<em>Copying</em> a given <u>segment</u> is the process in which a given<em> line segment</em> is drawn following the required <u>steps</u> so that both <u>object</u> and <u>image</u> have the same length. Therefore,
i. PQ = 12 cm
ii. MN = 12 cm
Thus, PQ = MN
Construction is a process that requires the use of <u>materials</u> and <u>instruments</u> to produce a required <em>image</em>. This involves following stated or required steps.
A given <em>line segment </em>can be copied by following appropriate steps. Such that both <u>lines</u> would have the same <u>length</u>, and would be <u>parallel </u>to each other or as required.
The given question requires following the stated <em>steps</em> to produce the required <em>construction</em>. Such that <u>line</u> segment NM is the image of PQ, and both have equal <u>length</u>.
The required <u>construction</u> for the question is <u>attached</u> to this answer.
For more clarifications on copying a given line segment, visit: brainly.com/question/1581615
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Answer:
it would take him to 7 hours drive 504 miles.
Step-by-step explanation:
360 miles → 5 hours
1 miles → (5/360) hours
504 miles → [(5/360)*504] hours
504 miles → 7 hours
Basically, the parabola has to have all points that are equidistant from the focus and the directrix, the directrix being a horizontal line, and the focus being a point given. To derive an equation from this you need to use the distance formula which I'm guessing you already know because you're already in precalc.
The gist of it is that we have a random point on the parabola (x,y), and the point (x,y) will be equidistant from both the focus and the directrix. If we use the distance formula, you get something like this:
![\sqrt{(y-(- \frac{1}{2} ))^2} = \sqrt{(x-2)^2+(y-(-1)^2}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%28y-%28-%20%5Cfrac%7B1%7D%7B2%7D%20%29%29%5E2%7D%20%3D%20%5Csqrt%7B%28x-2%29%5E2%2B%28y-%28-1%29%5E2%7D)
The square root of y-(-1/2) coming from the directrix, and the righthand side of the equal sign being derived from the focus.
All you need to do is simplify now!
<span>
![(y+\frac{1}{2})^2 = (x-2)^2+(y+1)^2 \\\ y^2+y+ \frac{1}{4} = x^2-4x+4 + y^2+2y+1 \\\ -y-\frac{3}{4} = x^2-4x+4 \\\ -y-\frac{3}{4} = (x-2)^2 \\\ -y = (x-2)^2+\frac{3}{4} \\\ y = -(x-2)^2-\frac{3}{4}](https://tex.z-dn.net/?f=%28y%2B%5Cfrac%7B1%7D%7B2%7D%29%5E2%20%3D%20%28x-2%29%5E2%2B%28y%2B1%29%5E2%20%5C%5C%5C%20y%5E2%2By%2B%20%5Cfrac%7B1%7D%7B4%7D%20%3D%20x%5E2-4x%2B4%20%2B%20y%5E2%2B2y%2B1%20%5C%5C%5C%20-y-%5Cfrac%7B3%7D%7B4%7D%20%3D%20x%5E2-4x%2B4%20%5C%5C%5C%20-y-%5Cfrac%7B3%7D%7B4%7D%20%3D%20%28x-2%29%5E2%20%5C%5C%5C%20-y%20%3D%20%28x-2%29%5E2%2B%5Cfrac%7B3%7D%7B4%7D%20%5C%5C%5C%20y%20%3D%20-%28x-2%29%5E2-%5Cfrac%7B3%7D%7B4%7D)
</span>
Hope I helped!
It is zero *more characters to fulfill answer requirements*
Converse (switch p and q)
If an angle is obtuse, then it measures 128°
This is false (a 127° angle is obtuse, but it does not measure 128°)
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Inverse (negations of p and q)
If an angle does not measure 128°, then it is not obtuse
This is false (a 127° angle does not measure 128°, but it is obtuse)
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Contrapositive (negations of p and q, then switch their places)
If an angle is not obtuse, it does not measure 128°
This is true (any 128° is obtuse; no exceptions)