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Answer: Since y = tan θ = y / x , and y and x are coordinates of a point, y can be any real number and x can be any real number except 0. Thus, the ratio y / x can be any real number, and we conclude that the range of y = tan θ is all real numbers. ... y = csc θ = r/ y , since sin θ and csc θ are reciprocals of one another.

Step-by-step explanation:

Since y = tan θ = y / x , and y and x are coordinates of a point, y can be any real number and x can be any real number except 0. Thus, the ratio y / x can be any real number, and we conclude that the range of y = tan θ is all real numbers. ... y = csc θ = r/ y , since sin θ and csc θ are reciprocals of one another.

The period of the function is the interval between repetitions of any function. A trigonometric function's period is the length of one whole cycle. As a starting point, we can use x = 0 for any trigonometry graph function. Trigonometric functions have a periodic nature. As opposed to tangent and cotangent, which have period, sine, cosine, secant, and cosecant all have period 2.

Studying the correlations between triangle side lengths and angles is the subject of trigonometry, a branch of mathematics. By using geometry to study astronomy, the field first appeared in the Hellenistic civilization during the third century BC. The earliest documented tables of values for trigonometric ratios (sometimes called trigonometric functions) such as sine were developed by mathematicians in India, while the Greeks concentrated on chord calculation.

Geodesy, surveying, celestial mechanics, and navigation are just a few of the fields where trigonometry has been used historically. The various identities of trigonometry are well recognized.

These trigonometric identities are frequently used to simplify, discover a more practical form for, or solve equations involving trigonometric expressions.

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complete question:

Explain what is meant by the period of a trigonometric function. what are the periods of the six trigonometric functions?

Answer:

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

To solve for the variable, we must isolate the variable, which is x.

[tex]\sqrt{x+4} -3=1[/tex]

3 is being subtracted from the square root of x+4. The inverse of subtraction is addition. Add 3 to both sides of the equation.

[tex]\sqrt{x+4} -3+3=1+3[/tex]

[tex]\sqrt{x+4} =1+3[/tex]

[tex]\sqrt{x+4} =4[/tex]

The square root of x+4 is being taken. The inverse of a square root is a square. Square both sides of the equation.

[tex](\sqrt{x+4})^2 =4^2[/tex]

[tex]x+4=4^2[/tex]

Evaluate the exponent.

4^2= 4*4=16

[tex]x+4=16[/tex]

4 is being added to x. The inverse of addition is subtraction. Subtract 4 from both sides of the equation.

[tex]x+4-4=16-4[/tex]

[tex]x=16-4[/tex]

[tex]x=12[/tex]

The solution to this equation is x=12.

[tex]\\ \sf\longmapsto b^2x^2+a^2y^2[/tex]

[tex]\\ \sf\longmapsto b^2(asin\Theta)^2+a^2(bcos\Theta)^2[/tex]

[tex]\\ \sf\longmapsto b^2a^2sin^2\Theta+a^2b^2cos^2\Theta[/tex]

[tex]\\ \sf\longmapsto a^2b^2(sin^2\Theta+cos^2Theta)[/tex]

[tex]\\ \sf\longmapsto a^2+b^2(1)[/tex]

[tex]\\ \sf\longmapsto a^2b^2[/tex]

Answer:

Divide by -8.

Step-by-step explanation:

48 is a multiple of 8, an we are trying to isolate p, so you should divide both sides by +/- 8.

Answer:

Step-by-step explanation:

You would do 48 divided by -8, and your answer would be -6

And just to clarify, -8 times -6 = 48. (You can use a calculator if still unsure)

Answer:

(1c times 9/5) +32

That is the way  to figure out °1c as 33.8°

Hope it helped

Answer:

0.07245

Step-by-step explanation:

Just work out 345*21 and then divide by 10,000 because 0.345 is 3 digits from zero and 2.1 has 1 digit from zero, so total of 4 zeroes (10,000 since 10,000 has 4 zeroes).

Answer:

(B) 9π in²

Step-by-step explanation:

I’m going to assume that by 6 inches you meant 6π inches.

If the circumference of a circle is 6π inches, then it’s radius will be half of 6 (because the circumference of a circle is [tex]2\pi r[/tex]).

[tex]6\div2=3[/tex]

So the radius is 3.

Now that we know the radius, we can find the area by using the equation [tex]\pi r^2[/tex].

[tex]\pi 3^2\\\pi9\\9\pi[/tex]

Hope this helped!

Answer:

Step-by-step explanation:

2πr = 6, r = 3/π

πr² = π(3/π)² = 9/π in.²

Answer:

[tex]\frac{14}{55}[/tex]

Step-by-step explanation:

note that

n! = n(n - 1)(n - 2) .... × 3 × 2 × 1

Given

[tex]\frac{8!9!}{5!12!}[/tex]

Cancel the terms from 8! ( 5 × 4 × 3 × 2 × 1 ) with the same terms from

5! ( 5 × 4 × 3 × 2 × 1 ) leaving

8 × 7 × 6 = 336 on the numerator

Similarly

Cancel the terms from 9! and 12!

leaving 12 × 11 × 10 = 1320 on the denominator, thus simplifies to

[tex]\frac{336}{1320}[/tex]

= [tex]\frac{14}{55}[/tex]

Answer:

Step-by-step explanation:

So we know that there are 213 oranges and Theresa fills each bag with 3 oranges, so we can represent each bag as 3x. She keeps filling until she reaches 51 oranges.

First. let's write this as an equation, She is starting with 213 oranges and filling x bags with 3 oranges to the point she has less than 51 oranges.

213 - 3x < 51

Now add 3x to both sides,

213 - 3x + 3x < 51 + 3x

213 < 51 + 3x

Now we subtract 51 from both sides,

213 - 51 < 51 - 51 + 3x

162 < 3x

Now we divide both sides by 3,

162/3 < 3x/3

We find the answer,

54 < x

x > 54 bags

If both are complementary then their sum will be 90°

[tex]\\ \sf\longmapsto m<A+m<B=90[/tex]

[tex]\\ \sf\longmapsto 2x-10+x-2=90[/tex]

[tex]\\ \sf\longmapsto 2x+x-10-2=90[/tex]

[tex]\\ \sf\longmapsto 3x-12=90[/tex]

[tex]\\ \sf\longmapsto 3x=90+12[/tex]

[tex]\\ \sf\longmapsto 3x=102[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{102}{3}[/tex]

[tex]\\ \sf\longmapsto x=34[/tex]

Now

[tex]\\ \sf\longmapsto <A=2x-10=2(34)-10=68-10=58[/tex]

Answer:

Both ends go down

Step-by-step explanation:

The end behavior of the function are Both ends go down. Therefore, Option C is true.

Given that,

The function is,

[tex]f (x) = - 2 (x - 17)^4[/tex]

Now the given function is defined at x → ∞,

f (x) = - 2 × ∞

f (x) → - ∞

As x goes to -∞

f(-∞) = -2(-∞)⁴

= -2 (∞)

= -∞

So, Both ends go to  -∞, or go down

Hence, The end behavior of the function are Both ends go down.

Therefore, Option C is true.

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Answer:

-2 + 2i

Step-by-step explanation:

[tex](1 + i)^{3}[/tex]

i = [tex]\sqrt{-1}[/tex]

[tex](1 + \sqrt{-1})^3[/tex]

[tex][(1 + \sqrt{-1})(1 + \sqrt{-1})] (1 + \sqrt{-1})[/tex]

distribute the first 2 expressions

(1 + 2[tex]\sqrt{-1}[/tex] - 1 ) [tex](1 + \sqrt{-1})[/tex]

distribute

1 + 2[tex]\sqrt{-1}[/tex] - 1 +

combine like terms

-2 + 2 [tex]\sqrt{-1}[/tex]

which is -2 + 2i

Answer:

x = 0

y = -2

Step-by-step explanation:

2304.06 is written in expanded form

4 is unit place. So, 4 *10⁰ = 4 * 1 = 1    {Any integer to the power of 0 is 1}

x = 0

6 is hundredth place = 6 * 1/100 = 6*10⁻²

y= -2

Answer:

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Step-by-step explanation:

Answer:

Rs 400

Step-by-step explanation:

Let us assume that the cost price of the article = x

Selling price = S.P

Cost price = C.P

Loss = %Loss × C.P(percentage loss × Cost Price)

S.P = C.P - Loss

In the question, Loss = 20%

S.P = x - 20x/100

Find the Lowest Common Multiple

S.P= 100x - 20x/100

S.P = 80x/100.........Equation 1

In the question, we are told if the article was sold for RS 160 more, it would have made a profit of 20%

Profit = %profit × C.P(percentage profit × Cost Price)

S.P = C.P + Profit

In the question, profit = 20%

S.P = x + 20x/100

Find the Lowest Common Multiple

S.P= 100x + 20x/100

S.P = 120x/100.........Equation 2

Hence,

Equation 2 - Equation 1 = Rs 160

= 120x/100 - 80x/100 = 160

= 40x/100 = 160

Cross multiply

40x = 100 × 160

40x = 16000

x = 16000/40

x = Rs 400

Since x = Cost price, the cost price of the table = Rs 400

Answer:

$19.15

Step-by-step explanation:

$1=0.626

$1/0.626=£1

$11.99=$11.99/0.626

=$19.15

Answer:

Step-by-step explanation:

 £ 0.626  =$ 1

£1 = $ [tex]\frac{1}{0.625}[/tex]

£ 11.99 = [tex]11.99*\frac{1}{0.625}= \frac{11.99*1000}{0.625*1000}\\\\[/tex]

           [tex]= \frac{11990}{626}\\\\[/tex]

          = $ 19.15

19.15 - 16.95 = $2.2

Jane pays $2.20  more dollars that George

Answer:

(mn+3m)(n+p)

Step-by-step explanation:

Answer:

(mn + 3m)(n + p)

Step-by-step explanation:

Factorize by grouping:

[tex]mn^2+mnp\\mn(n+p)\\\\3mn+3mp\\3m(n+p)\\\\(mn+3m)(n+p)[/tex]

Answer:

Step-by-step explanation:

Given the  ratio of  the profit, cost of  materials and labour  in the production of

an article to be 5:7:13 respectively, total ratio = 5+7+13 = 25

If the cost of labour is x, the cost of material will be 840+x (since the  cost of materials is Le  840 more than that of  labour)  .

Let the total cost of producing the article be y.

Cost of labour = 13/25 * y = x

Cost of labour  = 13y/25 = x.................... 1

Cost of material = 7/25*y = 840+x

Cost of material = 7y/25 = 840+x ..................... 2

From 1, 13y = 25x

x = 13y/25 ................... 3

Substituting equation 3 into 2:

7y/25 = 840+x

7y/25 = 840+13y/25

collect the like terms:

7y/25 - 13y/25 = 840

-6y/25 = 840

-6y = 25*840

y = 25*840/6

y = 3,500

Hence the total cost of producing the article is 3500

Step-by-step explanation:

1.answer is 6.9667738478

2 answer is 42.872454448

3answer is 14.1339764202

4answer is 0.0857449089.

Answer: 58unit²

Step-by-step explanation:

We will take 1 square as 1 unit

We will count the number of squares in in this figure.

Total squares = 58

Area = 58unit²

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Step-by-step explanation:

the absolute value simply removes a negative sign, if there is one. if there is no negative sign, it leaves the argument untouched.

so, we need to calculate the argument first :

2b + 4 = 2×-8 + 4 = -16 + 4 = -12

|-12| = 12

that's it.

Answer:

The greatest common factor is x

Step-by-step explanation:

Dimensions: x,x+1,x+8

Multiplication of thee dimensions:

⇒ Product      =   [tex]x(x+1)(x+8)\\x(x^{2}+8x+1x+8)\\x(x^{2} +9x+8)\\x^{3} +9x^{2} +8x[/tex]

By factorization ,

[tex]x^{3} +9x^{2} +8x\\x(x^{3} +9x+8)[/tex]

Therefore, the greatest common factor of these terms are x

Given Dimensions:

[tex]\to \bold{x, x+1,\ and\ x+8}[/tex]

Multiplying the three dimensions:

[tex]\to x(x+1)(x+8)\\\\\to x(x^2+ 8x+x+8)\\\\\to x(x^2+9x+8)\\\\\to x^3+9x^2+8x\\\\[/tex]

Therefore, the "greatest common factor" of the term is x.

Learn more:

Factor: brainly.com/question/18877132

Answer:

your inequality signs are correct so i'll skip those

-2.06, .9803

.67, .7486

Step-by-step explanation:

1.)

To do this one you need to standardize x by subtracting the mean and dividng by the standard deviation

(1000-3262)/1100= -2.056 which i will round to -2.06

with this as our z value use the table to find the associated probability

.9803

2.)

Same process

(4000-3262)/1100=.67

which has a probability of .7486

Answer:

Step-by-step explanation:

Given the expression (8x² −15x)−(x² −27x) = ax² +bx, we are to determine the value of b-a. Before we determine the vwlue of b-a, we need to first calculate for the value of a and b from the given expression.

On expanding the left hand side of the expression we have;

= (8x² −15x)−(x² −27x)

Open the paranthesis

= 8x² −15x−x²+27x

collect the like terms

= 8x²−x²+27x −15x

=  7x²+12x

Comparing the resulting expression with ax²+bx

7x²+12x =  ax²+bx

7x² = ax²

a = 7

Also;

12x = bx

b =12

The value of b - a = 12 - 7

b -a = 5

Hence the value of b-a is equivalent to 5

The value of b minus a is 5

Since the expression is

[tex](8x^2 -15x)-(x^2 -27x) = ax^2 +bx[/tex]

Here we have to expand the left-hand side of the expression so it should be like

[tex]= (8x^2 -15x)-(x^2 -27x)\\\\= 8x^2 -15x-x^2+27x\\\\= 8x^2-x^2+27x -15x\\\\= 7x^2+12x[/tex]

Now

[tex]7x^2+12x = ax^2+bx\\\\7x^2 = ax^2[/tex]

a = 7

Also;

12x = bx

b =12

So,

The value of b - a = 12 - 7

b -a = 5

Hence the value of b-a should be 5

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Answer:

67.02

Step-by-step explanation:

Answer:

classified info jk juss use a mf calculater

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

If n represents the amount of flowers they sold, then the correct answer should be 32. The cost for each flower they sold would be 3 x 4 and then add $20 for advertising.

Answer:

3 + 2y = 2 + 4y

Step-by-step explanation:

1. Create the equation

3 + 2y = 2 + 4y

There are 3 "1" blocks and 2 "y" blocks on the left. There are 2 "1" blocks and 4 "y" blocks on the right. The scale shows both are equal.

Answer:

3 + 2y = 2 + 4y

Step-by-step explanation:

To create an equation from this model, we look at both sides of the scale. The left has three 1 units and two y units, and there are two 1 units and four y units on the right side. Since the scale shows that both sides are equal in weight, we know that our equation would have an equal sign to show they are equal.

Left: Three 1 units can be written as 3 and two y units could be written as 2y.

Right: Two 1 units can be written as 2 and four y units could be written as 4y.

Now, we put these values together (with an equal sign) to get:

3 + 2y = 2 + 4y.

Hope this helps!

Answer:

Cos A =1.4

Step-by-step explanation:

3sinA=5-4cosA; square both sides: 9sin^2(A)=25-40cosA+16cos^2(A);

9-9cos^2(A)=25-40cosA+16cos^2(A); 25cos^2(A)-40cosA+16=0=(5cosA-4)^2.

cosA=4/5 so sinA=3/5 (√(1-16/25) and sinA+cosA=7/5=1.4.