9sin(Θ)-7=0. Solve the trigonometric equation

The two stem plots (with and without splitting the leaves) are plotted below using the data given in the attached picture :

The stem and leaf plots are given below:

Rounding the data to the nearest 10;

The values obtained are :

630, 670, 740, 650, 710, 740, 720, 700, 650, 600, 780, 780, 790, 810, 830, 860, 860, 900, 810, 790, 790, 960, 870

Ordering the data allows for easier generation of the plot.

Ordered data : 600, 630, 650, 650, 670, 700, 710, 720, 740, 740, 780, 780, 790, 790, 790, 810, 810, 830, 860, 860, 870, 900, 960

The stem plot without splitting :

STEM __ LEAF

6 ___ 00, 30, 50, 50, 70

7 ___ 00, 10, 20, 40, 40, 80, 80, 90, 90, 90

8 ___ 10, 10, 30, 60, 60, 70

9 ___ 00, 60

KEY :  6 | 00 = 600

The stem plot WITH splitting :

STEM __ LEAF

6 ___ 00, 30

6 ___ 50, 50, 70

7 ___ 00, 10, 20, 40, 40

7 ___ 80, 80, 90, 90, 90

8 ___ 10, 10, 30

8 ___ 60, 60, 70

9 ___ 00

9 ___ 60

KEY :  6 | 00 = 600

The stem plot with splitting gives a cleaner and more arranged output of the data as the values aren't congested on a single line.

Learn more on stem and leaf plot : https://brainly.com/question/12857419?

To solve this question, we use the factor theorem, and using it, the polynomial function is:

[tex]f(x) = x^3 - 2x^2 - 3x + 6[/tex]

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The factor theorem means that if k is a root of f(x), f(k) = 0.

Thus, applying the factor theorem for this question, we have to choose the function for which: [tex]f(2) = 0, f(\sqrt{3}) = 0, f(-\sqrt{3}) = 0[/tex]

------------------------------

Function 1:

[tex]f(x) = x^3 - 2x^2 - 3x + 6[/tex]

Testing the values:

[tex]f(2) = 2^3 - 2(2)^2 - 3(2) + 6 = 8 - 8 - 6 + 6 = 0[/tex]

[tex]f(\sqrt{3}) = \sqrt{3^3} - 2(\sqrt{3})^2 - 3\sqrt{3} + 6 = \sqrt{3^2\times3} - 6 - 3\sqrt{3} + 6 = 3\sqrt{3} - 3\sqrt{3} = 0[/tex]

[tex]f(-\sqrt{3}) = -\sqrt{3^3} - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 = -\sqrt{3^2\times3} - 6 + 3\sqrt{3} + 6 = -3\sqrt{3} + 3\sqrt{3} = 0[/tex]

Thus, since all three conditions are satisfied, [tex]f(x) = x^3 - 2x^2 - 3x + 6[/tex] is the polynomial function.

A similar question is given at https://brainly.com/question/11378552

9514 1404 393

Answer:

  r = 2.5

Step-by-step explanation:

The constant of proportionality can be found by solving the equation for r:

  r = y/x

Then any corresponding values of x and y can be used to find r:

  r = 25/10 = 2.5

The constant of proportionality is 2.5.

Answer:

False

Step-by-step explanation:

It can go in any direction

Answer:

False

Step-by-step explanation:

Rotations can be either clockwise or counterclockwise

Answer:

3y+13

Step-by-step explanation:

-3(y-5)+6y-2

Distribute

-3y +15 +6y-2

Combine like terms

-3y+6y  +15-2

3y            +13

[tex]\bf \large{\purple{ \implies}} \tt \: - 3(y - 5) \: + \: 6y \: - \: 2[/tex]

[tex]\bf \large{\purple{ \implies}} \tt \: - 3y \: + \: 15 \: + \: 6y \: - 2[/tex]

[tex]\bf \large{\purple{ \implies}} \tt \: - 3y \: + \: 6y \: + \: 15 \: - \: 2[/tex]

[tex]\bf \large{\purple{ \implies}} \tt \: 3y \: + \: 13[/tex]

Answer:

Slope is B. ¼

Step-by-step explanation:

Slope: is hypotenuse

[tex] = { \sf{ \frac{ \delta \: height}{ \delta \: base} }} \\ \\ { \sf{ = \frac{2.5}{10} }} \\ \\ = { \sf{ \frac{1}{4} }}[/tex]

Answer:

Bc is intersected by segment AD

Answer:

Bc is intersected by segment AD

Step-by-step explanation:

[tex]\\ \sf\longmapsto 5+n>2[/tex]

[tex]\\ \sf\longmapsto n>2-5[/tex]

[tex]\\ \sf\longmapsto n>-3[/tex]

Answer:

586 cm^3 and 486 in^2

Step-by-step explanation:

4) The volume of the triangular prims is (1/2)*(a*c*h) = 0.5*(8*9*16)=586 cm^3

5) Wrapping paper needed is equal to the surface area of the cube, 6s^2=486 in^2

Answer:

Step-by-step explanation:

Let the quadratic function be

y=a(x+4)²-1

∵(-7,8) lies on it.

8=a(-7+4)²-1

8+1=a(-3)²

9a=9

a=9/9=1

so quadratic function  is

f(x)=1(x+4)²-1

or

f(x)=x²+8x+16-1

so quadratic function is

f(x)=x²+8x+15

9514 1404 393

Answer:

  a) the degree of the polynomial

  b) count the x-intercepts, with attention to multiplicity

Step-by-step explanation:

The Fundamental Theorem of Algebra tells you the number of zeros of a polynomial is equal to the degree of the polynomial. That is, for some polynomial p(x), the number of solutions to p(x)=0 will be the degree of p.

__

On a graph, a real zero of the polynomial will be an x-intercept. The "multiplicity" of a zero is the degree of the factor giving rise to that zero. When the multiplicity is even, the graph does not cross the x-axis at the x-intercept. The greater the multiplicity, the "flatter" the graph is at the x-intercept.

If all solutions (zeros) are distinct, then the number of real solutions can be found by counting the number of x-intercepts of the graph.

_____

By way of illustration, the attached graph is of a 6th-degree polynomial with 6 real zeros. From left to right, they are -1 (multiplicity 1), 1 (multiplicity 2), 4 (multiplicity 3). The higher multiplicities are intended to show the flattening that occurs at the x-intercept, and the fact that the graph does not cross the x-axis where the multiplicity is even.

Answer:

cos F = adjacent/hypotenuse

= 15/28

Answer:

Each item could be included in a set or not included. That gives 2^5 = 32 ways to choose sets, including 1 set with no items, 5 sets of 1 item, 10 sets of 2 items, 10 sets of 3 items, 5 sets of 4 items, and 1 set of 5 items.

Answer:

Because it is not an equation.

Step-by-step explanation:

[tex] log(x) \times log(2) \\ = log(x + 2) [/tex]

Answer:

1,032,564 tickets

Step-by-step explanation:

Find how many tickets they sell in total by multiplying the capacity of the stadium by the number of games in the season:

86,047(12)

= 1,032,564

So, if every game sells out, 1,032,564 tickets will be sold.

(a) z = 3x ² - 4xy + 15y ²

has first-order partial derivatives

∂z/∂x = 6x - 4y

∂z/∂y = -4x + 30y

and thus second-order partial derivatives

∂²z/∂x ² = 6

∂²z/∂x∂y = -4

∂²z/∂y∂x = -4

∂²z/∂y ² = 30

where ∂²z/∂x∂y = ∂/∂x [∂z/∂y] and ∂²z/∂y∂x = ∂/∂y [∂z/∂x].

(b) z = 4x eʸ

∂z/∂x = 4eʸ

∂z/∂y = 4x eʸ

∂²z/∂x ² = 0

∂²z/∂x∂y = 4eʸ

∂²z/∂y∂x = 4eʸ

∂²z/∂y ² = 4x eʸ

(c) z = 6x ln(y)

∂z/∂x = 6 ln(y)

∂z/∂y = 6x/y

∂²z/∂x ² = 0

∂²z/∂x∂y = 6/y

∂²z/∂y∂x = 6/y

∂²z/∂y ² = -6x/y ²

Answer:

131.2 gallons

Step-by-step explanation:

1)16/5= 3.2 gallons - of water are lost in 1 hour;

2)3.2*41=131.2 gallons

Answer:

t=1, u=-2, w=-2

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

x<-3 means the values of x will be less than -3, do the dot will be blank and towards the left side of -3

Answer:

a. Less than $471

Step-by-step explanation:

The total price must be less than $578.10.

Let the price of the 4 tires = x.

He pays 10% tax on x. That means he pays x + 10%x = 1.1x including tax.

Then he pays the $60 fee.

He pays a total of 1.1x + 60

That must be less than $578.10

1.1x + 60 < 578.10

Subtract 60 rom both sides.

1.1x < 518.1

Divide both sides by 1.1

x < 471

Answer: a. Less than $471

Step-by-step explanation:

Set up f(x).

[tex] \sqrt[3]{11x - 3} = f(x)[/tex]

Replace f(x) with y

[tex] \sqrt[3]{11x - 3} = y[/tex]

Swap x and y

[tex] \sqrt[3]{11y - 3} = x[/tex]

Solve for y

Cube both sides

[tex]11y - 3 = {x}^{3} [/tex]

Add 3 to both sides

[tex]11y = {x}^{3} + 3[/tex]

Divide both sides by 11

[tex]y = \frac{x {}^{3} + 3 }{11} [/tex]

so

[tex]f {}^{ - 1} (x )= \frac{ {x}^{3} + 3}{11} [/tex]

What we need to memorize when finding the slope is this formula:

[tex] \displaystyle \large{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]

m here represents the slope. I hope this does not confuse you with line m.

The problem here is that we do not have any given points, but we have a way.

If we notice on the graph, the graph contains or passes through (2,-1) and (-2,1). We can use these points to find the slope. So let these be the following:

[tex] \displaystyle \large{(x_1,y_1) = (2 ,- 1)} \\ \displaystyle \large{(x_2,y_2) = ( - 2 ,1)} [/tex]

Then we substitute these points in the formula.

[tex] \displaystyle \large{m = \frac{ 1 - ( - 1)}{ - 2 - 2} }[/tex]

negative × negative = positive.

[tex] \displaystyle \large{m = \frac{ 1 + 1}{ - 2 - 2} } \\ \displaystyle \large{m = \frac{ 2}{ - 4} } \longrightarrow \boxed{m = - \frac{1}{2} }[/tex]

Since m represents the slope. Therefore, the slope of line m is -1/2

Answer:

10

Step-by-step explanation:

Applying the segment addition theorem, the value of x = 10

YZ = 60

The segment addition theorem states that if a point, C, lies between two endpoints of a segment, A and B, then: AC + CB = AB.

Given:

XY = 2x+1

YZ = 6x

XZ = 81

Thus:

XY + YZ = XZ (segment addition theorem)

2x + 1 + 6x = 81

Find x

8x = 81 - 1

8x = 80

x = 10

Find YZ:

YZ = 6x

Plug in the value of x

YZ = 6(10)

YZ = 60

Therefore, applying the segment addition theorem, the value of x = 10

YZ = 60

Learn more about the segment addition theorem on:

https://brainly.com/question/1397818

Answer:

x = 29

Step-by-step explanation:

The angles are corresponding angles and corresponding angles are equal when the lines are parallel

3x+17 = 4x-12

Subtract 3x from each side

3x+17-3x = 4x-12-3x

17 = x-12

Add 12 to each side

17+12 = x-12+12

29 =x

Answer:

D. 29

Step-by-step explanation:

If you plug in 29 in the missing values for L1 and L2, you get

L1 = 3(29) + 17 = 104

L2 = 4(29) - 12 = 104

I know I am correct because since both L1 and L2 are parallel and T in cutting them, I know that they are both going to be the same degrees, 104.

So, your answer would be D. 29

Hope the helps! :)

Answer:

the answer will be 3.........

Answer:

25

Step-by-step explanation:

I'm sorry but I rlly don't rember how I did it because I did this question on a quiz and the teacher said this was that answer but not how to get it.

Total number of possibilities is 10,000.

Step-by-step explanation:

Given:

Total number between (0-9) = 10 number

Frequency of unknown number = 4 times

Find:

Total number of possibilities

Computation:

Total number of possibilities when repetition is allowed;

Total number of possibilities when repetition is allowed = 10 × 10 × 10 × 10

Total number of possibilities when repetition is allowed = 10,000

Total number of possibilities when repetition is allowed = 10,000 times

Learn more:

https://brainly.com/question/10716370?referrer=searchResults

Given:

Overall number [tex]\bold{(0-9) = 10}[/tex]

Unknown source frequency [tex]= \bold{4\ times}[/tex]

Find:

The overall amount of opportunities=?

Calculation:

The total possible number for repeaters [tex]=\bold{ 10 \times 10 \times 10 \times 10}[/tex]

The total amount of repeat possibilities [tex]=\bold{ 10,000}[/tex]

Total amount of repeating options [tex]=\bold{ 10,000\ times}[/tex]

So, the "total number of possibilities is [tex]\bold{ 10,000}[/tex]"

Learn more:

brainly.com/question/17539761

9514 1404 393

Answer:

  6000 mL

Step-by-step explanation:

The prefix "milli-" is an SI standard prefix meaning 1/1000. So, 1 mL = (1/1000)L.

When doing dimension changes, you always want to use scale factors that have a value of 1, which is to say the numerator is equal to the denominator. For converting liters to milliliters, the scale factor you want will have mL in the numerator and L in the denominator:

  (1 mL)/(1/1000 L)   or   (1000 mL)/(1 L)

To do your conversion, multiply your liter volume by this factor.

  [tex](6\text{ L})\times\dfrac{1000\text{ mL}}{1\text{ L}}=\dfrac{6\times1000\text{ mL$\cdot$L}}{1\text{ L}}=6000\text{ mL}[/tex]

6 liters is 6000 milliliters.

__

You will notice that the dimensions "L" cancel, which is the point of the exercise.

_____

Additional comment

6 L is closer to 202.884 fluid ounces. The conversion factor is ...

  [tex]\dfrac{128\text{ fl oz}}{231\text{ in}^3}\times\dfrac{1\text{ in}^3}{(0.254\text{ dm})^3}\times\dfrac{1\text{ dm}^3}{1\text{ L}}=\dfrac{128\text{ fl oz}}{3.785411784\text{ L}}\quad\text{exactly}[/tex]

Answer:

y=-1/2x+3

Step-by-step explanation:

y=mx+c

5=-1/2*4+c

5=-2+c

c=5-2

c=3

y=-1/2x+3