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VikaD [51]
3 years ago
9

7 A triangle is right-angled if the sides are a = m2 − n2, b = 2mn and c = m2 + n2 where m and n are positive integers, and m &g

t; n.
Show that this is true by substituting into the equation c2 = a2 + b2.
Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
6 0
The general formula for the sides of right triangle is
a² + b² = c²

Subtitute the equation of a and b to the formula a² + b², evaluate if the answer will be the same as the equation of c²

a² + b²
= (m² - n²)² + (2mn)²
= (m² - n²)(m² - n²) + (2mn)(2mn)
= (m⁴ - 2m²n² + n⁴) + 4m²n²
= m⁴ + 2m²n² + n⁴

Factorize the result
m⁴ + 2m²n² + n⁴
= (m² + n²)(m² + n²)
= (m² + n²)²
= c²

It's proven by the formula that c² = (m² + n²)²
so the c will be m² + n²
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Helppppppppppppppp me plzzzzzzz
NeX [460]

Answer:

B = j + H

Step-by-step explanation:

Given:

j = - H + B

Solve the equation for B

j = - H + B

Add H to both sides of the equation

j + H = - H + B + H

j + H = B

B = j + H

8 0
3 years ago
SBC is an isosceles triangle with main vertex S.
stira [4]

Answer + Step-by-step explanation:

1) D be the symmetric of B with respect to C then CD = BC

A the symmetric of C with respect to B then AB = BC

We obtain :

CD = BC

AB = BC

Then AB = CD

2) m∠SBA = 180 - SBC = 180 - SCB = m∠SCD

3) we have :

BA = CD

BS = CS

m∠SBA = m∠SCD

Then

the triangles SBA and SCD are congruent

4)

the triangles SBA and SCD are congruent Then SA = SD

Therefore SAD is an isosceles triangle.

4 0
1 year ago
Express this number in scientific notation 763 thousandths
yan [13]
It would be 763 x 10^-4
3 0
3 years ago
What is 46/200 as a decimal
barxatty [35]
Simple way of finding the decimal value : -

=> 46/200
Divide numerator and denominator by 2
=23/100
As 100 is in denominator, shift decimal by 2, i.e
= 0.23

Answer = 0.23
6 0
3 years ago
A population, P(t) (in millions) in year t, increases exponentially. Suppose P(9)=16 and P(18)=24. a) Find a formula for the pop
jenyasd209 [6]

Answer:\frac{32}{3}\left ( 1.0460\right )^t

Step-by-step explanation:

Given

Population changes exponentially

P\left ( t\right )=ab^t

P\left ( 9\right )=16------1

P\left ( 9\right )=16=ab^8

P\left ( 18\right =24=ab^{18}-----2

divide 1 & 2 we get

\frac{24}{16}=\frac{b^{18}}{b^9}

\frac{3}{2}=b^9

Substitute b^9 in 1 we get

a=\frac{32}{3}

Thus P\left ( t\right )=\frac{32}{3}\left ( 1.0460\right )^t

8 0
3 years ago
Read 2 more answers
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