Identify each line or segment that intersects ⊙ S.

Answer:

A nice way to show it is through the unit circle.

In the unit circle, the point at angle theta from the origin has a y value of sin theta.

If you rotate a point 360-theta degrees from the origin, that is like rotating it theta degrees "backwards", or downwards, which is going to yield the same exact point, reflected through the x-axis. In other words, the y value, or sin(360-theta), is exactly -sin(theta).

Answer:

The verification is in the explanation.

Step-by-step explanation:

To solve this I'm going to use the difference identity for sine:

[tex]\sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a)[/tex].

[tex]\sin(360^\circ-\theta)=\sin(360^\circ)\cos(\theta)-\sin(\theta)\cos(360^\circ)[/tex]

We are going to apply that [tex]\sin(360^\circ)=0 \text{ while } \cos(360^\circ)=1[/tex]

[tex]\sin(360^\circ-\theta)=0 \cdot \cos(\theta)-\sin(\theta)\cdot 1[/tex]

[tex]\sin(360^\circ-\theta)=-\sin(\theta)[/tex]

Answer:

376

Step-by-step explanation:

This is a subtraction problem.

1,213 - 837 =

   1,213

-    837

-----------

     376

Answer: 376

Answer:376

Step-by-step explanation:1213-837=376

Answer:

B) f(x)=1.74(0.81)^3x

and

D) f(x)=156(1-0.19)^x

Step-by-step explanation:

The percentage will always be where the b is, or inside the parentheses. You just have to make sure that, when not greater than 1, you must find out WHAT SUBTRACTS FROM 1 TO GET THAT RESULT. So ask yourself, what decimal number subtracts from 1 to get 0.81?

0.81 is the equivalent to (1-0.19) because (1-0.19) = 0.81.

0.19 is 19%, which is what we're looking for!

The exponential function with a percentage rate of change of 19% is option D) f(x)= 156(1-0.19)ˣ, because it reflects a 19% decrease with the base 0.81 (which is equal to 1 - 0.19).

Exponential functions have a percentage rate of change of 19%, we need to identify the function where the base of the exponent reflects this rate of change. The percentage rate of change can be represented as a decimal where a 19% increase is 1.19 and a 19% decrease is 0.81 (since 1 - 0.19 = 0.81).

Now, let's analyze the given functions:

A) f(x) = 3182(0.9)²ˣ does not represent a 19% rate of change.

B) f(x) = 1.74(0.81)³ˣ does not represent a 19% rate of change as it involves 0.81 to the power of 3x, not x.

C) f(x) = 0.2(0.38)ˣ/² does not represent a 19% rate of change.

D) f(x) = 156(1-0.19)ˣ does represent a 19% rate of change because the base is 0.81 which is equivalent to 1 - 0.19.

Therefore, the correct answer is option D).

Answer:

[tex](x^{2} +x+1)(x-1)+2[/tex]

Step-by-step explanation:

The synthetic division can be used to divide a polynomial function by a binomial of the form x-c, determining zeros in the polynomial.

step 1:  Establish the synthetic division, placing the polynomial coefficients in the first row (if any term does not appear, assign a zero coefficient) and to the extreme left the value of c.

1 |     1   0   0   1

step 2: Lower the main coefficient to the third row.

1 |     1   0   0   1

       1

Step 3: Multiply 1 by the main coefficient 1.

1 |     1   0   0   1

            1

       1

step 4: Add the elements of the second column.

1 |     1   0   0   1

            1

       1    1

step 5: Then repeat step 4 until the constant term 1 is reached.

1 |     1   0   0   1

            1    1    1

       1    1   1     2

step 6: Enter the quotient and remainder

quotient:  [tex]x^{2} + x + 1[/tex]

remainder:  2

Solution:   [tex]x^{2} + x + 1[/tex] [tex](x+1)  + 2[/tex]

Answer:

x^2+x+1+[tex]\frac{2}{x-1}[/tex]

Step-by-step explanation:

Answer:

5 : 00 PM

Step-by-step explanation:

Given,

Church ring bells every 15 minutes,

School rings its bells every 20 minutes,

And, day care center rings its bells every 25 minutes,

Thus, the number of minutes after which they will ring together = LCM (15, 20, 25)

∵ 15 = 3 × 5,

20 = 2 × 2 × 5,

25 = 5 × 5,

Thus, LCM (15, 20, 25) = 300

Now, 1 minute = 1/60 hours ⇒ 300 minutes = 5 hours,

Hence, after 5 hours they will ring together,

If they rang at 12:00 PM,

Then they will ring after 5 hours that is 5:00 PM.

Answer:-28x^4y^2(-4x^3y^6)

Step-by-step explanation: Distribute and add exponents, put in parentheses to make it easier to understand but it's not necessary for the final answer.

Answer:

[tex]-28x^4y^6[/tex]

Step-by-step explanation:

The given expression is

[tex]-4x^3y^2(7xy^4)[/tex]

We need to place the indicated product in the proper location on the grid.

The given expression can be rewritten as

[tex](-4\times 7)(x^3x)(y^2y^4)[/tex]

[tex]-28(x^3x)(y^2y^4)[/tex]

Using the product property of exponent, we get

[tex]-28\times x^{3+1}\times y^{2+4}[/tex]          [tex][\because a^ma^n=a^{m+n}][/tex]

[tex]-28\times x^{4}\times y^{6}[/tex]

[tex]-28x^{4}y^{6}[/tex]

Therefore the answer of given product is [tex]-28x^{4}y^{6}[/tex].

Answer:

2x³  + 10x² + x + 5

Step-by-step explanation:

The coefficients of the dividend are represented by the top row, that is

2  10  1  5 → 2x³ + 10x² + x + 5

The divisor is ( x + 5) and

the quotient is represented by the first 3 numbers on the bottom row

2  0  1 → 2x² + 1

The last zero on the same row is the remainder

Since zero this indicates that (x + 5) is a factor of 2x³ + 10x² + x + 5

Answer:

b

Step-by-step explanation:

Answer:

  A.  20,000 square feet

Step-by-step explanation:

The description is that of a rectangle 200 ft long and 100 ft wide. The area is the product of those dimensions:

  area = (200 ft)(100 ft) = 20,000 ft²

The correct option is option A.

The area of a rectangle is the region covered by the rectangle in a two-dimensional plane.

The formula to finding the area of the rectangle is,

[tex]A=l\times b[/tex]

It is given that,

Length=100 ft

Breadth=200 ft

[tex]A=l\times b[/tex]

Now, substituting the given values into the above formula we get,

[tex]A=200 \times 100\\A=20000[/tex]

The required area is 20,000 square feet.

Learn more about the topic area of the rectangle:

https://brainly.com/question/11202023

Answer:

The lens is 1 inch from the mirror

Step-by-step explanation:

* Lets revise the equation of the hyperbola with center (0 , 0) and

 transverse axis parallel to the y-axis is y²/a² - x²/b² = 1

- The coordinates of the vertices are  (0 , ± a)

- The coordinates of the co-vertices are (± b , 0)  

- The coordinates of the foci are (0 , ± c) where c² = a² + b²

* Lets solve the problem

∵ The equation of the hyperbola is y²/16 - x²/9 = 1

∵ The form of the equation is y²/a² - x²/b² = 1

∴ a² = 16

∴ a = √16 = 4

∵ The coordinates of the vertices are  (0 , ± a)

∴ The coordinates of the vertices are  (0 , 4) , (0 , -4)

∴ b² = 9

∴ b = √9 = 3

∵ c² = a² + b²

∴ c² = 16 + 9 = 25

∴ c = √25 = 5

∵ The coordinates of the foci are (0 , ± c)

∴ The coordinates of the foci are (0 , 5) , (0 , -5)

∵ The camera is pointed towards the vertex of the hyperbolic mirror

   which is (0 , 4) and is positioned such that the lens is at the nearest

  focus to that vertex which is (0 , 5)

∴ The distance between the lens and the mirror equal the distance

   between the vertex and the focus

∵ The vertex is (0 , 4) and the nearest focus is (0 , 5)

∴ The distance = 5 - 4 = 1 inch

* The lens is 1 inch from the mirror

Answer:

60 ADULT TICKETS

40 KIDS UNDER 12 TICKETS

Step-by-step explanation:

By playing around with numbers, you can figure out what makes this situation true. By multiplying 4.50 by 60, you get 270. Then, by multiplying 2 by 40, you get 80. Finally, add 270 and 80, which results in 350, which satisfies the problem.

Hope this helps!

By setting up a system of equations, we find that 60 adult tickets and 40 kids tickets were sold for the Saturday matinee when 100 tickets are sold for a total of $350.

Let x be the number of adult tickets sold and y be the number of kids tickets sold. We then have the following system of equations:

x + y = 100 (Total number of tickets)

$4.50x + $2.00y = $350 (Total revenue)

2x + 2y = 200

4.5x + 2y = 350

2.5x = 150

x = 60

y = 100 - 60 = 40

So, 40 kids tickets were sold.

Answer :

22.5 is the answer

MARK ME AS BRANILIST

Answer: 90

Step-by-step explanation:

Basically you reflect twice and then rotate it

Answer:

1/4

23in * 19 in.

Step-by-step explanation:

The scale factor is 1/4 and the channel size is  92*1/4 * 76 * 1/4

= 23 in * 19 in screen.

Answer:

Scale factor = 1/2,  New screen 46 in by 38 in.

Step-by-step explanation:

The dimensions of screen is 92 in. by 76 in.

It has a feature that splits the screen to allow you to watch 4 channels at once as shown in the below figure.

All four parts are equal.

Let the dimensions of new screen be x in. by y in.

[tex]2x=92[/tex] and [tex]2y=76[/tex]

Divide both sides by 2.

[tex]x=46[/tex] and [tex]y=38[/tex]

Scale factor is

[tex]\text{Scale factor}=\frac{\text{New dimension}}{\text{Corresponding original dimension}}[/tex]

[tex]\text{Scale factor}=\frac{46}{92}[/tex]

[tex]\text{Scale factor}=\frac{1}{2}[/tex]

Therefore, the scale factor is 1/2.

Answer:

  d.  2/5+1/3=11/15

Step-by-step explanation:

The commutative property of addition allows you to change the order of the operands in a sum. 2/5 is the second operand in the original sum; it is the first operand in selection D.

Answer:

Tasha made her mistake in step 4.

Answer:

Step 4 is the incorrect.

Step-by-step explanation:

From the table attached,

Step 1. Find a pattern in the table.

Correct

Step 2. Find the value of [tex]4^{-3}=(\frac{1}{16})(\frac{1}{4})=\frac{1}{64}[/tex]

Correct

Step 3. Find the value of [tex]4^{-4}=(\frac{1}{64})(\frac{1}{4})=\frac{1}{256}[/tex]

Correct

Step 4. Rewrite the value of [tex]4^{-4}[/tex]

[tex](\frac{1}{256})=-\frac{1}{4^{-4} }[/tex]

Incorrect.

Because it should be [tex](\frac{1}{256})(\frac{1}{4})=\frac{1}{1024}[/tex]

Answer:

d

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x)

= x³ - 2x + 6 - (2x³ + 3x² - 4x + 2) ← distribute parenthesis by - 1

= x³ - 2x + 6 - 2x³ - 3x² + 4x - 2 ← collect like terms

= - x³ - 3x² + 2x + 4 → d

Answer:

The probability is 14/55

Step-by-step explanation:

The word replacement contains 11 letters.

In which 4 letters are vowel = e,a,e,e

And 7 letters are not vowel = r,p,l,c,m,n,t

The probability of getting the vowel in the first try = 4/11

The probability of getting something that is not a vowel = 7/10.

The denominator is one less because the vowel card is not replaced, meaning there is one less card to choose from.

Multiply the values:

=4/11 * 7/10

=28/110

=14/55

The probability is 14/55....

75 percent of the art club members voted in the election.

To calculate the percentage of art club members who voted in the election, use the formula for percentage: part/whole *100. In this case, the part is the number of members who voted, and the whole is the total number of members in the art club.

Here's the step-by-step calculation:

Count the number of members who voted: 9.

Count the total number of members in the art club: 12.

Divide the number of voters by the total number of members: 9 / 12 = 0.75.

Multiply the result by 100 to get the percentage: 0.75 * 100 = 75%.

Therefore, 75 percent of the art club members voted in the election.

Answer:

  Stretch in any direction (horizontal or vertical) means the corresponding coordinates are multiplied by the stretch factor: a horizontal stretch multiplies the x-coordinates by the stretch factor; a vertical stretch multiplies the y-coordinates by the stretch factor.

Step-by-step explanation:

If you know the coordinates, you can apply the stretch factor directly to the coordinates.

For example, consider the point (5, 25).

A horizontal stretch (only) by a factor of 3 will move this point to (15, 25).

A vertical stretch (only) by a factor of 3 will move the original point to (5, 75).

Note that only the corresponding coordinate is multiplied by 3.

___

The confusion can arise when this stretch concept is applied to the transformation of a function.

Consider the function f(x) = x^2. The point used in the example above is ...

  (5, f(5))

Vertical Stretch Function Transformation

If we want to transform the function to one that is vertically stretched by a factor of 3, we can simply multiply the function value by 3:

  g(x) = 3·f(x)

Then ...

  (5, g(5)) = (5, 75) . . . . . . the location of the vertically stretched point in the above example.

Horizontal Stretch Function Transformation

If we want to stretch the above f(x) function horizontally by a factor of 3, we want a h(x) function that will produce the point (15, h(15)) = (15, 25). We can get that using f(x), but the argument to f(x) for that y-coordinate must be 5, not 15. This means the transformation must be ...

  h(x) = f(x/3)

Dividing the function argument by the stretch factor means the argument must be larger by that factor in order to give the same function result.

  (15, 25) = (15, h(15)) = (15, f(15/3)) = (15, f(5))

_____

Summary

Vertical stretch of a coordinate by the factor "a": (x, y) ⇒ (x, ay)

Vertical stretch of a function by the factor "a": g(x) = a·f(x)

__

Horizontal stretch of a coordinate by the factor "a": (x, y) ⇒ (ax, y)

Horizontal stretch of a function by the factor "a":

  (x, y) ⇒ (ax, h(ax)), where h(x) = f(x/a), so h(ax) = f(ax/a) = f(x)

Answer:

A.

Step-by-step explanation:

If

[tex]y=x^2+2x+7[/tex] AND

y = x + 7, then by the transitive property of equality:

[tex]x^2+2x+7=x+7[/tex]

We can solve for the values of x by getting everything on one side of the equals sign and then solving for x:

[tex]x^2+x=0[/tex]

We can factor out the common x to get:

x(x + 1) = 0

which tells us by the Zero Product Property that either

x = 0 and/or x + 1 = 0 and x = -1

We are expecting 2 solutions for x since this is a second degree polynomial.  We will sub both -1 and 0 into y = x + 7 to solve for the corresponding values of y

y = 0 + 7 so

y = 7 and the coordinate is (0, 7)

y = -1 + 7 so

y = 6 and the coordinate is (-1, 6)

Answer:

  18 months

Step-by-step explanation:

The difference in payments is $651 -541 = $110 per month. The cost of the points is ...

  $98,000 × 0.02075 = $2033.50

So, it will take $2033.50/($110/mo) ≈ 18.48 mo to make up the cost.

It will take Todd 18 months to cover the cost of the discount points.

_____

Comment on rounding

The question asks for the answer to be rounded to the nearest whole month. Since the quotient is about 18.486, this rounds to 18. After 18 months, the cost of the points is not quite covered. $53.50 remains to be covered. It isn't until Todd's 19th payment that the cost of points has been fully covered. For "break even" problems such as this one, I prefer to round to the next higher integer, rather than the nearest integer.

Answer:

Step-by-step explanation:

[tex]cosecant=\dfrac{hypotenuse}{opposite}\\\\\text{We have}\ opposite=3b,\ \text{and}\ hypotenuse=22.5,\ \text{and}\ \csc x=\dfrac{5}{4}.\\\\\text{Substitute:}\\\\\dfrac{5}{4}=\dfrac{22.5}{3b}\qquad\text{cross multiply}\\\\(5)(3b)=(4)(22.5)\\\\15b=90\qquad\text{divide both sides by 15}\\\\b=6[/tex]

Answer:

Symmetric about the y-axis only

Step-by-step explanation:

Graph the function using a calculator

alternatively,

Sketch the graph via the following steps

-sketch cosθ

- reflect about the x-axis to get (- cosθ)

- multiply vertex values by 4 to get -4cosθ

- shift the graph in the positive y direction by 4 units to get 4 - 4cosθ

you will end up with the attached graph:

By observation, we can see that the graph is

1) NOT symmetric about the x-axis

2) Symmetric about the y-axis

3) Not symmetric bout the origin

to run a symmetry test on a polar, we can simply do a few ( r , θ ) replacements, if the equation resulting from the replacements, resembles the original, then it has that symmetry type, now, let's recall the symmetry trigonometry identity, cos(-θ) = cos(θ).

[tex]\bf r=4-4cos(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{testing with respect to the y-axis, using }-r,-\theta ~\hfill }{(-r)=4-4cos(-\theta )\implies -r=4-4cos(\theta )}\implies r=-4+4cos(\theta )~\hfill \bigotimes \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{testing with respect to the x-axis, using }-\theta ~\hfill }{r=4-4cos(-\theta )\implies r=4-4cos(\theta )}~\hfill \stackrel{\textit{symmetry with respect}}{\textit{to x-axis}~\hfill }\textit{\Large\checkmark} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{testing with respect to the origin, using }-r~\hfill }{(-r)=4-4cos(\theta )\implies r=-4+4cos(\theta )}~\hfill \bigotimes[/tex]

Answer:

223

Step-by-step explanation:

i honestly dont even know

Answer:b y=470+50x

Step-by-step explanation:

AnswEr:

Add the two, to both sides. -2+2=0

So, the equation would like like this

x -2= 9

+2 +2

Then solve, the 2’s cancel out leaving you with x by itself. Finishing the equation to look like this-> x=11

Answer:

  not rational

Step-by-step explanation:

√2 is irrational. Any arithmetic operation (addition, subtraction, multiplication, division) performed on that number and any rational number will result in an irrational number (except for multiplication by 0).

Answer:

Step-by-step explanation:

Because of that sqrt, this expression is irrational.  A rational expression is one that can be expressed as the ratio of two integers.

Answer:

2.25

Step-by-step explanation:

The total frequency is:

20 + 12 + 6 + 2 = 40

Calculate the probability of each score:

P(X=3) = 20/40 = 0.50

P(X=2) = 12/40 = 0.30

P(X=1) = 6/40 = 0.15

P(X=0) = 2/40 = 0.05

So the expected value is:

E = (3)(0.50) + (2)(0.30) + (1)(0.15) + (0)(0.05)

E = 2.25

Answer:

Step-by-step explanation:

The transformations you want are ...

Taken together, these make the transformation ...

  (x, y) ⇒ (-y+6, -x-1)

So, your points become ...

  A(0, 0) ⇒ A'(6, -1)

  B(8, 1) ⇒ B'(5, -9)

  C(5, 5) ⇒ C'(1, -6)

___

The attachment shows the original triangle in red and the progression to the final triangle in blue.

Final answer:

The total number of hours worked by the person is calculated by adding the working times from two segments of the day. The morning session contributes 3 hours and 15 minutes, and the afternoon session adds 4 hours and 45 minutes. The combined total working hours are 8 hours.

Explanation:

To calculate the total number of hours worked by the person, we need to break down their workday into segments and sum up the time they spent working.

Morning session: From 8:30 AM to 11:45 AM

Afternoon session: From 12:30 PM to 5:15 PM

Calculating each session separately, we get:

Morning session: 11:45 AM - 8:30 AM = 3 hours and 15 minutes

Afternoon session: 5:15 PM - 12:30 PM = 4 hours and 45 minutes

Adding both sessions together:

3 hours and 15 minutes + 4 hours and 45 minutes = 8 hours total

Final Calculation:

3 hours 15 minutes + 4 hours 45 minutes = 7 hours 60 minutes = 8 hours

Therefore, the total number of hours worked by this person was 8 hours.

Final answer:

The expression for the combined total profit made by TechWiz Electronics from MP3 and DVD players last week is 17x + 2754.

Explanation:

The profit TechWiz Electronics made from selling MP3 players can be represented by the expression 35x, where x is the number of MP3 players sold.

The profit from selling DVD players can be represented by the expression 18(153-x), where 153 is the total number of players sold and x is the number of MP3 players sold.

To find the combined total profit, we can add these two expressions together:

Combined Total Profit = 35x + 18(153-x)

Using the distributive property, we can simplify as:

Combined Total Profit = 35x + 2754 - 18x

Combining like terms, we can simplify further:

Combined Total Profit = 17x + 2754

Therefore, the expression for the combined total profit TechWiz made from MP3 and DVD players last week is 17x + 2754.