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2 years ago

(-x2y3)*(12xy3)(-2xy2)3

1 answer:

4 0

Assuming the numbers are exponents expect the coefficient of 2, top expression, -12x^3y^6, multiply bottom
and= 72x^4y^8

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Which statements about the ellipse are true? Check all that apply. The center is located at (2, - 1) . The major axis is 8 units

pshichka [43]

Answer:

The center is located at (2, –1).

The major axis is 8 units long.

The vertices are 4 units above and below the centre.

The foci are √7 units above and below the centre.

Step-by-step explanation:

Assume the ellipse looks like the one below.

The properties of a vertical ellipse are

$\textbf{Vertical ellipse}\\\dfrac{ (x - h)^{2} }{b^{2}} + \dfrac{(y - k)^{2}}{a^{2}} = 1\begin{cases}\text{Centre} = (h,k)\\\text{Dist. between vertices} = 2a\\\text{Vertices} = (h, k\pm a)\\\text{Dist. between covertices} = 2b\\ \text{Covertices}= (h\pm b, k)\\c = \sqrt{a^{2} - b^{2}}\\\text{Dist. of foci from centre} = c\\\text{Foci} = (h, k\pm c)\\\end{cases}$

A. Centre

TRUE. The centre is at (2,-1).

B. Major axis

TRUE

Length of major axis = 3 - (-5) = 3 + 5 = 8

C. Minor axis

False

Length of minor axis = 5 - (-1) = 5 + 1 = 6

D. Vertices

TRUE

Distance between vertices = 8 = 2a

a - 8/2 = 4

Vertices at (h, k ± a) = (2, -1 ± 4)

E. Foci

TRUE

c² = a² - b² = 4² - 3² = 16 - 9 = 7

c = √7

The foci are √7 above and below the centre.

F. Foci

False.

The foci are on a vertical line.

5 0

3 years ago

The deer population of a certain area is modeled by the formula: P=578e^0.045t where t is measured in years. In approximately ho

STatiana [176]

Answer:

36.6 years

Step-by-step explanation:

Here, we are to find the number of years it will take for the population of deers to reach 3,000

What to do here is simply substitute the value of 3,000 for P and use it to find t

3000 = 578e^0.045t

Divide through by 578

5.1903 = e^0.045t

Take the ln (natural logarithm of both sides)

Recall ln e = 1

ln 5.1903 = ln e^0.045t

ln 5.1903 = 0.045t

0.045t = 1.6468

t = 1.6468/0.045

t = 36.595 years which is 36.6 years

5 0

3 years ago

You charge $2

nika2105 [10]

When you are painting, tiling, wallpapering or doing anything that involves the region inside a figure, you are dealing with the area of the figure.To calculate the area of a triangle, you can use the formula A = 1/2 base*height. This tells you how many square units it takes to cover the region. Once you know the number of square units, you charge $2 for each square unit, so just multiply, and you've got your answer. So A = 1/2 *4*6 = 12 square units and you'll charge 2*12 = $24 for the job.<span>
</span>

7 0

2 years ago

A pool measuring 8 meters by 26 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the poo

Ainat [17]

Let the width path be x.
Length of the outer rectangle = 26 + 2x.
Width of the outer rectangle = 8 +2x.

Combined Area = (2x + 26)*(2x + 8) = 1008

2x*(2x + 8) + 26*(2x + 8 ) = 1008

4x² + 16x + 52x + 208 = 1008

4x² + 68x + 208 - 1008 = 0
4x² + 68x - 800 = 0. Divide through by 4.
x² + 17x - 200 = 0 . This is a quadratic equation.

Multiply first and last coefficients: 1*-200 = -200

We look for two numbers that multiply to give -200, and add to give +17

Those two numbers are 25 and -8.

Check: 25*-8 = -200 25 + -8 = 17

We replace the middle term of +17x in the quadratic expression with 25x -8x

x² +17x - 200 = 0

x² + 25x - 8x - 200 = 0

x(x + 25) - 8(x + 25) = 0

(x+25)(x -8) = 0

x + 25 = 0 or x - 8 = 0

x = 0 -25 x = 0 + 8

x = -25 x = 8

The width of the path can not be negative.

The only valid solution is x = 8.

The width of the path is 8 meters.

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2 years ago

311/500 write each fraction or mixed numbers as a decimals

Juliette [100K]

0.622 in decimal form

4 0

2 years ago

(-x2y3)*(12xy3)(-2xy2)3​

(-x2y3)*(12xy3)(-2xy2)3