Rachel has a large pond on her property. The pond contains many different kinds of fish including bass.

Answer:

[tex](x-3)^2 =21[/tex]

Step-by-step explanation:

[tex]~~~~~~~x^2-6x-12=0\\\\\implies x^2 -6x +9-21=0 \\\\\implies x^2 -2\cdot x \cdot 3 +3^2=21\\\\\implies (x-3)^2 =21[/tex]

Check the picture below.

[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2-r^2)~~ \begin{cases} r=\stackrel{smaller}{radius}\\ R=\stackrel{larger}{radius}\\[-0.5em] \hrulefill\\ r=2\\ R=3 \end{cases}\implies \begin{array}{llll} A=\pi (3^2-2^2)\implies A=5\pi \\\\\\ A\approx 15.71 \end{array}[/tex]

Step-by-step explanation:

here you go hope it helps

Answer:

a = 9

b = 9√3

Step-by-step explanation:

We have

tan(2x) = sin(2x) / cos(2x)

tan(2x) = (2 sin(x) cos(x)) / (2 cos²(x) - 1)

Recall that

sin²(x) + cos²(x) = 1

and since sin(x) is negative, it follows that

sin(x) = - √(1 - (2/3)²) = -√5/3

Then

tan(2x) = (2 (-√5/3) (2/3)) / (2 (2/3)² - 1) = 4√5

Answer:

X = 3

Step-by-step explanation:

math

Answer:

4 14/27

Step-by-step explanation:

The first five terms

6

-6/3

6/9

-6/27

+6/81

The first thing to do is change all the fractions denominators to 81.

Sum = 6*81/81 - 6(27)/81 + 6*9/81 - 6*3/81 + 6/81

Now add

Sum = 366/81

Sum = 4 14/27

Sum = 4.5185

Note the first term. It has been multiplied by 6*81/81. The 81 over 81 does not change the value of anything 6 * 81/81 is still 6. It just makes it easier to combine with the other members of the series.

Answer:

x = 7.5 units

Step-by-step explanation:

10   *   .75    = 7.5

[tex]\textbf{(i)}\\\\y=f(x)= \dfrac{x}{4+x}\\\\\\\dfrac{dy}{dx}= \lim \limits_{h \to 0} \dfrac{f(x+h)-f(x)}{h}\\\\\\~~~~~=\lim \limits_{h \to 0}\dfrac{\dfrac{x+h}{4+x+h}-\dfrac{x}{4+x}}{h}\\\\\\~~~~~~=\lim \limits_{h \to 0}\dfrac{\tfrac{(x+h)(4+x)-x(4+x+h)}{(4+x+h)(4+x)}}{h}\\\\\\~~~~~~= \lim \limits_{ h \to 0} \dfrac{4x+x^2 +4h+hx -4x-x^2 -hx}{h(4+x+h)(4+x)}\\\\\\~~~~~~=\lim \limits_{ h \to 0}\dfrac{4h}{h(4+x+h)(4+x)}\\\\\\~~~~~~=\lim \limits_{h \to 0} \dfrac{4}{(4+x+h)(4+x)}\\[/tex]

       [tex]~~~~~~~~= \dfrac{ 4}{(4+x+0)(4+x)}\\\\\\~~~~~~~~= \dfrac{4}{(4+x)^2}[/tex]

[tex]\textbf{(ii)}\\\\\text{Given that,}~ y = f(x) = \sin 2x\\\\\\\dfrac{dy}{dx} = \lim \limits_{h \to 0} \dfrac{f(x+h) - f(x) }{h}\\\\\\~~~~~~=\lim \limits_{h \to 0} \dfrac{\sin(2x+2h)-\sin 2x}{h}\\\\\\~~~~~~=\lim \limits_{h \to 0} \dfrac{2 \sin \left( \dfrac{2x +2h -2x}{2} \right) \cos \left(\dfrac{2x+2h+2x}{2} \right)}{h}\\\\\\~~~~~~=\lim \limits_{h \to 0} \dfrac{2 \sin \left( \dfrac {2h}2 \right) \cos \left(\dfrac{ 4x+2h} 2\right)}{h}\\\\\\[/tex]

    [tex]~~~~~~=\lim \limits_{h \to 0} \dfrac{2 \sin h \cdot \cos \left[ \dfrac{2(2x+h)}{2}\right] }{h}\\\\\\~~~~~~=\lim \limits_{h \to 0} \dfrac{2 \sin h \cdot \cos(2x+h) }{h}\\\\\\~~~~~~=2\left(\lim \limits_{h \to 0} \dfrac{\sin h}{ h} \right) \cdot \lim \limits_{h \to 0} \cos (2x+h)\\\\\\~~~~~~=2\cdot 1 \cdot \cos(2x+ 0)\\\\\\~~~~~~=2 \cos 2x[/tex]

Answer:

A = 20 percent

B = 41 percent

Step-by-step explanation:

simply use 300 as your denominator

60/300 = 20

123 / 300 = 41

Answer:

I got 58.5

I multiplied 3x9 to get 27

then 3x6 to get 18

then 3x9/2 to get 13.5 and added them all together.

Answer:

3000 square inches.

Step-by-step explanation:

First, scale this one up. Multiply each by 2. consider area of a trapezoid. A = 1/2 (b1 + b2) h. This will be 1/2 (20 + 30) * 20, so you'll get 500 square in. Then, multiply by 6 since Buffy is making 6 of them. 500 * 6 = 3000 square inches.

Answer:

(3x + 2)(-x^3 - 3) =

3x(-x^3 - 3) + 2(-x^3 - 3) =

-3x^4 - 2x^3 - 9x - 6 <== result of multiplying (3x+2)(-x^3-3)

now multiply that by (3+x)...

(3+x)(-3x^4 - 2x^3 - 9x - 6) =

3(-3x^4 - 2x^3 - 9x - 6) + x(-3x^4 - 2x^3 - 9x - 6) =

-9x^4 -6x^3 - 27x - 18 - 3x^5 - 2x^4 - 9x^2 - 6x =

-3x^5 - 11x^4 - 6x^3 - 9x^2 - 33x - 18 <== result of multiplying by (3 + x)

the coefficient of x^4 = -11 <==

Step-by-step explanation:

Answer:

(3x + 2)(-x^3 - 3) =

3x(-x^3 - 3) + 2(-x^3 - 3) =

-3x^4 - 2x^3 - 9x - 6 <== result of multiplying (3x+2)(-x^3-3)

now multiply that by (3+x)...

(3+x)(-3x^4 - 2x^3 - 9x - 6) =

3(-3x^4 - 2x^3 - 9x - 6) + x(-3x^4 - 2x^3 - 9x - 6) =

-9x^4 -6x^3 - 27x - 18 - 3x^5 - 2x^4 - 9x^2 - 6x =

-3x^5 - 11x^4 - 6x^3 - 9x^2 - 33x - 18 <== result of multiplying by (3 + x)

the coefficient of x^4 = -11 <==

Step-by-step explanation:

The x intercept is lies at the midpoint of (-6 and -4

so

And it's translation of logx

translated equation

Now the vertical asymptote is at

Option A

Answer:

The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6

Step-by-step explanation:

From inspection of the graph:

x-intercept is where the curve intercepts the x-axis → x = -5

y-intercept is where the curve intercepts the y-axis → y ≈ 0.75

An asymptote is a horizontal or vertical line which the curve gets infinitely close to, but never touches.

From the portion of the curve in the graph, it appears that the curve gets very close to but never touches:

(However, without seeing a large portion of the graph, we cannot be sure, particularly for the horizontal asymptote).

Therefore, from the given solution options:

The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6

Answer:

Option 4

Step-by-step explanation:

Answer:

length ≈ 0.599 feet

Step-by-step explanation:

volume = length³

0.215ft³ = length³

cube root both sides to isolate the length

∛(0.215ft³) = length

length ≈ 0.599 feet

Answer:

but how do you want it done?

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

sec(60) = 32 /x

2 = 32/x

x2 =32

x = 16

Let's see

[tex]\\ \rm\Rrightarrow \dfrac{sin^2x+cos^x}{sinx}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{sinx}[/tex]

[tex]\\ \rm\Rrightarrow cosecx[/tex]

Answer:

cosec x

(or csc x)

Step-by-step explanation:

Trig Identities

[tex]\sf \sin^2 x + \cos^2 x=1[/tex]

[tex]\sf \dfrac{1}{\sin x}=cosec\: x[/tex]

Therefore,

[tex]\begin{aligned}\implies \sf \dfrac{\sin^2x + \cos^2x}{\sin x} &= \sf\dfrac{1}{\sin x}\\\\ & = \sf cosec\:x \end{aligned}[/tex]

The graph which correctly shows the point A as the sum of the complex numbers z₁ and z₂ is graph number 4.

A complex number is the combination of real and imaginary number. In a complex number, real part and imaginary part of the number are written together. For example,

a+bi

Here, (a) is the real part while (b) is the imaginary part.

To add the two complex number on the graph, the addition as transition method is used.

In this one complex number is translated to the tip of the other graph. The resultant of addition is equal to the distance between them.

On the graph 4, the transition method of addition is applied.Thus, the graph which correctly shows the point A as the sum of the complex numbers z₁ and z₂ is graph number 4.

Learn more about the complex number here;

https://brainly.com/question/2218826

#SPJ1

Answer:

4.4 inches

Step-by-step explanation:

Here, we are interested in calculating the value of x.

Mathematically, a line that comes from the center of the circle and extends to a chord, divides the chord into two equal parts.

This means what we have is a right angled triangle with the radius being the hypotenuse, the half of the length of the chord as the other side of the triangle.

3.7 is half the length of the chord i.e 7.4/2

Thus;

using Pythagoras’ theorem

x^2 = 2.4^2 + 3.7^2

Pythagoras’ posited that the square of the hypotenuse is equal to the sum of the squares of the other two sides of the triangle.

Thus;

x^2 =5.76 + 13.69

x^2 = 19.45

x = √(19.45)

x = 4.41 inches which is 4.4 inches to the nearest tenth

Answer:

Central angle = 31 / 4 radians

=

Length of the arc = (3 1 / 4) (radius) = 45 in

=

=> radius = 45 in * 4 / (31) = 45 * 4 / (3 * 3.14) in

=

radius = 19.1 in

=

Answer: 19.1 in

Step-by-step explanation:

Correct me if I'm wrong

Answer:

28, 50, 51, 18, 31, 34, 56, 39, 60

Step-by-step explanation:

big math

Answer:

266.9 feet

thats the answer

sana makatulong poww huhu

Answer:

the 4th box is divided by 2. sorry but don't know the others

Step-by-step explanation:

1)

|-6-2|=|-8|=8

2)

G and I

3)

|-6+2|= |-4|=4

the point that is 4 units away from H and K is I

I=-2

Answer:

Check explanation below!

Step-by-step explanation:

» Solving

Step 1: Subtract 4x from both sides.

Step 2: Divide both sides by -5.

Answer:

3/5 = 0.6

2/3 = 0.6 (recurring)

0.6 x 0.6

= 0.36

Answer:

[tex] \dfrac{2}{5} [/tex]

Step-by-step explanation:

[tex]\dfrac{3}{5} \times \dfrac{2}{3} = \dfrac{3 \times 2}{5 \times 3} = \dfrac{3 \times 2}{3 \times 5} = \dfrac{3}{3} \times \dfrac{2}{5} = 1 \times \dfrac{2}{5} = \dfrac{2}{5}[/tex]

Answer:

23456789-123456789

Step-by-step explanation:

es la cuadricula

Answer:

just start at like 220 i am pretty sure

Step-by-step explanation:

Answer:

Step-by-step explanation:

4 * 3 = 12

4 * -2 = -8

12 * -8 = -96

= -90