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Mademuasel [1]
3 years ago
9

prove that points (2a,4a), (2a,6a), and (2a +√3a,5a) are the vertices of an equilateral triangle of side

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
8 0

Answer:

Let A (2a, 4a)

     B(2a, 6a)

    C (2a + sqrt (3a), 5a)

Side AC:

\sqrt{(2a+\sqrt{3a}-2a)^2+(5a-4a)^2 }=\sqrt{3a+a^2}

Side BC:

\sqrt{(2a+\sqrt{3a}-2a)^2+(5a-6a)^2 }=\sqrt{3a+a^2}

Hence AC = BC

It is an isoceles triangle.

Side AB:

\sqrt{(2a-2a)^2+(6a-4a)^2 }=\sqrt{2a^2}=2a

It proves that the triangle is NOT an equilateral triangle.

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Parallelogram abcd has verticals at A(0,0), B(3,6), C(5,5) and D(2,-1) which conclusion can be made ?
sertanlavr [38]

Answer:

A.

Step-by-step explanation:

when you plot the vertices;

Side AB is perpendicular to side BC

Side AB is parallel to side DC

Side AC is perpendicular to AB

Side AC is perpendicular to DC

Side AC is parallel to side BC

The conclusion made is that ABCD is a rectangle

8 0
3 years ago
(BRIANLEIST) HELP<br> True or False
viktelen [127]

Answer:

True

Step-by-step explanation:

5 0
3 years ago
Write an equation from for the amount of money that will be collected if boxes of chocolate bars are sold. Which is the independ
Georgia [21]
The equation would be:
m = 30b  where 'm' represents the amount of money and 'b' represents the number of boxes sold.

m is the dependent variable 
b is the independent variable
4 0
3 years ago
Theorem: the sum of any two even integers equals 4k for some integer k. "proof: suppose m and n are any two even integers. by de
icang [17]

Remark

The proof is only true if m and n are equal. Make it more general.

m = 2k

n = 2v

m + n = 2k + 2v = 2(k + v).

k and v can be equal but many times they are not. From that simple equation you cannot do anything for sure but divide by 2.

There are 4 combinations

m is divisible by 4 and n is not. The result will not be divisible by 4.

m is not divisible by 4 but n is. The result will not be divisible by 4.

But are divisible by 4 then the sum will be as well. Here's the really odd result

If both are even and not divisible by 4 then their sum is divisible by 4

3 0
3 years ago
Your sister can get $30 per day, d, for selling clothes at the market. But she has to pay $60 at first for renting a stand. You
Alex

Answer:

6 days

Step-by-step explanation:

pay 60 = -60

Let d = the number of days

30d - 60 = sister

20d = me

Equation:

30d - 60 = 20d                    Move 30 to the other side

-30d          -30d

-60 = 20d - 30d                    Combine liked terms

-60 = -10d                                

-10     -10                                Divide

d = 6

5 0
3 years ago
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