Answer:
Given the statement: Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P.
Properties of Kite:
- The diagonals are perpendicular
- Two disjoint pairs of consecutive sides are congruent by definition of kite
- One diagonal is the perpendicular bisector to the other diagonal.
It is given that: Side QR = 5m and diagonal QS = 6m.
Then, by properties of kite:
![QP = \frac{1}{2}QS](https://tex.z-dn.net/?f=QP%20%3D%20%5Cfrac%7B1%7D%7B2%7DQS)
Substitute the value of QS we get QP;
= 3 m
Now, in right angle ![\triangle RPQ](https://tex.z-dn.net/?f=%5Ctriangle%20RPQ)
Using Pythagoras theorem:
![QR^2= RP^2 +QP^2](https://tex.z-dn.net/?f=QR%5E2%3D%20RP%5E2%20%2BQP%5E2)
Substitute the given values we get;
![(5)^2= RP^2 +(3)^2](https://tex.z-dn.net/?f=%285%29%5E2%3D%20RP%5E2%20%2B%283%29%5E2)
or
![25= RP^2 +9](https://tex.z-dn.net/?f=25%3D%20RP%5E2%20%2B9)
Subtract 9 from both sides we get;
![16= RP^2](https://tex.z-dn.net/?f=16%3D%20RP%5E2)
Simplify:
![RP = \sqrt{16} = 4 m](https://tex.z-dn.net/?f=RP%20%3D%20%5Csqrt%7B16%7D%20%3D%204%20m)
Therefore, the length of segment RP is, 4m
The answer should be A
please let me know if this is wrong
Answer:
2x+8
Step-by-step explanation:
let the number=x
Twice the number=2x
sum of 8 and twice the number=2x+8
If the length of a confidence interval is 3 for inference concerning a mean, the required sample size is ![(z_\frac{\alpha }{2}*\frac{\sigma}{3} )^2](https://tex.z-dn.net/?f=%28z_%5Cfrac%7B%5Calpha%20%7D%7B2%7D%2A%5Cfrac%7B%5Csigma%7D%7B3%7D%20%29%5E2)
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more variables and numbers.
σ = standard deviation, n = sample size, the margin of error (E) is given by:
![E=z_\frac{\alpha }{2}*\frac{\sigma}{\sqrt{n} } \\\\E=3, hence:\\\\3=z_\frac{\alpha }{2}*\frac{\sigma}{\sqrt{n} } \\\\n=(z_\frac{\alpha }{2}*\frac{\sigma}{3} )^2](https://tex.z-dn.net/?f=E%3Dz_%5Cfrac%7B%5Calpha%20%7D%7B2%7D%2A%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%20%7D%20%20%5C%5C%5C%5CE%3D3%2C%20hence%3A%5C%5C%5C%5C3%3Dz_%5Cfrac%7B%5Calpha%20%7D%7B2%7D%2A%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%20%7D%20%5C%5C%5C%5Cn%3D%28z_%5Cfrac%7B%5Calpha%20%7D%7B2%7D%2A%5Cfrac%7B%5Csigma%7D%7B3%7D%20%29%5E2)
If the length of a confidence interval is 3 for inference concerning a mean, the required sample size is ![(z_\frac{\alpha }{2}*\frac{\sigma}{3} )^2](https://tex.z-dn.net/?f=%28z_%5Cfrac%7B%5Calpha%20%7D%7B2%7D%2A%5Cfrac%7B%5Csigma%7D%7B3%7D%20%29%5E2)
Find out more on equation at: brainly.com/question/2972832
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-23-(-113)
Subtract -113 from -23. This would also be the same as adding 113 to -23 because the two negative signs are equal to one positive sign.
Final Answer: 90