of Main Street on the diagram, found by using rise/run, is 2.  This means the bike path will also have a slope of 2 in order to be parallel.  The park entrance is at (0, 4).  This makes the equation y = 2x+4.

#5) Two lines with the same slope are always parallel.  They are never perpendicular.

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