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cestrela7 [59]
4 years ago
8

Given: The coordinates of rectangle DEFG are D(0, b), E(a, b), F(a, 0), and G(0, 0). Prove: The diagonals of a rectangle are con

gruent. As part of the proof, find the length of .
Mathematics
1 answer:
Mama L [17]4 years ago
6 0

Answer:

The answer to your question is below

Step-by-step explanation:

Data

D (0, b)

E (a, b)

F(a, 0)

G (0, 0)

From this information, we conclude that the diagonals are EG and DF.

To prove that they are congruent we must calculate their length.

dEG = \sqrt{(0- b)^{2} + (0 - a)^{2}}

dEG = \sqrt{b^{2} + a^{2}}

dDF = \sqrt{(a - 0)^{2} + (0 - b)^{2}}

dDF = \sqrt{a^{2} + b^{2}}

Conclusion

The length of EG is equal to the length of DF, so they are congruent.

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How is "y more than 4 is -36" written and what is the answer ​
Crazy boy [7]

Answer:

y+4=-36 and the answer is y=-40

Step-by-step explanation:

So the word is means equals, meaning we can change it to say

"y more than 4 = -36

and more than means addition so we can put a plus sign there and we get

y+4=-36

then to solve this equation we need to get y by itself on one side and to do that we can move the 4 to the other side by subtracting it on both sides to cancel out the addition and we get y=-40

I hope this helps and please don't hesitate to ask if there is anything still unclear!

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Step-by-step explanation:

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3 years ago
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At a playground, a child slides down a slide that makes a 42° angle with the horizontal direction. the coefficient of kinetic fr
enyata [817]
Assuming metric units, metre, kilogram and seconds

Best approach: draw a free body diagram and identify forces acting on the child, which are:
gravity, which can be decomposed into normal and parallel (to slide) components 
N=mg(cos(theta)) [pressing on slide surface]
F=mg(sin(theta))  [pushing child downwards, also cause for acceleration]
   m=mass of child (in kg)
   g=acceleration due to gravity = 9.81 m/s^2
   theta=angle with horizontal = 42 degrees

Similarly, kinetic friction is slowing down the child, pushing against F, and equal to
Fr=mu*N=mu*mg(cos(theta))
  mu=coefficient of kinetic friction = 0.2

The net force pushing child downwards along slide is therefore
Fnet=F-Fr
=mg(sin(theta))-mu*mg(cos(theta))
=mg(sin(theta)-mu*cos(theta))   [ assuming sin(theta)> mu*cos(theta) ]

From Newton's second law,
F=ma, or 
a=F/m
=mg(sin(theta)-mu*cos(theta))  /  m
= g(sin(theta)-mu*cos(theta))   [ m/s^2]

In case imperial units are used, g is approximately 32.2 feet/s^2.
and the answer will be in the same units [ft/s^2] since sin, cos and mu are pure numbers.



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4 years ago
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