Complete the identities.
1+cot²θ=

Answers

Answer 1

Answer:

[tex]\csc ^2(\theta)[/tex]

Step-by-step explanation:

Using Pythagorean identity,

[tex]\mathrm{1+\cot ^2(x)=\csc ^2(x)}\\\mathrm{=\csc ^2(\theta)}[/tex]

Answer 2

Answer:

1 + cot² θ = sec² θ

Step-by-step explanation:

1 + cot²θ =

I know this identity to be true:

sin² θ + cos² θ = 1

Divide both sides by sin² θ.

sin² θ / sin² θ + cos² θ / sin² θ = 1 / sin² θ

1 + cot² θ = sec² θ


Related Questions


Use the properties of exponential and logarithmic functions to solve each system. Check your answers.

2 x+y=16
4 x-y=1

Answers

The solved logarithmic function is log (2x + y) = 4 log (2) and log (4x - y) = 0 for 2x + y = 2⁴ and 4x - y = 1 respectively.

What is a logarithmic and exponential function?

Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet,  e. For example log 10 = 1 and e^2.

Solving the given expressions: 2x + y = 16 and 4x - y = 1

Applying given properties of logarithmic and exponential function;

log a + log b = log (ab)

4 log x = log x⁴

e^(log x) = 1

e^(x + y) = (e^x) × (e^y)

Take the expression, 2x + y = 16

Applying log on both sides, we get,

log (2x + y) = log (16)

log (2x + y) = log (2⁴)

log (2x + y) = 4 log (2)

To Check Results,

Taking exponential on both sides,

e^[log (2x + y)] = e^(4 log 2)

2x + y = e^(log 2⁴)

2x + y = 2⁴

2x + y = 16

Thus, the answer is verified.

Take expression, 4x - y = 1

Applying log on both sides, we get,

log (4x - y) = log 1

log (4x - y) = 0

To Check Results,

Taking exponential on both sides,

e^[log (4x - y)] = e^0

4x - y = 1

Thus, the answer is verified.

Hence, the solved expression is log (2x + y) = 4 log (2) and log (4x - y) = 0 for 2x + y = 2⁴ and 4x - y = 1 respectively.

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#1 You are in charge of ordering hats for a youth
baseball team. Each hat costs $22.50. There are at
least 10 but no more than 16 players on the
baseball team. The total cost of ordering hats can
be modeled by the function f(x)=22.50x,
where x represents the number of hats ordered. answer

Answers

The range of the function f(x) = 2.250x is 22.5 <= f(x) <= 36

What is the range of a function?

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

How to determine the range of the function?

The function is given as

f(x) = 2.250x

Where there are at least 10 but no more than 16 players on the baseball team

This means that the domain of the function is

10 <= x <= 16

Substitute the domain values in the given function

So, we have

f(x) = 2.250x

f(10) = 2.250 * 10

Evaluate

f(10) = 22.5

f(x) = 2.250x

f(16) = 2.250 * 16

Evaluate

f(16) = 36

The range of the function is then represented as

f(10) <= f(x) <= f(16)

So, we have

22.5 <= f(x) <= 36

Hence, the range of the function f(x) = 2.250x is 22.5 <= f(x) <= 36

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Complete question

ou are in charge of ordering hats for a youth baseball team. Each hat costs $22.50. There are at least 10 but no more than 16 players on the baseball team. The total cost of ordering hats can be modeled by the function f(x)=22.50x, where x represents the number of hats ordered.

What is the range of the function?

3. Kaitlin has two puppies. Puppy A
weighs 12 pounds and is gaining
1.5 pounds each week. Puppy B
weighs 18 pounds and is gaining
0.75 pounds each week. How
many weeks, x, will it take for
the two puppies to weight the
same amount? put in a equation or inequality

Answers

Answer:

X = 8

Step-by-step explanation:

On a fantasy football team the Titans score is 11.15 points and a running back score is 11.75 points a wide receiver score is 1.05 points less than the run pack how many total points do three players scored

Answers

Answer: The total would be 33.6 points.

Step-by-step explanation:

Titans Score: 11.15

Running Back Score: 11.75

Wide Receiver: 1.05 less than Running Back (11.75 - 1.05), which would be 10.7 points.

11.15 + 11.75 + 10.7 = 33.6 total points

Answer: the problem was a little confusing but I'm assuming the answer is 10.7 making the final answer 32.97

Step-by-step explanation: if the titans scored (11.15) points and the running back scores (11.75) points and the wide receiver scores 1.05 points less then the running back it would be...

  11.75 (the running backs points)

- minus

  1.05

__________

=10.07(how many points the wide receiver had)

Then 10.07+ 11.15+ 11.75=32.97

Hope I got it right! <3

The two triangles displayed are scaled copies of one another. Find the scale factor.

Answers

Answer: 6

Step-by-step explanation:

what is the gravity of someone falling down ​

Answers

Answer: free fall

Step-by-step explanation: A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name.

Determine which line the point (2,-1) lies on.

Answers

Answer:

the point will not lie on any line. it will come in the first coordinate

ASAP PLEASE HELP IF RIGHT ANSWER WILL GIVE BRAINLIEST, 15 POINTS, AND 5 STAR OVERALL!!!! IF WRONG ANSWER OR INVALID WILL REPORT, PLEASE, PLEASE, PLEASE!!
Which graph best represents the solution set of y ≤ 3/4x − 4?

Answers

The graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)

What are inequality expressions?

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

How to determine the graph of the inequality expression?

The inequality expression is given as

y ≤ 3/4x − 4

The inequality symbol in the above inequality expression is

This implies that the inequality expression is a less than or equal to

When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line

Also, the inequality symbol implies that the bottom part is shaded

Hence, the graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)

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What is the greatest common factor of 9 and 48?

Answers

Answer:

3 is the greatest common factor that can go into 9 and 48

The greatest common factor of 9 and 48 is 3.

What is the greatest common factor?

The greatest common factor (GCF) is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that is a factor of both (or all) of the given numbers.

For example, the GCF of 12 and 18 is 6, beca

To find the greatest common factor (GCF) of 9 and 48, we need to determine the largest number that both 9 and 48 can be divided by evenly.

We can start by listing the factors of each number:

9: 1, 3, 9

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Then we can look for the greatest factor that appears in both lists. In this case, the greatest common factor of 9 and 48 is 3, since it is the largest number that appears in both lists of factors.

Therefore, the GCF of 9 and 48 is 3.

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What is the multiples of 2/5

Answers

Answer:

Step-by-step explanation: 2x5=10

:) have a good day

Need the answer for the function as stated in the photo

Answers

The average rate of change of [tex]f[/tex] over an interval [tex][a,b][/tex] is the difference quotient

[tex]\dfrac{f(b) - f(a)}{b - a}[/tex]

Over the interval [tex]3\le x\le5[/tex], we have

[tex]\dfrac{f(5) - f(3)}{5 - 3} = \dfrac{27 - 3}{5 - 3} = \dfrac{24}2 = \boxed{12}[/tex]

what is the missing value in x^2 y^8 times x^3 y^? = x^5 y^5?

Answers

Hence , the missing value y  in x^2 y^8 times x²y⁸ x³ y = x⁵ y⁵ is -3 .

Definition of law of exponents

- one in every of a collection of rules in algebra: exponents of numbers are additional once the numbers are increased, subtracted once the numbers are divided, and increased once raised by still another exponent: a^m × aⁿ = a^(m+n)

We have given an expression x²y⁸ x³ y = x⁵ y⁵ .

LHS  = x²y⁸ x³ yⁿ

Let the power of y in LHS be "n" .

On using exponents rule , we get

LHS  = x⁵y⁹⁺ⁿ

RHS =  x⁵ y⁵

As LHS = RHS

x⁵y⁹⁺ⁿ =  x⁵ y⁵

On comparing power of y  , we get

 9 + n = 5

      n = -3

Hence , the power of y in LHS is -3 .

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Are ∠2 and ∠5 vertical angles? Explain your reasoning.

Answers

Answer:

no

Step-by-step explanation

an example of vertical angles would be 6 and 8

pls give brainliest :)

Four stores are having a sale on cans of Sprite. The sale prices are listed below:
Shop A: 6 cans for $5.10
Shop B: 6 cans for $5.70
Shop D: 12 cans for $10.80
Shop C: 12 cans for $9.60
Which store has the best buy?

Answers

Answer:

Shop C

Step-by-step explanation:

Without any calculations, you can eliminate stores B and D.

Shop A: $5.10/6 = $0.85/can

Shop C: $9.60/12 = $0.80/can

Answer:

It would be B

Step-by-step explanation:

Because A is 1.17 per can

B is 1.05 per can

D is 1.11 per can

and C is 1.25 per can


Simplify each radical expression. Use absolute value symbols when needed. ∛-0.027

Answers

The simplified form is -0.3.

As an instance, 3√(8) method to locate the diced root of 8. If there may be no superscript range, the novel expression is asking for the rectangular root. The term underneath the unconventional image is referred to as the radicand.

An intensive expression is an expression containing a rectangular root. Radicand - a variety of expressions in the radical symbol. Radical equation - An equation containing radical expressions with variables inside the radicands.

A few examples of radicals are √7, √2y+1, etc. an intensive also can be associated with the subsequent terms: An equation this is inside a radical is referred to as a thorough equation. An expression that lies interior a rectangular root is referred to as an intensive expression.

Applying radical rule,

[tex]\sqrt[n]{-a} =-\sqrt[n]{a} \\\sqrt[3]{-0.027}=-\sqrt[3]{0.027}\\ = -0.3[/tex].

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11. Chris buys six guppies. Every month his guppy population doubles. [4]
a) How many guppies will there be after 1 month? 2 months? 3 months?
b) Create a formula that would express the statement above. In your formula let n
equal the number of months, and G equal the total population of guppies.
c) How many guppies will there be after 6.5 months?
d) Can the fish population continue to grow at this rate? Explain

Answers

Answer:

G = 6(2)^n

Step-by-step explanation:

a) At 1 month he will have 12 guppies, at 2 months he will have 24 guppies and at 3 months he will have 48 guppies.

b) G = 6(2)^n

This is following the exponential formula.

c) G = 6(2)^6.5 = 543 guppies

d) At this rate, there will be no room for the guppies to continue growing.

SOLVE THE FOLLOWING EQUATION FOR Y

Answers

Answer: 74

Step-by-step explanation: calculator

Distance between (4,2) and (-3,4)

Answers

it is 22 units <3 your welcome

I think the answer is 7.28010988
4 - (-3) = 7^2 = 49
2- 4 = -2 ^ -2 = 4
Then we add them and get 53.
Since the number isn't a perfect square we have to use the perfect square of other numbers to find the decimal for this number. We have a square root of 49 is 7. Then we have the square root of 64 is 8. So our number has to be 7. Something.

pls help me..................

Answers

Hello.
With what?

~Roni

Answer:

$142.60

Step-by-step explanation:

an increase of 15% on the original cost of 100% means

percentage increase = 100% + 15% = 115% , then

cost = 115% × $124 = [tex]\frac{115}{100}[/tex] × $124 = 1.15 × $124 = $142.60

What is the remainder when 316 is divided by 13?

Answers

Answer:

24 reminder 4

Step-by-step explanation:

Reminder is 4

316/13 = 24 R 4

Which is a benefit of being an employee paid commission?
You receive more paid time off than other types of pay.
Excellent job performance is rewarded with higher pay.
The work schedule is typically weekdays 9:00 a.m. to 5:00 p.m.
Commission is typically paid monthly making budgeting easier.

Answers

Answer:b

Step-by-step explanation:

b

A benefit of being an employee paid commission is option B.) “Excellent job performance is rewarded with higher pay.”

The Oxford Dictionary quotes that the denotation of a commission is “an amount of money, typically a set percentage of the value involved, paid to an agent in a commercial transaction.” When an employee is paid commission, it often is because he or she has worked hard, done extra work, or simply had excellent job performance.

Hence, option B is a benefit of being an employee paid commission.

Aisha buys 2 packets of bread rolls costing £1.20 for each packet 1 bottle of ketchup costing £2.10 3 packets of biscuits Aisha pays with a £10 note. She gets 70p change. Work out the cost of one packet of biscuits. You must show how you get your answer. Optional working Answer: £|​

Answers

The cost of one packet of biscuit is £1.60.

What is the cost of one packet of biscuit?

The total amount that Aisha paid for the items she purchased is a function of the total cost of bread rolls, ketchup and biscuits.

Total cost of the items purchased = total cost of bread rolls + total cost of biscuits + total cost of ketchup

Total cost of bread rolls = cost per packet x number of packets bought

2 x £1.20 = £2.40

Total cost of ketchup = cost of one bottle x number of bottles bought

1 x £2.10 = £2.10

Total cost of biscuits = cost of one packet  x number of packets bought

3 x b = 3b

Total cost = £2.40 + £2.10 + 3b = £4.50 + 3b

Total amount paid by Aisha = note given - change received

£10 - 70p

£10 - £0.70 = £9.30

Total amount paid by Aisha =  total cost

£9.30 = £4.50 + 3b

£9.30 - £4.50 = 3b

£4.80 = 3b

b = £4.80 / 3

b = £1.60

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Death valley is a desert in northern california with many place of interest. one such place is the badwater basin, the elevation is
-282 feet. at another location, salt creek trail, the elevation is-220 feet. write an inequality to compare the elevations and state
which elevation is closer to sea level.

Answers

The inequality comparing the elevations is -220 > -282  and -220 feet is closer to sea level.

The elevation of Bad Water Basin = -282 feet

The elevation of the Salt Creek = -220 feet

We are asked to compare the elevations and find which is greater than the other.

So we know that on a number line -220 is greater than -282.

This can be understood in the same sense that -1 > -2 on the number line.

So the inequality comparing the elevations is -220 > -282.

Now consider the sea level as 0 on the number line.

Then clearly -220 is closer to 0 on number line.

Hence the elevation closer to the sea level = -220 feet.

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How many minutes have passed, m, when Tank A contains the following amounts of water?
a. 151 liters
b. 191.5 liters
c. 270.25 liters
d. p liters

Answers

The minutes that have passed, m, when Tank A contains the following amounts of water will be:

151 liters = 3 minutes

191.5 liters = 7.5 minutes

270.25 liters = 16.25 minutes

p liters = (p-124) / 9 min

How to calculate the minutes?

It should be noted that for 151 lit = (151 - 124)/9 = 3 min

Also, for 191.5 lit = (191.5-124) /9

= 67.5/9 = 7.5 min = 7 min 30 sec

It should be noted that for 270.25 lit = (270.25 - 124)/9 = 146.25/9 = 16.25 = 16 min 15 sec

For p lit = (p-124) / 9 min

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Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.

How many minutes have passed, m, when Tank A contains the following amounts of water?

151 liters

191.5 liters

270.25 liters

p liters

Follow • 1


Solve each equation.
3x⁺²=27²x

Answers

After solving the equation, x = 2/5 is the value of x in [tex]3^{X+2} = 27^{2x}[/tex]

⇒ [tex]3^{X+2} = 27^{2x}[/tex]

⇒ [tex]3^{X+2} = ((3)^3)^{2x}[/tex]

⇒ [tex]3^{X+2} = (3)^{6x}[/tex]

⇒ [tex]3^{X+2} = (3)^{6x}[/tex]

⇒ x+2 = 6x

⇒ 2 = 6x - x

⇒ 2 = 5x

x = 2/5

How to solve an equation?

To solve linear equations, utilize the steps that are provided below.

Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Write the ratio that compares the championships won by Australia to the total number of championships. Then explain it's meaning

Answers

The ratio that compares the championship won by Australia to the total number of championship is 6/41 which means that of the total 41 championship Australia has won 6 of the championship.

According to the question we have been given that,

 Total number of championship = 41

  Total number of championship won by Australia = 6

Thus we need to find the ratio that compares the championship won by Australia to the total number of championship.

For this the ratio will be :   [tex]\frac{number of championship won by Australia}{Total number of championship }[/tex]

                                       = 6/41

Hence the ratio that compares the championship won by Australia to the total number of championship is 6/41 which means that of the total 41 championship Australia has won 6 of the championship.

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Write each logarithmic expression as a single logarithm.

(2logbx/3 + 3logby / 4) - 5logbz

Answers

The value of logarithmic expression (2logbx/3 + 3logby / 4) - 5logbz is logbx/3^2(by / 4)^3/logbz^5.

By considering the given logarithmic expression

(2logbx/3 + 3logby / 4) - 5logbz

logb(x/3)^2 +log(by / 4)^3-log(bz)^5

logb(x/3)^2(by / 4)^3-logbz^5

logbx/3^2(by / 4)^3/logbz^5

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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Let athe event of getting at least one defective calculator when four are randomly selected with replacement from a batch. Write a statement describing event

Answers

Answer: do you have a pic??

Step-by-step explanation:

in science class, zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution

Answers

When zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 1/5 degrees as the. ending temperature, the change in temperature is 1/2 degree.

How to illustrate the information?

It should be noted that from the information, science class, zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 9/10 degrees as the. ending temperature.

Therefore,the change in temperature will be the subtraction of the temperature given. This will be illustrated as:

= 1/5 - (-3/10)

= 1/5 + 3/10

= 2/10 + 3/10

= 5/10

= 1/2

The change on temperature is 1/2 degree.

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In science class, zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 1/5 degrees as the. ending temperature. What was the change in temperature?

Megan is thinking of a number that is divisible by both 9and 7. What is the smallest possible number that Megan is thinking?

Answers

Answer:

Step-by-step explanation:

63
because 9x7=63

and 7x9=63

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