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3 years ago

Solve the system of equations y=3x. y=x^2-4

Mathematics

1 answer:

aleksandr82 [10.1K]3 years ago

8 0

Answer:

(x, y) = (-1, -3) or (4, 12)

Step-by-step explanation:

A graphing calculator can show the solutions to this system.

You can equate expressions for y and solve for x.

3x = x^2 -4

x^2 -3x = 4 . . . . add 4-3x

x^2 -3x +2.25 = 6.25 . . . . complete the square by adding (-3/2)^2 where -3 is the coefficient of x.

(x -1.5)^2 = 2.5^2 . . . . . . rewrite as squares

x -1.5 = ±2.5 . . . . . . . . . . take the square root

x = 1.5 ± 2.5 = -1, +4

y = 3x = -3, +12, respectively

Solutions are ...

(x, y) = (-1, -3) . . . . and . . . . (4, 12)

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<h3>Answer:</h3>

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<h3>Solution:</h3>

We are given that:

Area of rectangle is 30√3570
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Hence, putting the values in the formula:

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$\implies\quad \sf{3\sqrt{250}\times w = 30\sqrt{3750} }$

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3 years ago

Find two numbers such that their product, sum and difference are in the ratio 5:4:1'

wel

Answer:

3 1/3 and 2

Step-by-step explanation:

Let the numbers be x and y and let z be the constant of proportion. Then

xy = 5z ...............(1)

x + y = 4z ...........(2)

x - y = z ..............(3) Adding (2) and (3)

2x = 5z

x = 5z/2 ................(4)

Substituting for x in equation 1:

5z/2 * y = 5z

y = (5z * 2) / 5z = 2.

Substituting for y in equations (2) and (3):

x + 2 = 4z

x - 2 = z Subtracting:

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z = 4/3.

Substituting for z in equation (4)

x = 5(4/3) /2

x = 20/6 = 10/3 = 3 1/3.

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Checking the results:

xy = 2 * 10/3 = 20/3 = 5 * 4/3 = 5z

x + y = 10/3 + 2 = 16/3 = 4 * 4/3 = 4z.

x - y = 10/3 - 2 = 4/3 = z.

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