[PRECALC] Verify the following trigonometric identity using sin2x + cos2x = 1

Answer:

[tex]a_n=3n-2[/tex]

Step-by-step explanation:

General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]

where:

Create expressions for the 4th and 6th terms:

[tex]\implies a_4=a+(4-1)d=a+3d[/tex]

[tex]\implies a_6=a+(6-1)d=a+5d[/tex]

The ratio of the 4th term to the 6th term is 5:8, therefore:

[tex]\implies \dfrac{a_4}{a_6}=\dfrac{5}{8}[/tex]

[tex]\implies \dfrac{a+3d}{a+5d}=\dfrac{5}{8}[/tex]

[tex]\implies 8(a+3d)=5(a+5d)[/tex]

[tex]\implies 8a+24d=5a+25d[/tex]

[tex]\implies 8a-5a=25d-24d[/tex]

[tex]\implies 3a=d \quad \leftarrow \textsf{Equation 1}[/tex]

Sum of the first n terms of an arithmetic series:

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

The sum of the first 7 terms of an arithmetic progression is 70:

[tex]\implies S_7=70[/tex]

[tex]\implies \dfrac{7}{2}[2a+(7-1)d]=70[/tex]

[tex]\implies 2a+6d=20[/tex]

[tex]\implies a+3d=10 \quad \leftarrow \textsf{Equation 2}[/tex]

Substitute Equation 1 into Equation 2 and solve for [tex]a[/tex]:

[tex]\implies a+3(3a)=10[/tex]

[tex]\implies a+9a=10[/tex]

[tex]\implies 10a=10[/tex]

[tex]\implies a=1[/tex]

Substitute found value of [tex]a[/tex] into Equation 1 and solve for [tex]d[/tex]:

[tex]\implies 3(1)=d[/tex]

[tex]\implies d=3[/tex]

Finally, substitute found values of [tex]a[/tex] and [tex]d[/tex] into the general form of the arithmetic sequence:

[tex]\implies a_n=1+(n-1)3[/tex]

[tex]\implies a_n=1+3n-3[/tex]

[tex]\implies a_n=3n-2[/tex]

Answer:

6.25 bags of popcorn

Answer:

6.25 Bags

or

6 whole bags

Step-by-step explanation:

= 25 * 0.25 <-- (This is how you write percentage algebraically)

= 6.25 Bags

Answer:

560

Step-by-step explanation:

16 times 5 times 4=320

6 times 16 divide 2 then multiple 5

Answer:

The correct answer is:

P(nuts)=7/9

Step-by-step explanation:

The experimental probability that the next sundae sold will have nuts is

7/9

Experimental probability calculates the probability of some event from the results of experiments.

For an event E, we get the experimental probability of that event

[tex]P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}[/tex]

where, [tex]P_e(E)[/tex]  is denoting the experimental probability of occurrence of E.

We are given that At Frosty Freeze, 14 of the last 18 sundaes sold had nuts.

Therefore,

Probability that the next sundae has nuts is 14/18 = 7/9.

Thus, Probability that the next sundae does not have nuts = 2/9

P(nuts)=7/9

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Answer:

g

Step-by-step explanation:

Answer:

3 cm

Step-by-step explanation:

Formula :

Given :

Solving :

[tex]\tt 3(x+2)-9=15-4(5x-2)[/tex]

To solve this equation, let's apply the distributive property:-

Multiple 3 by ( x+2)/ Subtract 9 from 6 = -3/ and then use the distributive property to multiply −4 by (5x-2) :-

[tex]\tt 3x - 3=15 - 20x+8[/tex]

Add 15 and 8 = 23

[tex]\tt 3x - 3=23 - 20x[/tex]

Now, add 20x to both sides:-

[tex]\tt 3x - 3=23 - 20x[/tex]

Combine like terms:-

[tex]\tt 23x-3=23[/tex]

Add 3 to both sides:-

[tex]\tt 23x=23+3[/tex]

[tex] \tt 23x=26[/tex]

Divide both sides by 23:-

[tex]\tt \: x = \dfrac{26}{23} [/tex]

- :)

Answer:

There are many ways to describe a data set using a single measure. Some common ways are to find the mean, median, or mode of the data set.

Step-by-step explanation:

A single measure can be used to describe a data set in the form of a statistic. This statistic can be used to measure the central tendency, dispersion, or shape of the data set. For example, the mean can be used to describe the central tendency of a data set, while the standard deviation can be used to describe the dispersion of a data set.

Answer:

x = 10.

Step-by-step explanation:

By similar triangles:

3x - 5 / (3x - 5 +10) = 20 / 28

3x-5 / 3x+5 = 5/7

7(3x - 5) = 5(3x + 5)

21x - 35 = 15x + 25

6x = 60

x = 10.

Answer:

x= 10

Step-by-step explanation:

By similar triangles:

3x - 5 / (3x - 5 +10) = 20 / 28

3x-5 / 3x+5 = 5/7

7(3x - 5) = 5(3x + 5)

21x - 35 = 15x + 25

6x = 60

x = 10.

Answer:

Domain = x ≥ 0

Range = f( x ) ≥ 1

Step-by-step explanation:

The graph starts from 0 in the x - axis and 1 in the y hence the given domain and range.

Answer:

  1, 5, 10, 10, 5, 1

Step-by-step explanation:

The coefficients for the expansion of the 5th power of a binomial are found on the 5th row of Pascal's triangle. They are ...

  1, 5, 10, 10, 5, 1

__

Algebraically, they are computed using the formula for 5 things taken k at a time:

  5!/(k!(5-k)!)

Answer: 921 bags

Step-by-step explanation:

      We will subtract bags used from the total number of bags.

953 - 32 = 921

        The bakery still has 921 bags of sugar.

Answer:

Step-by-step explanation:

Given circle with area of:

Find its radius

Substitute the values and find the value of r:

Now compare this with answer choices:

Answer:

c

Step-by-step explanation:

Answer:

the 3rd choice

Step-by-step explanation:

Answer: 11.8 km

Step-by-step explanation:

The resulting figure is a right angled triangle shown below

[tex]$$Apply the Pythagorean theorem to find out the magnitude of the resultant vector $A B$ in the triangle $A B C$ as follows -$$\begin{aligned}&A B^{2}=B C^{2}+C A^{2} \text { (Hypotenuse }{ }^{2}=\text { Base }^{2}+\text { Adjacent }^{2} \text { ) } \\&=7.4^{2}+9.2^{2} \\&=139.4 \\&A B=11.806777 \\&\quad A B \approx 11.8 \mathrm{~km} \text { (Rounded off to the nearest tenth) }\end{aligned}$$[/tex]

Answer:

A) The amount of money deposited monthly

Step-by-step explanation:

y = 35x (slope) (amount deposited each month)+ 250 (y-intercept) (starting amount)

Step-by-step explanation:

First, use the Pythagorean theorem to find cos x.

[tex] \sin {}^{2} (x) + \cos {}^{2} (x) = 1[/tex]

[tex] (\frac{7}{9} ) {}^{2} + \cos {}^{2} (x) = 1[/tex]

[tex] \cos {}^{2} (x) = 1 - \frac{49}{81} [/tex]

[tex] \cos {}^{2} (x) = \frac{32}{81} [/tex]

[tex] \cos(x) = \frac{4 \sqrt{2} }{9} [/tex]

Now, use the quotient identity

[tex] \tan(x) = \frac{ \sin(x) }{ \cos(x) } [/tex]

[tex] \tan(x) = \frac{ \frac{7}{9} }{ \frac{4 \sqrt{2} }{9} } [/tex]

[tex] \tan(x) = \frac{7}{4 \sqrt{2} } [/tex]

[tex] \tan(x) = \frac{7 \sqrt{2} }{8} [/tex]

The answer is A

Answer:

Hey!!!!

the answers are 2, 6, 3, 12, 4, 1

Please read the explanation... it always helps..

Step-by-step explanation:

Alrighty... let's begin....

A factor is any number that you can multiply by another number to get a product

So choose the numbers you can mutiply by another number to get twelve... which are...  2, 6, 3, 12, 4, 1

if you are wondering why twelve well... 12 x 1 = 12

i hope this helps!!!!

Answer:

x = 25.84

Step-by-step explanation:

Secx = hyp /adj

Secx = 30/27

x = ArcSec(30/27)

x = 25.84

Answer:

its is true just keep practicing applying urself love<33

So, basically this is the formula to calculate weight mean.

Thank you.

Step-by-step explanation:

this is the answer

hope it help

Fatima's claim that she has 0.413 kilogram of rose petals left is wrong

The given parameters are:

The amount left is the difference between the amount purchased and the amount used.

So, we have:

Remaining  = 0.454 + 0.056 - 0.02 - 0.095

Evaluate

Remaining  = 0.395

This means that the remaining amount is 0.395kg, not 0.413 kg

Hence, Fatima's claim that she has 0.413 kilogram of rose petals left is wrong

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Answer: she is left with 0.395 kilogram of rose pedals

Step-by-step explanation: she misalinged the first step,

0.454 - 0.02 = 0.434 + 0.056 = 0.490 - 0.095 = 0.395

The translation is 8 units to the right and 5 units downwards, and the scale factor is k = 0.8

First, we have a translation that goes from F to F', to identify it, we need to find the centers of the two circles.

F = (-5, 4)

F'= (3, -1)

To get the translation we take the difference between the two centers:

F' - F =  (3, -1) - (-5, 4) = (8, -5)

So the translation moves 8 units to the right and 5 units downwards.

To get the dilation we need to find the quotient between the radius of F' and the radius of F.

This is:

k =  4/5 = 0.8

So the scale factor is 0.8

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Answer: b=840

Step-by-step explanation:

edge 2022

do good on your tests !!

There are 840 ways can he arrange his family members into a row of five seats if Jose must sit in the first seat

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Since, the order matters, we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

ⁿPₓ = n! / (n - x)!

In this question:

The first seat is Jose's.

The remaining four are organized among the other 7 members. So

There is no difference. So, 7 people can be sit in different ways as;

ⁿPₓ = n! / (n - x)!

⁷P₄ = 7! / (7 - 4)!

     = 7! / 3!

     = 840

So, the correct answer is, 840

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Answer:

7(5-2)+6

Step-by-step explanation:

difference - subtraction

putting the 7 next to it means that it will multiply times that first

Answer:

4, 45, 75

Step-by-step explanation:

15 miles per 2 min = 7.5 miles per 1 min

2 min = 15 min

4 min = 30 min

6 min = 45 min

10 min = 75 min

Answer:

2.4

Step-by-step explanation:

set up an equation to find x, the number.

[tex]25x+8=68[/tex]

subtract 8 from both sides

[tex]25x=60[/tex]

divide both sides by 25 to get x (the variable) alone

[tex]x=\frac{60}{25}=\frac{12}{5}=2.4[/tex]

The 200 random customers is the group in which he surveys to determine which colour of shirt will have the greatest number sold, option third is correct.

A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.

We have:

Jeff sells shirts at a store in the mall.

The selecting the colour of the shirts is subjective.

It also depends on that how many colours that store sell.

Female customers cannot be an option because men also buy shirts and affect the result of the survey.

Customers who are wearing blue data only tells that how many blue shirts sold.

200 random customers. 200 is a sample from a population, so it will give appropriate results about the colour of shirt will have the greatest number sold

Thus, the 200 random customers is the group in which he surveys to determine which colour of shirt will have the greatest number sold, option third is correct.

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Answer:

B

Step-by-step explanation:

first of all articles are perfect and there is . sign at the last of the sentence