How to factor a quadratic equation y=-2x^2+8x-6

Answers

Answer 1

Answer: first factor out that -2
y=-2(x^2-4x+3)
what 2 number muitply to 3 and add to -4
-1 and -3
y=-2(x-3)(x-1)

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If x = − 8 and y = 2, evaluate the following expressions: (4y)² −(2x)² =

Answers

Answer:

-192

Step-by-step explanation:

x = -8

y = 2

(4y)² −(2x)² =

(4(2))² −(2(-8)² =

(8)² − (-16)² =

64 − 256 = -192

Kyle is pulled back on a swing so that the rope forms an angle of 30° with the vertical. The distance from the top of the swing set directly to the ground is 12 feet. Find Kyle’s height off the ground, x, when he is in the pulled-back position. Round the answer to the nearest hundredth.

Answers

When Kyle is in the pulled-back position with the rope forming a 30° angle with the vertical, his height off the ground is 6 feet.

To find Kyle's height off the ground, x, when he is in the pulled-back position, we can use trigonometry.

First, let's draw a diagram to visualize the situation.

The swing set is represented by a vertical line, and the rope forms an angle of 30° with the vertical.

The distance from the top of the swing set to the ground is given as 12 feet.

Now, we can use the concept of sine to solve for Kyle's height off the ground.

The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse.

In this case, the height off the ground is the opposite side, and the hypotenuse is the distance from the top of the swing set to the ground.

So, we can set up the following equation: sin(30°) = x / 12

To find x, we can multiply both sides of the equation by 12: 12 * sin(30°) = x

Using a calculator, we can find that sin(30°) is equal to 0.5: 12 * 0.5 = x Simplifying the equation: 6 = x

Therefore, Kyle's height off the ground, x, when he is in the pulled-back position, is 6 feet.

In summary, when Kyle is in the pulled-back position with the rope forming a 30° angle with the vertical, his height off the ground is 6 feet.

To know more about trigonometry here

brainly.com/question/24349828

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This would be 12 - 12*cos(30) = 12 - 6 $√(3)$ = 1.608 ft off the ground.

Which formula represents the hyperbola on the graph shown below? Note: Answer choices and graph attached below...

Answers

Answer:

Your answer choice is appropriate

Step-by-step explanation:

The orientation is vertical, so the parent function is

... y² - x² = 1

The vertical offset is -3 and the horizontal offset is positive, so the variables will be of the form (y+3)² and (x-something)². At this point, you're able to choose the correct answer.

The distance center to vertex is 13, so we know the y-term denominator is 13². We cannot tell from this graph what the x-term denominator should be, but all the answer choices are in agreement that it should be 81.

The appropriate choice is ...

... (y+3)²/169 - (x-2)²/81 = 1

Answer:

If you are looking for the answer to a graph that looks similar but slightly different, the answer is C.

This graph looks like the one above, but it is inverted, the top hyperbola reaches 15, and the bottom reaches 10. This is correct for A.P.E.X

Hope this helps I couldn't find it anywhere else on brainly.

Solve. Good luck! Please do not try to google this. $(x^2+x-2)/(6x^2-3x) = √(2x) + (3x^2)/(2)$

Answers

$(x^(2) + x - 2)/(6x^(2) - 3x) = √(2x) + (3x^(2))/(2)$
$(x^(2) + 2x - x - 2)/(3x(x) - 3x(1)) = (2√(2x))/(2) + (3x^(2))/(2)$
$(x(x) + x(2) - 1(x) - 1(2))/(3x(x - 1)) = (2√(2x) + 3x^(2))/(2)$
$(x(x + 2) - 1(x + 2))/(3x(2x - 1)) = (2√(2x) + 3x^(2))/(2)$
$((x - 1)(x + 2))/(3x(2x - 1)) = (2√(2x) + 3x^(2))/(2)$
$((x - 1)(x + 2))/(3x(2x - 1)) = (2√(2x) + 3x^(2))/(2)$
$3x(2x - 1)(2√(2x) + 3x^(2)) = 2(x + 2)(x - 1)$
$3x(2x(2√(2x) + 3x^(2)) - 1(2√(2x) + 3x^(2)) = 2(x(x - 1) + 2(x - 1))$
$3x(2x(2√(2x)) + 2x(3x^(2)) - 1(2√(2x)) - 1(3x^(2))) = 2(x(x) - x(1) + 2(x) - 2(1)$
$3x(4x√(2x) + 6x^(3) - 2√(2x) - 3x^(2)) = 2(x^(2) - x + 2x - 2)$
$3x(4x√(2x) - 2√(2x) + 6x^(3) - 3x^(2)) = 2(x^(2) + x - 2)$
$3x(4x√(2x)) - 3x(2√(2x)) + 3x(6x^(3)) - 3x(3x^(2)) = 2(x^(2)) + 2(x) - 2(2)$
$12x^(2)√(2x) - 6x√(2x) + 18x^(4) - 9x^(3) = 2x^(2) + 2x - 4$
$12x^(2)√(2x) - 6x√(2x) = -18x^(4) + 9x^(3) + 2x^(2) + 2x - 4$
$6x√(2x)(2x) - 6x√(2x)(1) = -9x^(3)(2x) - 9x^(3)(-1) + 2(x^(2)) + 2(x) - 2(2)$
$6x√(2x)(2x - 1) = -9x^(3)(2x - 1) + 2(x^(2) + x - 2)$

Final answer:

To solve the given equation, first simplify both sides. Factor the numerator and denominator on the left side, then solve the quadratic equation obtained.

Explanation:

To solve the given equation:

$(x^2+x-2)/(6x^2-3x) = √(2x) + (3x^2)/(2)$

First, we need to simplify both sides of the equation. By factoring the numerator and denominator of the left side, we get:

x+22x.

Next, we can simplify the equation further by multiplying both sides by 2x. Finally, we solve the quadratic equation obtained by moving all terms to one side:

2x+4.

Therefore, the solution to the given equation is x = -2.