Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. −2y2 + 6y = −2

Answers

Answer 1
Answer: -2y^2 + 6y + 2 = 0
a = -2, b = 6, c = 2
x = (- b + - sqrt(b^2-4ac))/(2a)
x=(-6+-sqrt(36-4*-2*2))/-4
x=(-6+-sqrt(36+16))/-4
x=(-6+-sqrt(52))/-4
x = (-6 +- 2sqrt13)/-4
x = (3 + - sqrt13)/2
Answer 2
Answer:

Answer:

-0.3 Or 3.3

Step-by-step explanation:

-2y^2 + 6y + 2 = 0

X = -6 + 7.21/-4 or -7 - 7.21/-4

X = -0.3 or X = 3.3


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Answers

Answer:

Step-by-step explanation:

There is no solution.

3(x+4)=3x+4

No matter what you use for x, it will not equal.

Answer:

There is no solution

Step-by-step explanation:

A swimming pool can be filled using either a pipe, a hose, or both. Using the pipe alone takes 12 hours. Using both it takes 8(4)/(7) hours. How long does it take using the hose alone?

Answers

(1)/(x)+(1)/(12)=(1)/(8(4)/(7))\n(1)/(x)=(1)/((60)/(7))-(1)/(12)\n(1)/(x)=(7)/(60)-(1)/(12)\n(1)/(x)=(7)/(60)-(5)/(60)\n(1)/(x)=(2)/(60)\n(1)/(x)=(1)/(30)\nx=30

30 hrs

Final answer:

The time it would take to fill the pool using the hose alone is 15 hours. This was calculated using the information given on the time it takes to fill the pool using the hose and the pipe together, and the time it takes to fill the pool using just the pipe, to find the individual rates of filling and then solve for the time for the hose alone.

Explanation:

The subject of this problem is rates, specifically the rate at which the pool is being filled with water. Let's denote the rate of the pool filling with the pipe as P, and the rate of the pool filling with the hose as H. We know that the pool fills in 12 hours with only P, so P = 1/12 pools/hour.

Additionally, we know that it takes 8 4/7 hours to fill the pool with both P and H. So, the rate of P + H = 1/(8 4/7) pools/hour, which simplifies to 7/60.

Given that we know P, we can solve for H by subtracting P from the combined rate. H = P + H - P = 7/60 - 1/12 = 1/15 pools/hour. Therefore, to fill the pool using the hose alone, it will take 1/H = 1/(1/15) = 15 hours.

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A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y equals negative 0.04x squared plus 8.3x plus 4.3, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from its starting point will the rocket land? Round your answer to the nearest hundredth meter. (1 point)
208.02 m
416.03 m
0.52 m
208.19 m

Answers

ok

y=-0.04x^2+8.3x+4.3
when the rocket reaches the ground (when height=0, ie when y=0), then the rocket will land, find the x coordinate

set y=0
0=-0.04x^2+8.3x+4.3
use quadratic formula
if you have ax^2+bx+c=0, then
x=\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}
a=-0.04
b=8.3
c=4.3
x=\frac{-8.3+/- \sqrt{8.3^(2)-4(-0.04)(8.3)} }{2(-0.04)}
x=208.017 or -0.516785
xrepresents horizontal distance
you cannot have a negative horizontal distance unless you fired and theh wind blew it backwards
therefor x=280.017 is the answer
208.02 m


if 9 to the power of x = 27, what is x.

Method as well plz!

Answers

9^x=27\n\n(3^2)^x=3^3\n\n3^(2\cdot x)=3^3\n\n3^(2x)=3^3\iff 2x=3\ \ \ /:2\Rightarrow x=1.5
You can use logarithms:

Log9(27) which will give you the value of x

X= 1.5

A particular computer takes 11 minutes to download a 44 minute TV show. How long will it take the computer to download a 1.5 hour movie?

Answers

44/11= 4
4 minutes of the movie are downloaded each minute.
1.5 hours= 90 min
90/4= 22.5 minutes
Divide 44 by 11 which equals 4Then 1.5 is 1 hour and 30 minutes so add 60 +30 Which equals 90Then multiply 90 ×4 = 360 minutes

Find the perimeter of a rectangle whose length is 3 square root 5 and width is 2 square root 7

Answers

The rectangle has a length of 3√5 and a width of 2√7. The perimeter is calculated as 23.9 approximately.

Use the concept of a rectangle defined as:

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

Given that,

Length of the rectangle: 3√5

Width of the rectangle: 2√7

To find the perimeter of a rectangle,

Use the formula P = 2(length + width).

In this case,

The length is 3√5 and the width is 2√7.

Applying the formula, we get:

P = 2(3√5 + 2√7)

To simplify this expression, distribute the 2:

P = 6√5 + 4√7

p ≈ 23.9

Hence,

The perimeter of the rectangle is approximately 23.9.

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Answer:

Step-by-step explanation:

Area=Length times width

A=3√(5)*2√(7)

A=6√(35)