vy = a sin( k ( x - d)) + c and y = a cos( k ( x - d)) + c

Triagonometric function tan(A+B)/cot(A−B) is tan²A-tan²B/1-tan²Atan²B

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

tan(A+B)/cot(A-B)

tan(A+B)/1/tan(A-B)

(tanA+tanB/1-tanAtanB)/1/(tanA-tanB/1+tanAtanB)

tanA+tanB/1-tanAtanB)×tanA-tanB/1+tanAtanB

We know algebraic identity

(a+b)(a-b)=a²-b²

(tanA+tanB/1-tanAtanB)×(tanA-tanB/1+tanAtanB)

tan²A-tan²B/1-tan²Atan²B

Hence, triagonometric function tan(A+B)/cot(A−B) is tan²A-tan²B/1-tan²Atan²B

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ1

The table of values which represent the equation y = 7x - 3 is: table D.

In Mathematics, an ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

In order to determine the true ordered pair that is a solution for the given linear equation, we would have to test the ordered pair contained in each table by substituting it into the linear equation as follows;

For ordered pair (-2, -1), we have:

y = 7x - 3

-1 = 7(-2) - 3

-1 = -14 - 3

-1 = -17 (False).

For ordered pair (-2, -19), we have:

y = 7x - 3

-19 = 7(-2) - 3

-19 = -14 - 3

-19 = -17 (False).

For ordered pair (-2, -15), we have:

y = 7x - 3

-15 = 7(-2) - 3

-15 = -14 - 3

-15 = -17 (False).

For ordered pair (-2, -17), we have:

y = 7x - 3

-17 = 7(-2) - 3

-17 = -14 - 3

-17 = -17 (True).

In this context, we can logically deduce that all of the coordinates in table D represents the equation y = 7x - 3.

Read more on ordered pair here: https://brainly.com/question/24880873

#SPJ1

Total 241 adult ticket and 220 student ticket are sold.

system of equations, orsimultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

a + s = 461       or    s = 461 -a

Value of student tickets sold = s × 3   = 3 × (461-a)

Value of adult ticket sold =  4 a              

Summed they total 1624

System of equations :

s = 461-a3 (461-a) + 4a

  = 16241383 -3a +4a

  = 1624a

  = 241    

then  s = 461 -a = 220 ticket

Learn more about cost here;

https://brainly.com/question/1153322

#SPJ1

Answer: x=5

Step-by-step explanation:

Answer:

(x - 1)² = 16

Step-by-step explanation:

x² - 2x - 15 = 0

x² - 2x + 1 = 15 + 1

(x - 1)² = 16

The triangles ΔPQR ~ ΔPXY are similar by using the AA test for the similarity of triangles.

What is the Angle-Angle similarity theorem of triangles?

The AA Similarity Theorem states: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

In the given figure,

In ΔPQR and ΔPXY

∠P ≅ ∠P ----- Common Angle

∠PQR ≅ ∠PXY ----Corresponding angles.

So, ΔPQR ~ ΔPXY -----(AA test)

Hence, the triangles ΔPQR ~ ΔPXY are similar by using the AA test for the similarity of triangles.

To learn more about the AA Similarity Theorem, visit:

https://brainly.com/question/21247688

#SPJ1

1. It can be piecewise linear; from x = 1 to x = 4, the y-value increases by the same amount each time. From x = 0 to x = 1, the y-value stays the same.

However, if it is supposed to be a single function, it would be non-linear because it changes slope.

2. It is discrete because there is no data between the points.

By using multiplication, it can be calculated that

The complete table is

Number of yogurt bars                       Cost of yogurt bars ($)

             1                                                       1.80

             2                                                      3.60

             3                                                      5.40

             4                                                      7.20

             5                                                      9.00

What is multiplication?

Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.

This is a word problem on multiplication

Cost of 2 yogurt bars = $1.80 [tex]\times[/tex] 2 = $3.60

Cost of 3 yogurt bars = $1.80 [tex]\times[/tex] 3 = $5.40

Cost of 4 yogurt bars = $1.80 [tex]\times[/tex] 4 = $7.20

Cost of 5 yogurt bars = $1.80 [tex]\times[/tex] 4 = $9.00

So the table is

Number of yogurt bars                       Cost of yogurt bars ($)

             1                                                       1.80

             2                                                      3.60

             3                                                      5.40

             4                                                      7.20

             5                                                      9.00

To learn more about multiplication, refer to the link-

https://brainly.com/question/10873737

#SPJ1

The square root of 80 is 4√5 ≅ 8.92.

What is a square root of a number?

In mathematics, the square root of a number is a value that gives the original number on multiplication by itself. The positive number, when multiplied by itself, represents the square of the number. Thus, the square root of the square of a positive number gives the original number.

Using Prime Factorization:

The first step in this method is to find the prime factors of 80.

80 = 2 × 2 × 2 × 2 × 5

To find the root from here, we can simplify this to

√80 = √(2 × 2 × 2 × 2 × 5)

√80 = 4√5

We can either leave it at this or find the root of 5 which is 2.23 and simplify further.

Hence, Square Root of 80 = 4√5 ≅ 8.92.

To learn more about square roots from the given link:
https://brainly.com/question/2160360
#SPJ1

Answer: 30 wpm.

Step-by-step explanation:  

Do 225 divided by 7.5 and you get 30.

30 words in one minute.

1)  image of the coodinate A(6,2) be A'(-2,6)

image of the coodinate B(3,4) be B'(-4,3)

image of the coodinate C(2,8) be C'(-8,2)

2) A transformation that preserves congruence is called an isometry

3) A dilation would produce a similar figure.

What do you mean by transformation?

Transformation is a collective term for four specific ways of manipulating the shape and position of points, lines, or geometric figures. The original shape of the object is called the master, and the final shape and position of the object is the image under transformation. There are four types of transformations in mathematics

1) When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x).

Therefore, image of the coodinate A(6,2) be A'(-2,6)

image of the coodinate B(3,4) be B'(-4,3)

image of the coodinate C(2,8) be C'(-8,2)

2) A transformation that preserves congruence is called an isometry.  In other words, a transformation in which the Image and Pre-Image have the same side lengths and angle measurements. Translations, reflections, and rotations are isometries.

3) A dilation would produce a similar figure.

To learn more about the transformation from the given link.

https://brainly.com/question/2689696

#SPJ1

$699.95×20%=$139.99,  is the finance charge.

A finance charge is any fee that reflects the cost of credit or borrowing under American law.

Some forms of credit have fees and interest that accrue over time. [1] In addition to interest, it also includes additional costs, like those for financial transactions.

The Truth-in-Lending Act and Regulation Z, which were issued by the Statutory Reserve Board, contain information about the federal definition of a finance charge.

A financing charge in personal finance is just the cash amount paid to borrow money, whereas interest is the amount paid as a percentage, such as the annual percentage rate (APR).

Compared to standard dictionary definitions or accounting definitions, these definitions are more specific.

Lenders and creditors both calculate finance charges in different ways. a majority.

Hence, $699.95×20%=$139.99,  is the finance charge.

learn more about finance charge click here:

https://brainly.com/question/3436429

#SPJ4

Answer:

126+20+8h=250

Step-by-step explanation:

Answer: the answer is 8

Step-by-step explanation:

The Answer is: 8

Simply divide 149 by the numbers you see,

The kicked football is an example of a projectile. The football's greatest height is 144 m.

A projectile is any object that is launched into space and moves under the influence of gravity and air resistance. A kicked football is a good example of a projectile. Given the height of the kicked football to be:h = -16t² + 96tThus, the height of the kicked football is a function of time taken. So that differentiating the equation of the height with respect to time, we have;0 = -32t + 9632t = 96t = [tex]\frac{96}{32}[/tex]  = 3

Thus the greatest height of the kicked football is attained when the time is 3 seconds.

Thus,h = -16t² + 96t   = -16 (3)² + 96 (3)   = -144 + 288h = 144

Therefore the football's greatest height is 144 m.

Learn more about the height of a projectile at https://brainly.com/question/24216590

#SPJ1

Answer:

142.6

Step-by-step explanation:

100% + 15% = 115%
115÷100 = 1.15
1.15 x 124 = 142.6

Hope that helped

Answer:

m = 2k/v²

Step-by-step explanation:

K = ½mv²

multiply both sides by 2

2 × k = ² × ½mv²

2k = mv²

divide both sides by (v²)

m = 2k/v²

i hope this helped

When the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.

What is a annual inflation rate?

A percentage is used to represent the inflation rate. For instance, a yearly inflation rate of 2% indicates that the cost of products and services as a whole has increased by 2%. As an illustration, a product that cost $10 last year will cost $10.20 this year.

Here, we have

Given

The cost of the gallon of milk earlier was $2.81

The cost of a gallon of milk now is $3.48.

The total time period is 10 years.

r = (F/P)ⁿ⁻¹ - 1

r = {(3.48/2.81)^(1/10) - 1}×100

r = {(1.238)^(1/10) - 1}×100

r = 0.0215 ×100

r = 2.15

Hence, when the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.

To learn more about the annual inflation rate from the given link

https://brainly.com/question/24723238

#SPJ1

Answer:

translation down 2 and reflection across x axis

The required expression for the term of the given sequence is aₙ = 625 × (1/5)ⁿ⁻¹.

In order to check a geometric sequence, find the ratios of the consecutive terms of the given sequence. If they are equal, the given sequence is geometric.

The given sequence is as follows,

625, 125, 25, 5, 1

The first term is given as a₁ = 625

And, the ratio of the consecutive terms are,

125/625 = 1/5

25/125 = 1/5

Since the ratio of two consecutive terms are equal, the given sequence is a geometric sequence.

The nth term of a geometric sequence is given as aₙ = a₁rⁿ⁻¹.

Thus, the expression for the given sequence is aₙ = 625 × (1/5)ⁿ⁻¹.

Hence, the term for the given sequence can be written in general form as  aₙ = 625 × (1/5)ⁿ⁻¹.

To know more about geometric sequence click on,

https://brainly.com/question/11266123

#SPJ1

Andrew will have $251.91 in his account after 5 years, assuming he does not add or withdraw any money from the account and that interest is compounded semiannually at a rate of 2.9%.

The fee that a lender assesses on a borrower is known as the interest rate, which is expressed as a percentage of the principal, or the loaned amount. Usually, the annual percentage rate (APR), which is how loans' interest rates are expressed, is indicated (APR).

Once your loan is fully repaid, interest will have an impact on the overall cost you pay. For instance, if the interest rate on a $100 loan is 5%, you will have to pay the lender $105 in order to repay the money. $5 will be profit for the lender.

To know more about Interest Rate visit:

https://brainly.com/question/13324776

#SPJ4

Answer:

14 cups

Step-by-step explanation:

3 + 6 = 9
9 + 4 = 13

13 + 1 = 14

14 plus fraction

To determine a mixture that will make the same shade of green but a smaller amount, we can divide both the yellow and blue amounts by the same number.

To solve this problem, we can use the principle of proportionality, which states that if two ratios are equal, then the quantities they represent are proportional.

A. To find a mixture that will make the same shade of green but a smaller amount, we can divide both the yellow and blue amounts by the same number. For example, if we divide both amounts by 2, we get 1 cup of yellow and 1.75 cups of blue. This will create a smaller amount of the same shade of green.

B. To find a mixture that will make the same shade of green but a bigger amount, we can multiply both the yellow and blue amounts by the same number. For example, if we multiply both amounts by 2, we get 4 cups of yellow and 7 cups of blue. This will create a larger amount of the same shade of green.

C. To find a mixture that will make a different shade of green that is bluer, we can increase the amount of blue relative to the amount of yellow. For example, we could use 2 cups of yellow and 4 cups of blue, which would create a green that is bluer than the original shade.

D. To find a mixture that will make a different shade of green that is more yellow, we can increase the amount of yellow relative to the amount of blue. For example, we could use 3 cups of yellow and 2 cups of blue, which would create a green that is more yellow than the original shade.

Learn more about proportions on:

brainly.com/question/1781657

#SPJ1

Diego rows 300 meters per minute

Information given in the question include

The graph shows the relationship between the time in the distant, Diego rows

The data is plotted as a linear function

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

The slope is represented as m, The slope by definition is the change of the output values to the input values

the slope, m calculating using the points on the graph (1, 300) and  (2, 600)

m = (y₀ - y₁) / (x₀ - x₁)

m = (600 - 300) / (2 - 1)

m = 300 / (1)

m = 300

The number of meters Diego rows per minute is solved to be 300

Learn more about slope of linear functions at:

https://brainly.com/question/20277632

#SPJ1

Answer:

The Answer is 20 inches tall

Answer:

Should be 1/12

Step-by-step explanation:

7/30x5/14

Simply multiply the numerators and denominators separately:

5/14× 7/30 = 5 × 7/14 × 30 = 35/420

After reducing the fraction, the answer is

1/12

Answer:

  19%

Step-by-step explanation:

You want the change from February to April if 4100 bottles were manufactured in February, 7% more were manufactured in March, and 500 more were manufactured in April.

The change from February to March is given as 7%.

The change from March to April is 500 bottles. In terms of the February quantity, this is ...

  500/4100 × 100% ≈ 12.2%

Then the total of changes from February to April is ...

  change = 7% +12.2% = 19.2% ≈ 19%.

The number of bottles manufactured increased by about 19% from February to April.

__

Additional comment

When working with percentages, one must always be aware of the base amount—what it is that represents 100%. Here, we know the 7% number for March uses the February value as its base.

Since we want a percent change from the February base, we can use that same base to find the percent difference from March to April. Then the total difference from February is the difference to March plus the difference from March to April.

<95141404393>

Answer:

C)w-3, w-1, w, w + 1, w+3

Step-by-step explanation:

I'm not great with standard deviation, but I know that the greater the standard deviation, the more spread out the data is.

C) is the correct answer, the data points do not repeat and are spread out more than A.

You can check this by calculated each standard deviation (but only if you are crazy ;] )

Hope this helps,

:]

The factorise quadratic equation x² + 18x + 45 = 0 is (x + 3)(x + 15)

A quadratic equation is a polynomial equation that contains the second degree, but no higher degree, of the variable.

Therefore, quadratic equation can be represented as follows:

ax² + bx + c

where

Hence, let's factorise x² + 18x + 45 = 0

x² + 18x + 45 = 0

Let's find the two numbers to add to get 18 and multiply to get 45

Therefore, the numbers are 3 and 15

x² + 18x + 45 = 0

x² + 3x + 15x + 45 = 0

x(x + 3) + 15(x + 3) = 0

(x + 3)(x + 15) = 0

learn more on quadratic equation here:https://brainly.com/question/29125439

#SPJ1

Answer:

12 hours

Step-by-step explanation:

1 pair per hour ?

The following are five different examples of parametric models: exponential distributions, poisson distributions, normal distributions, the Weibull distribution, and linear regressions.

Types of Parametric test–

To learn more about parametric refer to:

https://brainly.com/question/12297627

#SPJ1