Which of the following functions best represents the graph?

f(x) = (x + 3)(x − 3)(x − 9)
f(x) = (x + 3)(x − 3)(x + 9)
f(x) = (x + 3)(x − 3)(x − 1)
f(x) = (x + 3)(x − 3)(x + 1)

Recall some identities:

sin²(x) + cos²(x) = 1

cos(2x) = cos²(x) - sin²(x)

and from the first identity, you can establish that

cos(2x) = 2 cos²(x) - 1

So, rewrite the integrand as much as possible in terms of cos(x) :

[tex]\sin^3(x) \cos(2x) = \sin(x) \sin^2(x) (\cos^2(x)-\sin^2(x)) \\\\ \sin^3(x) \cos(2x) = \sin(x) (1-\cos^2(x)) (2\cos^2(x) - 1)[/tex]

Then in the integral, substitute u = cos(x) and du = -sin(x) dx. With some rewriting, you end up with

[tex]\displaystyle \int_1^2 \sin^3(x) \cos(2x) \,\mathrm dx = -\int_{x=1}^{x=2} (1-\cos^2(x))(2\cos^2(x)-1) (-\sin(x)\,\mathrm dx) \\\\ = -\int_{u=\cos(1)}^{u=\cos(2)} (1-u^2)(2u^2-1)\,\mathrm du \\\\ = \int_{\cos(1)}^{\cos(2)} (1-3u^2+2u^4) \,\mathrm du \\\\ = \left(u-u^3+\frac25u^5\right)\bigg|_{\cos(1)}^{\cos(2)} \\\\ = \left(\cos(2)-\cos^3(2)+\frac25\cos^5(2)\right) - \left(\cos(1)-\cos^3(1)+\frac25\cos^5(1)\right) \\\\ = \boxed{\cos(2) - \cos^3(2) + \frac 25 \cos^5(2) - \cos(1) + \cos^3(1) - \frac25 \cos^5(1)}[/tex]

Answer:

The answer above me is correct!

Step-by-step explanation:

Give them BRAINLIEST! have a good day<3 :)

Answer:

610023626728387383838

Answer:

8x-6=14

Step-by-step explanation:

Whenever you see less next to a number, you know it's gonna be -6. If it said 6 minus 8x though, then you would do 6-8x etc. Hope this helped.

Answer:

-21b + 180 / 5

Step-by-step explanation:

Hey there!

b^3 - 21/5b + 9

= 3^3 - 21/5(3) + 9

= 27 - 63/5 + 9

= 72/5 + 9

= 117/5

Answer: 117/5

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

The figure is divided into a rectangle and a right-triangle.

The area of the figure is the sum of the individual areas of the rectangle and triangle

Area of rectangle = Length x Width = 10 ft x 8 ft = 80 ft²

Area of triangle = 1/2 x Base X Height = 1/2 x 6 ft x 8 ft =24ft²

Hence, the area of the figure is:

80 ft²+ 24ft² = 104 ft²

Answer:

104 ft^2

Step-by-step explanation:

The figure consist a rectangle and a triangle

to calculate triangle's area we multiply height and base then divide it  by two

the height of the triangle is 8 ft (the given is a special right triangle)

8*6/2 = 24 ft^2

to calculate the area of the rectangle we multiply width and length

8*10 = 80 ft^2 the total area of the figure is :

24 + 80 = 104 ft^2

Answer:

8/5 = x

Step-by-step explanation:

6 = 5x - 2

~Add 2 to both sides

8 = 5x

~Divide 5 to both sides

8/5 = x

Best of Luck!

Answer:

[tex]2 {b}^{2} - 5b - 63[/tex]

Step-by-step explanation:

[tex](b - 7) \times (2b + 9)[/tex]

[tex]b \times 2b + 9b - 7 \times 2b - 7 \times 9[/tex]

[tex]2 {b}^{2} + 9b - 14b - 63[/tex]

[tex]2 {b}^{2} - 5b - 63[/tex]

Answer:

the cost of the bench is $806

Step-by-step explanation:

853 minus 47 is 806

[tex]\\ \sf\longmapsto 8\dfrac{1}{2}\div \left(4\dfrac{4}{5}-7\dfrac{7}{10}\right)[/tex]

[tex]\\ \sf\longmapsto \dfrac{17}{2}\div \left(\dfrac{24}{5}-\dfrac{77}{10}\right)[/tex]

[tex]\\ \sf\longmapsto \dfrac{17}{2}\div\left(\dfrac{48-77}{10}\right)[/tex]

[tex]\\ \sf\longmapsto \dfrac{17}{2}\div \left(\dfrac{29}{10}\right)[/tex]

[tex]\\ \sf\longmapsto \dfrac{17}{2}\times \dfrac{10}{29}[/tex]

[tex]\\ \sf\longmapsto \dfrac{17(10)}{2(29)}[/tex]

[tex]\\ \sf\longmapsto \dfrac{170}{58}[/tex]

[tex]\\ \sf\longmapsto \dfrac{85}{29}[/tex]

[tex]\\ \sf\longmapsto 2\dfrac{27}{29}[/tex]

Answer:

Step-by-step explanation:

The positive difference is the result of subtraction of the smaller number from the greater number.

The positive difference of 4 4/5 and 7 7/10 is:

Now division:

Answer:

use cymath

Step-by-step explanation:

Answer:

17 1/2

Step-by-step explanation:

19+7÷2-5

Solve using PEMDAS

Divide first

19 + 7/2 -5

Then add and subtract from left to right

Getting a common denominator

38/2 + 7/2 - 10/2

45/2 - 10/2

35/2

17 1/2

Step-by-step explanation:

[tex]4x - 2 = 18x + 5[/tex]

Collect like terms and simplify

[tex] - 2 - 5 = 18x - 4x \\ - 7 = 14x[/tex]

Divide both sides of the equation by 14

[tex] \frac{ - 7}{14} = \frac{14x}{14} \\ - \frac{1}{2} = x[/tex]

Answer:

x = -1/2

Step-by-step explanation:

4x-2=18x+5

-2-5=18x-4x

-7=14x

-7/14=14/14x

-1/2=x

Answer:

Sorry about that, I did not see the decimal. As liamly said, it is positive but is not a natural number because of the decimal.

Step-by-step explanation:

Answer:

3.16 miles

Step-by-step explanation:

Hi there!

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

We're given that the campsite is located at (1,7) and the checkpoint station is located at (4,6). We must calculate the distance between them. Plug these points into the formula:

[tex]d=\sqrt{(x_2-1)^2+(y_2-7)^2}\\d=\sqrt{(4-1)^2+(6-7)^2}\\d=\sqrt{(3)^2+(-1)^2}\\d=\sqrt{9+1}\\d=\sqrt{10}\\d\approx3.16[/tex]

Therefore, the distance between the campsite and the checkpoint is 3.16 miles when rounded to the nearest hundredth.

I hope this helps!

Answer:

This is 3.747*11/sqrt(5)=18.4

the interval is (49.9,86.7), the SE added to and subtracted from the mean.

It is B

                          Thank You

Answer:

[tex]243 {x}^{2} {y}^{5} [/tex]

Step-by-step explanation:

[tex] \frac{(3xy {)}^{5} }{ {x}^{3} } [/tex]

[tex] \frac{243 {x}^{5} {y}^{5} }{ {x}^{3} } [/tex]

simplify:

[tex]243 {x}^{2} {y}^{5} [/tex] ✅

Answer:

Step-by-step explanation:

The question is not totally clear. I will assume that the spinner has 2 colors, red and blue.

Your chances of rolling a 3 are 1 in 6 = 1/6

Your chance of getting blue is 1/2

Your chances are 1/2 * 1/6 = 1/12

As a decimal that is 0.0833333

As a % it is 8.3333 %

Answer:

x=10

Step-by-step explanation:

10 a 8 son dos, entonces 14 ax es 4

Answer:

La explicación sería:

//////////////////////////

=> 9 * 2 + 4/2 = 20

=> 18 +2 =20

=> 20 =20

//////////////////////////

=> 5*2 + 8/2 = 14

=> 10 +4 =14

=> 14 =14

//////////////////////////

=> 3*2 + 10/2 = x

=> 6 + 5 = x

=> 11 = x

General Arithmetic Terms

[tex] \displaystyle \large{a_n = a_1 + (n - 1)d}[/tex]

We want to find a8; we know:

Substitute in the formula.

[tex] \displaystyle \large{a_n = 9 + (n - 1)4} \\ \displaystyle \large{a_n = 9 + 4n - 4} \\ \displaystyle \large{a_n = 4n + 5}[/tex]

To find a8, substitute n = 8

[tex] \displaystyle \large{a_8= 4(8) + 5} \\ \displaystyle \large{a_8= 32 + 5} \\ \displaystyle \large{a_8= 37}[/tex]

Hence, the 8th term of sequence is 37

Answer:

64

Step-by-step explanation:

Since each student must get the same amount of chips and water, the ratio of the number of chips to water received by each student is 1:1.

Hence, a maximum of 64 students can be invited to the party, as the bags of chips is lower than that of the number of bottles of water, and we take it as a 64.

Answer:

3.   15

6.   4

Step-by-step explanation:

Put  3 instead of x

3.    5x

     = 5 × 3

    = 15

6.   12 ÷ x

     = 12 ÷ 3

     = 4

Answer:

When X is 3 it will be

5(3)=15

Then for the second one it will be 12/3

The answer is 4

Hope I helped

Answer:

135

Step-by-step explanation:

250 x 54%=135

9514 1404 393

Answer:

  (c)  -0.5

Step-by-step explanation:

Starting from standard form ...

  ax +by = c

and solving for y, we get the slope-intercept form ...

  y = (-a/b)x +c/b

The coefficient of x is the slope: -a/b.

For your equation x+2y=16, the slope is -1/2 = -0.5.

Answer:

188 units cubed

Step-by-step explanation:

The value of the required expression (x- 3 ) using the given equation -5(3x - 9) = -15 is equal to 1.

Let's solve for the value of "x" in the given equation:

-5(3x - 9) = -15

First, distribute the -5 on the left side of the equation:

-15x + 45 = -15

Now, subtract 45 from both sides to isolate the term with "x":

-15x = -60

Divide both sides by -15 to solve for "x":

x = 4

Now that we have the value of "x," we can find the value of (x - 3):

x - 3

= 4 - 3

= 1

Therefore, the value of (x - 3) is 1.

learn more about value here

brainly.com/question/29168716

#SPJ3

Answer:

[tex]\frac{49}{75}[/tex]

Step-by-step explanation:

y= [tex]\frac{11}{15}[/tex]-[tex]\frac{2}{25}[/tex]

y= [tex]\frac{49}{75}[/tex]

Answer:

49/75

Step-by-step explanation:

y + 2/25 = 11/15

now, we could do it like the other answer and do fraction arithmetic, or we try and multiply everything out to eliminate the fractions :

15y + 30/25 = 11

375y + 30 = 275

375y = 245

y = 245/375 = 49/75

the same result, of course, but a slightly different way to get there.

Answer:

0.189x1000=189

1.75x1000=1750

189÷1750 = 0.108

Answer:

[tex]volume \: of \: rectangular \: prism = base \: area \: \times height \\ \\ = length \times width \times height[/tex]