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Serggg [28]
3 years ago
14

Prove that any median in a triangle is less than the half of the triangle's perimeter.

Mathematics
1 answer:
klemol [59]3 years ago
8 0

See image for naming of the sides: the medians are

ab, bc, and ac; and sides are a, b, and c

Pick one median, say, ab. The following are true:

ab < a

ab < b

->

ab + ab < a + b

ab < 0.5*(a+b)     | add 0.5*c to the right hand side (does not change inequality)

ab < 0.5(a+b+c) = half perimeter

so ab < half perimeter

Same argument for bc, and ac holds.



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adell [148]

Answer:

2. x ²  +  y ² =  4

3. x² + y² = 23

Step-by-step explanation:

The equation of a circle with center  

( a , b )  and radius  r  is:

( x − a )²   +  ( y − b ) ² =  r ²

Explanation:

Here,

 a = 0 ,  b = 0 ,  r = 2  

The equation is:

( x -0 ) ² +  ( y -0 ) ² =  ( 2  ) ²

that is:  x ²  +  y ² =  4  

Thus:

x ²  +  y ² =  4

3. Each point on a circle has the same distance from the center. This distance is the radius  r  of the circle.

 Here, ( -3 , 4 )  is a point on the circle, meaning that the radius of the circle is the distance between  ( 0 , 0 ) , the center, and  ( -3 , 4 ) .

thus  a circle centered on the origin will have an equation of:

x² + y² =r²

And,  ( -3 , 4 )  lies on the circle, we have:

(-3)² + (4)² = r²

9 + 14 = 23

substituting;

x² + y² = 23

8 0
2 years ago
A cube has sides with a length of 1/3 cm. What is its volume?
kompoz [17]

Answer:

1 / 27 cm^3

Step-by-step explanation:

Given,

side = 1 / 3 cm

To find : Volume ( cube ) = ?

Formula : -

Volume ( cube ) = ( side )^3

Volume ( cube )

= ( 1 / 3 )^3

= 1^3 / 3^3

= 1 / 27

= 1 / 27 cm^3

7 0
2 years ago
Read 2 more answers
How do you solve -3x-4&gt;5
Salsk061 [2.6K]

Answer: x < -3

Step-by-step explanation:

-3*x-4-(5)>0

7 0
3 years ago
A: What are the solutions to the quadratic equation x2+9=0? B: What is the factored form of the quadratic expression x2+9? Selec
Paraphin [41]

Answer:

A. The solutions are x=3i,\:x=-3i.

B. The factored form of the quadratic expression x^2+9=(x-3i)(x+3i)

Step-by-step explanation:

A. To find the solutions to the quadratic equation x^2+9=0 you must:

\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\\\x^2+9-9=0-9\\\\\mathrm{Simplify}\\\\x^2=-9\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{-9},\:x=-\sqrt{-9}

x=\sqrt{-9} = \sqrt{-1}\sqrt{9}=\sqrt{9}i=3i\\\\x=-\sqrt{-9}=-\sqrt{-1}\sqrt{9}=-\sqrt{9}i=-3i

The solutions are:

x=3i,\:x=-3i

B. Two expressions are equivalent to each other if they represent the same value no matter which values we choose for the variables.

To factor x^2+9:

First, multiply the constant in the polynomial by i^2 where i^2 is equal to -1.

x^2+9i^2

Since both terms are perfect squares, factor using the difference of squares formula

a^2-i^2=(a+i)(a-i)

x^2+9=x^2+9i^2=\left(-3i+x\right)\left(3i+x\right)

5 0
3 years ago
Doug dives from a platform that is 10 meters above water. His dive takes him 3.8 meters below the
Lynna [10]

Answer:

13.8

Step-by-step explanation:

His dive once he hits the water and goes below the surface water line is in the same direction as his dive off the platform. That's very important when you start to consider direction. So you add. Be sure and read this paragraph again.

Dive = platform + under the surface

Dive = 10 + 3.8

Dive = 13.8

4 0
2 years ago
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