MATHEMATICS HIGH SCHOOL

Let be the integers a,b,c with a^2-4b=c^2

To be shown that the number a^2-2b can be written as a sum of 2 perfect squares.

Answers

Answer 1
Answer: a^2 - 4b = c^2 <=> a^2 - c^2 = 4b <=> ( a + c )( a - c ) = 4b, cu a, b, c nr. intregi ;
Avem doua posibilitati :
a) a = 2x si b = 2y;
Atunci ( a + c )( a - c ) = 4b <=> x^2 - y^2 = b;
Relatia  a^2 -2b devine 2x^2 +2y^2 = (√(2) x)^2 + (√(2) y)^2, adica suma a doua patrate perfecte ;

b) a = 2x + 1 si b = 2y + 1 ;
In mod analog. obtii ca x^2 - y^2 + x - y = b;
si, dupa ce prelucrezi, ai ca a^2 - 2b = [√(2) ( x + 1 / 2 )]^2 + []√(2) ( y + 1 / 2 )^2, adica, suma a doua patrate perfecte .

Bafta!
Answer 2
Answer: { a }^( 2 )-4b={ c }^( 2 )\n \n { a }^( 2 )-4b+2b={ c }^( 2 )+2b\n \n { a }^( 2 )-2b={ c }^( 2 )+{ \left( \sqrt { 2b } \right) }^( 2 )

b={ 2 }^( n )\n \n n>0

(n) is the set of odd natural numbers greater than 0.

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Evaluate (3+8i)(-2-i)​

Answers

Answer:

2 - 19i

Step-by-step explanation:

note that i² = - 1

given

(3 + 8i)(- 2 - i) ← expand using FOIL

= - 6 - 3i - 16i - 8i²

= - 6 - 3i - 16i - 8(- 1)

= - 6 - 3i - 16i + 8 ← collect like terms

= 2 - 19i

Mathematics fractions to lowest term 34 over 40

Answers

34 / 40

2 into 34 is 17, and 2 into 40 is 20.

34 / 20 = 17 / 20

No other number can go into 17 and 20

Answer = 17 / 20  to lowest term.

Solve for x in the equation x squared + 2 x + 1 = 17.x = negative 1 plus-or-minus StartRoot 15 EndRoot
x = negative 1 plus-or-minus StartRoot 17 EndRoot
x = negative 2 plus-or-minus 2 StartRoot 5 EndRoot
x = negative 1 plus-or-minus StartRoot 13 EndRoot

Answers

Answer:

Option B.

Step-by-step explanation:

The given equation is

x^2+2x+1=17

Subtract both sides by 17.

x^2+2x+1-17=17-17

x^2+2x-16=0          .... (1)

If a quadratic equation is ax^2+bx+c=0, then by quadratic formula

x=(-b\pm √(b^2-4ac))/(2a)

In equation (1), a=1, b=2 and c=-16. Using quadratic formula we get

x=(-(2)\pm √((2)^2-4(1)(-16)))/(2(1))

x=(-2\pm √(4+64))/(2)

x=(-2\pm √(68))/(2)

x=(-2\pm 2√(17))/(2)

Taking out common factors.

x=(2(-1\pm √(17)))/(2)

x=-1\pm √(17)

Therefore, the correct option is B.

Answer:

The answer to your question is the second option

Step-by-step explanation:

Process

1.- Write the equation

                                 x² + 2x + 1 = 17

Factor the first term

                                 (x + 1)² = 17

Get the square root

                                 \sqrt{(x+1)^(2) }  = √(17)

                                 (x + 1) = √(17)

Result

                                x₁ = - 1 + √(17)

                                 x₂ = -1  - √(17)                                

                               

                                 

A sine function can be used to model light waves. Green light has a wave length, or period of about 510 nm . which equation best models green light? a. y= sin pi/510 theta b. y= sin pi/255 theta c. y= sin 510/pi theta d. sin 255/pi theta

Answers

Answer:

y=\sin((\pi \theta)/(255))

B is correct.

Step-by-step explanation:

A sine function can be used to model light waves. Green light has a wave length, or period of about 510 nm .

Equation of sine wave:

y=\sin(ax)

As we know the period of sine function is 2π

Period of this function y=\sin(ax) is 2π/a

We are given the period of function is 510

Thus, 510=(2\pi)/(a)

Now we will solve for a

a=(2\pi)/(510)

a=(\pi)/(255)

Required equation: y=\sin((\pi \theta)/(255))

Hence, The equation for best models green light is y=\sin((\pi \theta)/(255))
A sine function can be used to model light waves. Green light has a wave length, or period of about 510 nm. The equation that best models green light is y= sin 510/pi theta. The answer is letter C.

Functions 1 and 2 are shown below:Function 1: f(x) = −3x2 + 2
A graph of a parabola with x intercepts of negative 0.5, 0 and 2, 0 and a vertex of 0.5, 4 is shown.

Which function has a larger maximum? Type your answer as 1 or 2.

Answers

Answer:

The function 2 has a larger maximum.

Step-by-step explanation:

The vertex form of the parabola is

f(x)=a(x-h)^2+k              .... (1)

Where, (h,k) is the vertex.

The given functions are

f(x)=-3x^2+2                 ..... (2)

Since the leading coefficient is negative, therefore it is a downward parabola. It means the vertex of the parabola is the maximum point.

On comparing (1) and (2), we get

h=0,k=2

Therefore the maximum value of the function is 2 at x=0.

The second function has x intercepts of (-0.5, 0) and (2, 0) and a vertex of (0.5, 4).

It is also a downward parabola because the parabola has two x-intercepts and the vertex lies above the x-axis.

Since the vertex is (0.5, 4), therefore the maximum value of the function is 4 at x=0.5.

Maximum(F_1)=2

Maximum(F_2)=4

Therefore function 2 has a larger maximum.

Answer:

the anwser is 2 guys. i got it correct

Convert 129/7 into a mixed number

Answers

18 and 3/7
Because i can write by phone. So just write 18 in the left side of 3/7
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