A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. Which rule could represent this dilation

Answer:

[tex]f(theta)=sin(theta) - cos(theta)[/tex] + C

This is my first time doing a double integral, so im only 90% sure in my answer

Step-by-step explanation:

You pretty much want to take the double integral of sinx + cosx

The anti-derivative of sinx = -cosx

The anti-derivative of cosx = sinx

So f' = -cosx + sinx

Now lets take the integral of f':

The anti-derivative of -cosx = sinx

The anti-derivative of sinx = -cosx

So, f(x) = sinx - cosx

============================================================

Work Shown:

I'll use x in place of theta since its easier to type on a keyboard.

f '' (x) = sin(x) + cos(x)

f ' (x) = -cos(x) + sin(x) + C ..... integrate both sides; dont forget the plus C

f ' (0) = 1

f ' (0) = -cos(0) + sin(0) + C

-cos(0) + sin(0) + C = 1

-1 + 0 + C = 1

C = 1+1

C = 2

So,

f ' (x) = -cos(x) + sin(x) + C

turns into

f ' (x) = -cos(x) + sin(x) + 2

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

Now integrate both sides of the first derivative to get the original f(x) function

f ' (x) = -cos(x) + sin(x) + 2

f(x) = -sin(x) - cos(x) + 2x + D .... apply integral; D is some constant

f(0) = -sin(0) - cos(0) + 2(0) + D

f(0) = 0 - 1 + 0 + D

f(0) = D - 1

f(0) = 2

D-1 = 2

D = 2+1

D = 3

We have f(x) = -sin(x) - cos(x) + 2x + D update to f(x) = -sin(x) - cos(x) + 2x + 3

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

So f '' (x) = sin(x) + cos(x) becomes f(x) = -sin(x) - cos(x) + 2x + 3 when f(0) = 2 and f ' (0) = 1

The last step is to replace every x with theta so that we get back to the original variable.

f(x) = -sin(x) - cos(x) + 2x + 3   turns into   f(θ) = -sin(θ) - cos(θ) + 2θ + 3

Hey there! I'm happy to help!

We want to find out how much Lana pays per month. Let's dissect each payment we are given so we can find our monthly expense.

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

AUTOMOBILE INSURANCE

$300 for automobile insurance semiannually

The prefix semi- means half. Annual means year. So, she is paying $300 every half year, or six months. So, we can divide 300 by 6 to find how much she pays in one month!

300/6=50

Therefore, she pays $50 a month for automobile insurance.

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

HEALTH INSURANCE

We are told here that she pays $100 every month for health insurance. We don't need do anything else here!

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

LIFE INSURANCE

We see that Lana pays $700 per year on life insurance. We can divide this by 12 to find out how much there is in 1 month!

700/12≈58.33

Therefore, she pays $58.33 every month on life insurance.

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

SOLUTION

Now, we just add all of these monthly totals up to find Lana's monthly expense.

50+100+58.33=208.33

Therefore, Lana's monthly expense is $208.33.

I hope that this helps! Have a wonderful day!

Answer:

B=25

Step-by-step explanation:

Answer:  The answer has one solution:

_______________________________

      →  x = 1 ;   y =  -4 ;  or, write as:  [1, -4].

_______________________________

Step-by-step explanation:

_______________________________

Given:

  y  =  - 1x – 3

  y  =   -7x + 3 ;

_______________________________

    -1x – 3  =   -7x + 3  ;  Solve for "x" ;

Add:  " +1x" ; and add " +3 " ;  to Each Side of the equation:

Subtract " 1x " ; and Subtract " 1 " ; from Each Side of the equation:

   -1x  + 1x  – 3  + 3  =  -7x  + 1x + 3 + 3 ;

         to get:  

             0  =  -6x + 6

          ↔  -6x + 6 = 0 ;

Now, subtract " 6 " from Each Side of the equation:

                -6x + 6 – 6  = 0 – 6  ;

       to get:

               -6x = -6 ;

Now, divide Each Side of the equation by " -6 ";  

      to isolate "x" on one side of the equation;

      & to solve for "x" ;

              -6x /-6  =  -6/-6 ;

      to get:

                x = 1 .

_______________________________

Now, let us solve for "y" ;  

We are given:  

 y =  -x – 3  ;

Substitute our solved value for "x" ; which is:  " 1 " ; for " x " ; into this given equation; to obtain the value for " y " :

 y =  -x – 3  ;

    =  -1  – 3  

 y =   - 4 .

_______________________________

Let us check our answers by plugging the values for "x" and "y" ;

" 1 " ; and " -4 "; respectively);  into the second given equation; to see if these values for " x " and " y"  ; hold true:

Given:   y  =    - 7x  +  3 ;

           →  -4   =?  -7(1) + 3 ??  ;

           →  -4   =?   -7   + 3  ??  ;

           →  - 4 =?   -4 ?? ;

           →  Yes!

_______________________________

The answer has one solution:

      →  x = 1 ;   y =  - 4 ;  or, write as:  [1, -4 ].

_______________________________

Hope this is helpful!  Best wishes!

_______________________________

Answer: THE SECOND ONE

Step-by-step explanation:

Answer: the second one

Step-by-step explanation:

Answer:

y=cosx

Step-by-step explanation:

cosx has a domain of all real numbers

Answer: A

Step-by-step explanation:

You want to make them both have common denominators. What number does the denominators both go into? Thats easy, its 60.

Multiply 7/12 by 5/5 to get 35/60

Now multiply 4/15 by 4/4 to get 16/60

You need to add a negative number to 35/60 in order to get 16/60

Do 16-35 to get -19/60

Answer:

615.44

Step-by-step explanation:

The area in terms of π is 196π

196 * 3.14 = 615.44

Answer:

615.75

Step-by-step explanation:

Area equals pi times r times 2

A equals 3.14 times 14 times 2

Answer:

10

-5

Step-by-step explanation:

5 - -5

Subtracting a negative is like adding

5+5 = 10

-9 - -4

-9+4

-5

Answer:

Step-by-step explanation:

5+5 = 10

-9+4 = -5

Step-by-step explanation:

-8x + 4 > 5 - 3x

-8x + 3x > 5 - 4

-5x > 1

x > 1 / - 5

Answer:

x = 15

Step-by-step explanation:

3x = 45

x = 45/3

x = 15

Answer:

15

Step-by-step explanation:

3x = 45

Dividing 3 from both sides gives you

[tex]x = 45/3\\\\[/tex]

Now that isolated x.

[tex]45/3 = 15[/tex]

So x = 15

:D

Answer:

X = 2 and Y = -3

Step-by-step explanation:

2x+5y=-11    - equation 1

10x+3y=11    - equation 2

from equation 1, 2X = -11 - 5y

                           X = -11/2 - 5Y/2

                           X = -5.5 - 2.5Y

insert X = -5.5 - 2.5Y into equation 2

     therefore, 10x+3y=11

                       10(-5.5 - 2.5Y) + 3y = 11

                       -55 -25Y +3Y = 11

                        -22Y = 11+55

                      Y = -66/22

                      Y = -3

insert Y = -3 into equation 1

      thus 2x + 5(-3) = -11

              2x - 15 = -11

              2x = -11 + 15

              2x = 4

              x = 4/2

              x = 2

ordered pair: X = 2 and Y = -3

Answer:

I think that angles 1 and 2 are complementary

Step-by-step explanation:

option 1

plz mark brainliest!

Answer:a

Step-by-step explanation:

Answer:

A right triangle consists of two legs and a hypotenuse.

Step-by-step explanation:

The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle. There are a couple of special types of right triangles, like the 45°-45° right triangles and the 30°-60° right triangle.

Answer:

The 85% confidence interval is ( 7.7 , 8.0 )

Step-by-step explanation:

In order to find the 85% confidence interval you use the following formula:

[tex]\overline{x}\pm Z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]       (1)

where

[tex]\overline{x}[/tex]: mean of number of bacteria reproduces per hour = 7.8

σ: standard deviation = 2.2

n: sample size = 967

α: 1 - 0.85 = 0.15

Zα/2: Z factor of the density distribution = 1.44

You replace the values of all parameters in the equation (1):

[tex]7.8\pm (1.44)\frac{2.2}{\sqrt{697}}\\\\7.8\pm0.119\\\\[/tex]

Then, the confidence interval is:

[tex](7.8-0.119,7.8+0.119)\\\\(7.7,8.0)[/tex]

Answer:

The volume of the space outside the pyramid but inside the prism is 225 cubic centimeters.

Step-by-step explanation:

To find this, you subtract the volume of the pyramid from the volume of the rectangular prism.

The prism and pyramid's bases is 25 cm²

The pyramid's height is 12÷2 or 6 cm

The volume formula for a prism is l×w×h

The volume formula for a pyramid is [tex]\frac{1}{3}[/tex] ×b×h

The area of the prism is 5×5×12 or 300 cm³

The area of the pyramid is [tex]\frac{1}{3} *25*6[/tex] or 75 cm³

300 cm³-75 cm³=225 cm³

The volume outside the pyramid but inside the prism is 225 cm³.

Answer:

  θ = ±2π/3 +2kπ . . . . . for any integer k

Step-by-step explanation:

  2·cos(θ) +1 = 0

  cos(θ) = -1/2 . . . . . subtract 1, divide by 2

The cosine function has the value -1/2 for θ = ±2π/3 and any integer multiple of 2π added to that.

  θ = ±2π/3 +2kπ . . . . . for any integer k

Answer:

The volume of the prism is 75 cubic inches

Step-by-step explanation:

The volume of the prism is the amount of space contained on the interior of the prism.

Now we have that this entire space is filled with cubes of defined volumes. Therefore, to get the volume of the prism, we can simply get the total volume occupied by all the cubes. This should give us our answer.

From the information we are given, we know that the there are 3 layers of cubes each containing 25 cubes.

This gives the total number of cubes to be 3 X 25 = 75 cubes in total

We also know that the volume of 1 cube is 1 cubic inch.

Hence the volume of 75 cubes will be 75 X 1 cubic inch = 75 cubic inches.

Answer:

[tex] x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

Where a = 2 , b= 3, c= -5, replacing we have this:

[tex]x =\frac{-3 \pm \sqrt{(-3)^2 -4(2)(-5)}}{2*2}[/tex]

And simplifying we got:

[tex] x = \frac{-3 \pm \sqrt{49}}{4}[/tex]

And the two solutions are:

[tex] x_1 = \frac{-3+7}{4}= 1[/tex]

[tex] x_2 = \frac{-3-7}{4}= -\frac{5}{2}[/tex]

And the correct options are:

B and C

Step-by-step explanation:

We have the following equation given:

[tex] 2x^2 +3x -5=0[/tex]

And if we use the quadratic formula given by:

[tex] x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

Where a = 2 , b= 3, c= -5, replacing we have this:

[tex]x =\frac{-3 \pm \sqrt{(-3)^2 -4(2)(-5)}}{2*2}[/tex]

And simplifying we got:

[tex] x = \frac{-3 \pm \sqrt{49}}{4}[/tex]

And the two solutions are:

[tex] x_1 = \frac{-3+7}{4}= 1[/tex]

[tex] x_2 = \frac{-3-7}{4}= -\frac{5}{2}[/tex]

And the correct options are:

B and C

Answer:

B and C

Step-by-step explanation:

Answer=6 . S/R . 4T

This is the answer because u have to simplify so to do this u have to divide all of this by R

Answer:

Step-by-step explanation:

What function ?

Answer:

Step-by-step explanation:

We have to find the reported happiness of person of family income of $25,000, $35,000 and $45,000

Given that the formula for finding relation between a people happiness and his income is

y = 0.065x - 0.613

a) find the happiness of person of family income os $25,000

we put x = 25 as in the equation above

[tex]y=0.065(25)-0.613\\\\=1.625-0.613\\\\=1.02 \approx 1[/tex]

Hence, person happiness with with family income of $25,000 on a scale of 3 is y = 1

That means they come under catergory "not to happy"

b) Find the happiness of person of family income os $35,000

we put x = 35 as in the equation above

[tex]y=0.065(35)-0.613\\\\=1.667-0.613\\\\=1.667 \approx 1.7[/tex]

Hence, person happiness with with family income of $35,000 on a scale of 3 is y = 1.7

That means they come under catergory "not to happy" and "fairly happy"

c) Find the happiness of person of family income os $45,000

we put x = 45 as in the equation above

[tex]y=0.065(45)-0.613\\\\=2.925-0.613\\\\=2.312 \approx 2.3[/tex]

Hence, person happiness with with family income of $45,000 on a scale of 3 is y = 2.3

That means they come under catergory  "fairly happy"

The scale would show the data as follows:

Happiness Scale at Income 25, 35, 45 & 55 thousand :

1.012 (Not too happy), 1.662 (Fairly Happy), 2.315 (Fairly Happy) , 2.965 (Very Happy)

Important Information :

Relationship between happiness scale 'y' and income in 1000s 'x' :y = 0.065x − 0.613, for people in income group between [tex]25000 & 55000[/tex]

Happiness scale : At level of income, between 25 and 55 thousands.

Putting value of income 'x' to find scale of happiness i.e. 'y'

For income 'x' = 25 thousand : [tex]y = 0.065 (25) - 0.613 = 1.625 - 0.613 = 1.012[/tex] For income 'x' = 35 thousand : [tex]y = 0.065 (35) - 0.613 = 2.275 - 0.613 = 1.662[/tex]For income 'x' = 45 thousand : [tex]y = 0.065 (45) - 0.613 = 2.925 - 0.61 = 2.315[/tex] For income 'x' = 55 thousand :[tex]y = 0.065 (55) - 0.613 = 3.575 - 0.61 = 2.965[/tex]

Learn more about "Happiness Scale" here:

brainly.com/question/25609130

Answer:

[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And using this formula we have this:

[tex] P(X<11) = \frac{11-0}{12-0}= 0.917[/tex]

Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917

Step-by-step explanation:

Let X the random variable of interest that a woman must wait for a cab"the amount of time in minutes " and we know that the distribution for this random variable is given by:

[tex] X \sim Unif (a=0, b =12)[/tex]

And we want to find the following probability:

[tex] P(X<11)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And using this formula we have this:

[tex] P(X<11) = \frac{11-0}{12-0}= 0.917[/tex]

Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917

Answer:

Step-by-step explanation:

Area of a sector = [tex]\frac{\theta}{360} * \pi r^{2}\ where\ \pi r^{2} \ is\ the\ area\ of\ the\ circle[/tex]

theta is the sector's central angle

Area of the sector = [tex]\frac{\theta}{360} * \ area\ of\ a\ circle[/tex]

Given area of a circle = 18πin² and area of a sector = 6πin²

On substituting;

6π = [tex]\theta/360 * 18 \pi[/tex]

Dividing both sides by 18π we have;

1/3 = [tex]\theta/360[/tex]

[tex]3 \theta = 360\\\theta = 360/3\\\theta = 120^{0}[/tex]

The sector's central angle is 120°

Answer and Step-by-step explanation:

The computation of annual and quarterly mortality rates per 100,000 population is shown below:-

Quarterly mortality rates are

[tex]= \frac{Deaths}{Population\ in\ the\ city}\times Population[/tex]

For the first quarter

[tex]= \frac{54}{450,000}\times 100,000[/tex]

= 12  death per 100,000 population

For the second quarter

[tex]= \frac{43}{450,000}\times 100,000[/tex]

= 9.5  death per 100,000 population

For the third quarter

[tex]= \frac{35}{450,000}\times 100,000[/tex]

= 7.7  death per 100,000 population

For the fourth quarter

[tex]= \frac{39}{450,000}\times 100,000[/tex]

= 8.6  death per 100,000 population

Now the annual mortality is

[tex]= \frac{Deaths}{Population\ in\ the\ city}\times Population[/tex]

[tex]= \frac{171}{450,000}\times 100,000[/tex]

= 38 death per 100,000 population

Answer:

Step-by-step explanation:

The bottom (or top) of the U is called the vertex, or the turning point. The vertex of a parabola opening upward is also called the minimum point. The vertex of a parabola opening downward is also called the maximum point.

The x-intercepts are called the roots, or the zeros. To find the x-intercepts, set ax^2 + bx + c = 0.

The parabola is symmetric (a mirror image) about a vertical line drawn through its vertex (turning point). This line is called the axis of symmetry.

If possible, please mark brainliest

The quadratic function can be expressed in the form of vertex form and the parabola is symmetric about the line which is passing through focus.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

The important features for the graph of a quadratic function will be

The parabola is symmetric about the line which is passing through focus.

The quadratic function can be expressed in the form of vertex form.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

More about the quadratic equation link is given below.

https://brainly.com/question/2263981

#SPJ2

Answer:

Y=(-1,0)

G=(0,1)

F=(-1,3)

Step-by-step explanation:

Answer:

$3,485.48

Step-by-step explanation:

For computing the money required at the end of the account term we need to apply the Future value formula i.e be to shown in the attachment below:

Given that,  

Present value = $3,000

Rate of interest = 3% ÷ 365 days  = 0.00821917

NPER = 5 years × 365 days  = 1,825

PMT = $0

The formula is shown below:

= FV(Rate;NPER;PMT;PV;type)

So, after applying the above formula

the amount of future value is $3,485.48

Answer: It’s 2

Step-by-step explanation:

look at picture