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kumpel [21]
3 years ago
12

Hugo is writing a coordinate proof to show that the midpoints of a quadrilateral are the vertices of a parallelogram. He starts

by assigning coordinates to the vertices of quadrilateral RSTV and labeling the midpoints of the sides of the quadrilateral as A, B, C, and D. Quadrilateral R S T V in a coordinate plane with vertex R at 0 comma 0, vertex S in the first quadrant at 2 a comma 2b, vertex T also in the first quadrant at 2 c comma 2 d, and vertex V on the positive side of the x-axis at 2 c comma 0. Point A is between points R and S, point B is between points S and T, point C is between points T and V, and point D is between points R and V. Enter the answers, in simplified form, in the boxes to complete the proof. The coordinates of point A are ( , ). The coordinates of point B are ( , ). The coordinates of point C are (2c, d) . The coordinates of point D are (c, 0) . The slope of both AB¯¯¯¯¯ and DC¯¯¯¯¯ is . The slope of both AD¯¯¯¯¯ and BC¯¯¯¯¯ is −bc−a . Because both pairs of opposite sides are parallel, quadrilateral ABCD is a parallelogram.

Mathematics
1 answer:
lesantik [10]3 years ago
8 0

Answer: Heres the answers!

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A circle is shown. Secants P N and L N intersect at point N outside of the circle. Secant P N intersects the circle at point Q and secant L N intersects the circle at point M. The length of P N is 32, the length of Q N is x, the length of L M is 22, and the length of M N is 14.

In the diagram, the length of the external portion of the secant segment PN is <u>X</u>

The length of the entire secant segment LN is <u>36</u>.

The value of x is <u>15.74</u>

Step-by-step explanation:

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2 years ago
todd Has a collection of 8cds and sally has a collection of 18 cds Todd is adding 9cds a month to his collection while sally is
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Answer:

Step-by-step explanation:

Let's create some equations first.

Say M = number of months, T = Todd and S = Sally.

We know that Todd starts with 8 cds and sally starts with 18 cds.

This means when M= 0,  T = 8 and S = 18

After one month (M = 1), Todd adds 9 cds.

This means can write the following equation:

T = 8 + 9M

So after the first month (where M = 1), we can find out that Todd has

T = 8 + 9 x 1 = 8 + 9 = 17 cds

For Sally, we know she adds 7 cds per month.

S = 18 + 7M

After one month (M = 1),

S = 18 + 7 x 1 = 25 cds.

Now we are trying to find when they will have the same number of cds and how many.

This means we are trying to figure out what M = ? when Todd and Sally are equal.

So we want to find when T = S

Remember, earlier we wrote :

T = 8 + 9M

S = 18 + 7M

If T = S, this means:

8 + 9M = 18 + 7M

Gather the like terms and solve for M.

Subtract 8 from both sides.

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Divide both sides by 2

M = 5.

So in 5 months, we are saying T = S (Todd and Sally will have the same number of cds).

Put M = 5 back into our earlier equations to find out how many cds they have after 5 months.

T = 8 + 9M

T = 8 + 9 x 5

T = 53

Therefore, after 5 months Todd and Sally will have 53 cds each :)

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3 years ago
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Step-by-step explanation: This is right bro.

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