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2 years ago

Find the quadratic function .. 3x2 - y2 = 9 x2 + 2y2 = 38

Mathematics

1 answer:

ruslelena [56]2 years ago

6 0

Answer:

Step-by-step explanation:

3x2 - y2 = 9.........(1)

x2 + 2y2 = 38......(2)

Let x^2 = a and y^2 = b

:- the two equations becomes

3a - b = 9..........(3)

a + 2b = 38.......(4)

Multiplying (4) by 3

3a + 6b = 114........(5)

Substracting (3) from (5)

3a - 3a + 6b - (-b) = 114 - 9

6b +b = 105

7b = 105

b = 105/7

b = 15

And 3a - b = 9 putting b = 15

3a - 15 = 9

3a = 15+9

3a = 24

a = 24/3

a = 8

And

x^2 = a

x^2 = 8

x = √8

x = √(4×2)

x = 2√2

Also y^2 = b

y^2 = 15

y = √15

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Need help. i dont understand this!!!

Ilia_Sergeevich [38]

By the quadratic formula, the solution set of the quadratic equation is formed by two real roots: x₁ = 0 and x₂ = - 12.

<h3>How to find the solution of quadratic equation</h3>

Herein we have a quadratic equation of the form a · m² + b · m + c = 0, whose solution set can be determined by the quadratic formula:

x = - [b / (2 · a)] ± [1 / (2 · a)] · √(b² - 4 · a · c) (1)

If we know that a = - 1, b = 12 and c = 0, then the solution set of the quadratic equation is:

x = - [12 / [2 · (- 1)]] ± [1 / [2 · (- 1)]] · √[12² - 4 · (- 1) · 0]

x = - 6 ± (1 / 2) · 12

x = - 6 ± 6

Then, by the quadratic formula, the solution set of the quadratic equation is formed by two real roots: x₁ = 0 and x₂ = - 12.

To learn more on quadratic equations: brainly.com/question/1863222

#SPJ1

7 0

1 year ago

<img src="https://tex.z-dn.net/?f=2x%20-%206%20%3D%205y%20-%203x" id="TexFormula1" title="2x - 6 = 5y - 3x" alt="2x - 6 = 5y - 3

Zigmanuir [339]

Answer:

( 2x - 3 ) / 5

Step-by-step explanation:

2x - 6 = 5y - 3

2x - 6 + 3 = 5y

2x - 3 = 5y

y = ( 2x - 3 ) / 5

6 0

2 years ago

Solve the system of equations. −4x+3y=−2 y=x−1 x- y-

Kobotan [32]

Answer: x= -1

y= -2

Step-by-step explanation:

-4x+3y= -2

y=x-1

-------------------

-4x+3(x-1)= -2

-4x+3x-3= -2

-x=1

x= -1

y=-1-1

y=-2

6 0

3 years ago

Read 2 more answers

A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. A previous study indicates that the propo

never [62]

Answer:

A sample of 997 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

A previous study indicates that the proportion of left-handed golfers is 8%.

This means that $\pi = 0.08$

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a p-value of $1 - \frac{0.02}{2} = 0.99$ , so $Z = 2.327$ .

How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%?

This is n for which M = 0.02. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.02 = 2.327\sqrt{\frac{0.08*0.92}{n}}$

$0.02\sqrt{n} = 2.327\sqrt{0.08*0.92}$

$\sqrt{n} = \frac{2.327\sqrt{0.08*0.92}}{0.02}$

$(\sqrt{n})^2 = (\frac{2.327\sqrt{0.08*0.92}}{0.02})^2$

$n = 996.3$

Rounding up:

A sample of 997 is needed.

3 0

3 years ago

In Jamie's drawer are 3 pairs of blue socks, 1 pair

Effectus [21]

Answer:

24%

Step-by-step explanation:

I think this is right. im sorry if its not but i went to a percent calculator and checked my answer. hope this helped :)

6 0

2 years ago