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2 years ago

Is the origin a solution to the system graphed?

Mathematics

1 answer:

Neporo4naja [7]2 years ago

5 0

Answer:

Step-by-step explanation:

y < - 3x

y ≥ 2x + 2

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Find the value of the variable y, where the sum of the fraction 2/y-3 and 6/y+3 is equal to the quotient.

NISA [10]

Answer:

Here we need to solve:

$\frac{2}{y - 3} + \frac{6}{y + 3 } = \frac{\frac{2}{y-3}}{\frac{6}{y + 3} }$

The sum of the fractions is equal to the quotient between the fractions.

Notice that the two values:

y = 3

y = -3

make the denominator equal to zero, so those values are restricted.

We can simplify the right side to get:

$\frac{2}{y - 3} + \frac{6}{y + 3 } = \frac{\frac{2}{y-3}}{\frac{6}{y + 3} } = \frac{2*(y + 3)}{6*(y - 3)} = 3*\frac{y + 3}{y - 3}$

Now we can multiply both sides by (y - 3)

$(y - 3)*(\frac{2}{y - 3} + \frac{6}{y + 3 }) = 3*(y + 3)\\2 + 6*\frac{y -3}{y + 3} = 3*(y + 3)$

Now we can multiply both sides by (y + 3)

$(2 + 6*\frac{y -3}{y + 3})*(y + 3) = 3*(y + 3)*(y + 3)$

$2*(y + 3) + 6*(y - 3) = 3*(y + 3)*(y + 3)\\\\2*y + 6 + 6*y - 18 = 3*(y^2 + 2*y*3 + 9)\\\\8*y - 12 = 3*y^2 + 6*y + 33\\\\0 = 3*y^2 + 6*y + 33 - 8*y + 12\\\\0 = 3*y^2 - 2*y + 45$

First, let's see the determinant of that quadratic equation:

$D = (-2)^2 - 4*3*45 = -536$

We can see that it is negative, thus, there are no real solutions of the equation.

Thus, there is no value of y such that the origina equation is true,

6 0

3 years ago

Which of the following is a prime number between 40 and 50? A. 41 B. 45 C. 44 D. 49

Snowcat [4.5K]

Answer:

A.41

Step-by-step explanation:

7 0

3 years ago

I need some help Math

jenyasd209 [6]

I think it will be c

3 0

4 years ago

What is the equation of a line that is parallel to the line y = 2x+1 and passes

kondor19780726 [428]

Answer: It should be y=2x-2

Step-by-step explanation:

5 0

3 years ago

Two or more angles are supplementary if their sum is 180. An angle is twice the size of its supplement. Set up and solve an equa

vekshin1

Answer:

angle: 120°
its supplement: 60°

Step-by-step explanation:

Let "a" represent the measure of the angle. Then 180-a is the measure of its supplement. Your equation can be ...

a = 2(180-a) . . . an equation

a = 360 -2a . . . . eliminate parentheses

3a = 360 . . . . . . add 2a

a = 120 . . . . . . . . divide by 3 to find "an angle"

180-a = 60 . . . . . find "its supplement"

The measure of the angle is 120°, of its supplement, 60°.

8 0

4 years ago