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lisabon 2012 [21]
3 years ago
12

Find the coordinates of the midpoint of a line segment with the given endpoints (14,-8), (12,-1)

Mathematics
1 answer:
Flauer [41]3 years ago
4 0

Answer:

The coordinates of the midpoint of a line segment with the given endpoints (14,-8), (12,-1) are \mathbf{(13,\frac{-9}{2})}

Step-by-step explanation:

We need to find the coordinates of the midpoint of a line segment with the given endpoints (14,-8), (12,-1)

The midpoint of line segment can be found using formula:

Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

We have x_1=14, y_1=-8, x_2=12, y_2=-1

Putting values and finding midpoint

Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\Midpoint=(\frac{14+12}{2},\frac{-8-1}{2})\\Midpoint=(\frac{26}{2},\frac{-9}{2})\\Midpoint=(13,\frac{-9}{2})

So, the coordinates of the midpoint of a line segment with the given endpoints (14,-8), (12,-1) are \mathbf{(13,\frac{-9}{2})}

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Which angle number is a vertical angle to
VMariaS [17]

Answer:

Angle 7 or angle DHG

Step-by-step explanation:

Vertical means the opposite angle, or in dictionary definition means each of the pairs of opposite angles made by two intersecting lines. So the vertical angle to angle LHI (angle 9) will be angle DHG (angle 7)

5 0
3 years ago
The coordinates of point A are (p, q) and coordinates of point B are (p+2q, q+2p). Provide your complete solutions and proofs in
Dafna1 [17]

Answer:

The mid-point (p + q , q + p) of AB is the same distance from the x-axis and the y-axis

Step-by-step explanation:

*<em> Lets explain how to solve the problem</em>

- Any point will be equidistant from the x-axis and the y-axis must have

 equal coordinates

- Ex: point (4 , 4) is the same distance from the x-axis and the y-axis

 because the distance from the x-axis to the point is 4 (y-coordinate)

 and the distance from the y-axis and the point is 4 (x-coordinate)

- If (x , y) is the mid-point of a segment its endpoints are

 (x_{1},y_{1})  and (x_{2},y_{2}), then

 x=\frac{x_{1}+x_{2}}{2} and y=\frac{y_{1}+y_{2}}{2}

* <em>Lets solve the problem</em>

∵ Point A has coordinates (p , q)

∵ Point B has coordinates (p + 2q , q + 2p)

- The mid-point of AB is (x , y)

∵ x=\frac{p+p+2q}{2}

∴ x=\frac{2p+2q}{2}

- Take 2 as a common factor from the terms of the numerator

∴ x=\frac{2(p+q)}{2}

- Divide up and down by 2

∴ x = p + q

∵ y=\frac{q+q+2p}{2}

∴ y=\frac{2q+2p}{2}

- Take 2 as a common factor from the terms of the numerator

∴ y=\frac{2(q+p)}{2}

- Divide up and down by 2

∴ y = q + p

∴ <em>The mid point of AB is (p + q , q + p)</em>

- p + q is the same with q + p

∵ The x-coordinate of the mid point of AB is p + q

∵ The y-coordinate of the mid point of AB is q + p

∵ p + q = q + p

∴ The coordinates of the mid-point of AB are equal

- According the explanation above

∴ The mid-point (p + q , q + p) of AB is the same distance from the

   x-axis and the y-axis

8 0
3 years ago
Which of the following is NOT a requirement of testing a claim about a population proportion using a formal method of hypothesis
Pie

Answer:

A. The lowercase​ symbol, p, represents the probability of getting a test statistic at least as extreme as the one representing sample data and is needed to test the claim.

Step-by-step explanation:

The conditions  required for testing  of a claim about a population proportion using a formal method of hypothesis​ testing are:

1) The sample observations are a simple random sample.

2) The conditions for a binomial distribution are satisfied

3) The conditions np5 and nq5 are both satisfied. i.e n: p≥ 5and q≥ 5

These conditions are given in th options b,c and d.

Option A is not a condition for testing  of a claim about a population proportion using a formal method of hypothesis​ testing.

8 0
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Which point is a reflection of Z(5 1/2,3) across the y axis
RSB [31]

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Step-by-step explanation:

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katen-ka-za [31]

Answer:

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Step-by-step explanation:

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Group        I   II

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p 0.533333333 0.533333333

q 0.466666667 0.466666667

se 0.014401646 0.045542003

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Z 2.314550249 0.731925055

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we find that though p is the same, std error is very small for larger sample size thus making z statistic much bigger.  So we get p value less than 0.05 whereas for 120 sample size, std error is large so Z statistic is small thus making p value to accept null hypothesis

3 0
3 years ago
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