Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.
Select one:
a. an = 2 • 3n - 1
b. an = 2 • (-3)n - 1
c. an = 2 • 3n
d. an = 2 • (-3)n + 1

To find x you can use cosine since you know the adjacent side and the hypotenuse. Remember that for cosine it is adjacent over hypotenuse

cos(x) = [tex]\frac{28}{72}[/tex]

cos(x) = [tex]\frac{7}{18}[/tex]

To find the x we must take the inverse of cosine:

[tex]cos^{-1}[/tex]([tex]\frac{7}{18}[/tex] = x

x = 67.1146...

x ≈ 67.1 degrees

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

67.1

Step-by-step explanation:

i took the test

Answer:

131 m³

Step-by-step explanation:

The volume (V) of a cone is

V = [tex]\frac{1}{3}[/tex] area of base × height

  = [tex]\frac{1}{3}[/tex] × π × 5² × 5

  = [tex]\frac{1}{3}[/tex] π × 125 ≈ 131

Answer:

  5/11 amperes ≈ 0.455 amperes

Step-by-step explanation:

The applicable formula for the current (I) is ...

  I = P/V . . . . where P is power in watts, and V is voltage in volts

  I = (50 watts)/(110 volts) = 5/11 amperes

Answer:

-560a^4b^3

Step-by-step explanation:

Given:

(2a - b)^7

By using Binomial theorem:

128a^7 - 448a^6b + 672a^5b^2 - 560a^4b^3 + 280a^3b^4 - 84a^2b^5 + 14ab^6-b^7

Here the fourth term is -560a^4b^3 !

Answer:

-560a^4 b^3.

Step-by-step explanation:

The (r + 1)th term of (a + x)^n = nCr a^(n-r) x^r.

So, the 4th term of (2a - b)^7 =  7C3 (2a)(7-3)x^3

=  35*16a^4(-b)^3

= -560a^4 b^3.

Answer:

The answer is B. 0.04

Step-by-step explanation:

too lazy to write

There are 2 ways that you and your friend can both be chosen as contestants.

The question is on the concept of probability. There are 8 people in the front row, including you and your friend.

The host randomly chooses 3 people to be contestants.

The order in which they are chosen does not matter.

Since you and your friend are both in the front row, there are 2 cases where you both can be chosen: either you are chosen and your friend is chosen, or your friend is chosen and you are chosen.

So the total number of ways you and your friend can both be chosen is 2.

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Answer:

circle should be the answer

The answer is A. Circle

Answer:

22 quarters

Hope this helps! Correct me if im wrong.

It is so jard for me .

so by drawing construction i have done it.Value of x i haven't done.due to no perfect angle

Answer:

2/10 simplify into 1/5

Step-by-step explanation:

Since there is a total of 10 cards in the deck, the denominator would be 10. As there is only two 'I's in the deck it would be the numerator.

Hope this will help :)

Answer:

2/130 = 1/65

Step-by-step explanation:

There are  4 kings out of 52  cards total.  Your chances of drawing a king are 4/52

Incredible has 10 letters 2 of which are 'i's' So your chances of picking 2  eyes   is 2/10

Combined  you have

4/52 * 2/10 = 2/ 130 = 1/65

bart has a choice of twelve different movies at 5 different times each so you just multiply twelve and five to get 60 choices

Answer:

Step-by-step explanation:

Givens

To find the total number of choices of movies and showtime that Bart have, we just need to multiply. Because, if each movie is shown at five different times, and there are 12 movies, then the total number of choices are

[tex]12 \times 5 = 60[/tex]

Therefore, Bart has 60 choices to watch a movie.

Answer: [tex]x=\frac{8}{3}[/tex]

Step-by-step explanation:

By the Intersecting secants theorem, we know that:

[tex]EC*ED=EB*EA[/tex]

Then, substituting, we get:

[tex](x+4)(x+4+1)=(x+1)(x+1+11)\\\\(x+4)(x+5)=(x+1)(x+12)[/tex]

Now we need to expand the expression:

[tex]x^2+5x+4x+20=x^2+12x+x+12[/tex]

Simplifying, we get that the value  of "x" is:

[tex]x^2+9x+20=x^2+12x+12\\\\9x+20=12x+12\\\\20-12=12x-9x\\\\8=3x\\\\x=\frac{8}{3}[/tex]

Answer:

12x - 15 dollars

Step-by-step explanation:

Sunny earns $12 per hour for delivering cakes.

She worked for x hours this week.

Unfortunately, she was charged $15 for a late delivery on Tuesday

She was supposed to earn $12 × x = $12x this week

But she was charged $15 for late delivery on Tuesday

So her net earning this week is; $12x - $15

Answer:

12x-15

Step-by-step explanation:

Answer:

a)

The total number of students who participated in the survey is 97

b)

P(male) = 0.5361

c)

P(A) = 0.2474

d)

The events male and TV show B are not mutually exclusive since 5 males prefer TV show B.

e)

The events female and TV show C are mutually exclusive since no female participant prefers TV show C

Step-by-step explanation:

a)

The total number of students who participated in the survey is obtained as;

Number of male participants + number of female participants

52 + 45 = 97

b)

P(male)

This is the probability that a randomly selected individual would be a male;

P(male) = ( number of male participants) / ( total participants)

             = 52/97 = 0.5361

c)

P(A)

This is the probability that a randomly selected participant would prefer TV show A;

P(A) = ( participants who prefer TV show A) / (total participants)

       = 24/97 = 0.2474

d)

Two events are said to be mutually exclusive if they cannot happen at the same time. Another word that means mutually exclusive is disjoint. If two events A and B are disjoint, then the probability of them both occurring at the same time is 0.

The events male and TV show B are not mutually exclusive since 5 males prefer TV show B. The probability is thus not 0.

e)

Two events are said to be mutually exclusive if they cannot happen at the same time. Another word that means mutually exclusive is disjoint. If two events A and B are disjoint, then the probability of them both occurring at the same time is 0.

The events female and TV show C are mutually exclusive since no female participant prefers TV show C. The probability is thus 0.

Answer:

maximum value y = 30

Step-by-step explanation:

Given

- x² + 10x + 5

To complete the square the coefficient of the x² term must be 1

factor out - 1

= - (x² - 10x) + 5

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 10x

= - (x² + 2(- 5)x + 25 - 25) + 5

= - (x - 5)² + 25 + 5

= - (x - 5)² + 30 ← in vertex form

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Hence vertex = (5, 30)

The max/ min occurs at the vertex

Since a < 0 then vertex is a maximum

Hence maximum value is y = 30

Answer:

The correct answer would be (8,2.40).

Step-by-step explanation:

Option one(-3, -0.9) and two (-2.5, -0.75) Would not be a viable solution because the value of number of days can not be negative and in option one and two, value of days -3 and -2.5 is negative.

Option three(4.5, 1.35) can not be correct because library charges fee for a full day so the number for days would be a whole number. Library would not charge for 4.5 days, they would either charge of 4 days or 5 days because 4.5 is not an whole number.

Option four(8, 2.40) is the correct answer because it satisfies our equation;

Y= 0.30 * X

2.40= 0.30 * 8

2.40 = 2.40

hope this helps :)

D is the right answer

By comparing the perimeters, we can deduce the scaling factor:

[tex]k = \dfrac{34}{20} = 1.7[/tex]

The areas scale with the square of the scaling factor, so the new area is

[tex]19.6 \cdot 1.7^2 = 56.644[/tex]

Answer:

78.9  degrees to the nearest tenth.

Step-by-step explanation:

This equals the angle whose tangent is 320/62.5 ( opposite side / adjacent side).

The angle of elevation from the coin to the top of the tower

The angle formed by the line of sight and the horizontal plane for an object above the horizontal.

Given that:

The coin  lands 62.5m away from the center of the base of the 320m- high structure.

Height= 320 m

Base= 62.5 m

Now, tan [tex]\theta[/tex] = [tex]\frac{P}{B}[/tex]

                  =[tex]\frac{320}{62.5}[/tex]

                  = 5.12

               [tex]\theta[/tex]= [tex]tan^{-1} (5.12)[/tex]

               [tex]\theta[/tex]= [tex]78.94^{0}[/tex]

The angle of elevation is: 78.94 degrees.

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Intersecting Chord Theorem:

X = 1/2(78 + 76)

X = 1/2(154)

x = 77

Answer:

A. 5x^2 − 2x − 24 = 0

Step-by-step explanation:

height = 5b-2

b =x

We can rewrite the height as

h = 5x-2

We know the formula for area of a triangle

A = 1/2 bh

A =1/2 x * (5x-2)

Distributing the x

A=    1/2 (5x^2 - 2x)

We know A =12

12 = 1/2 (5x^2 - 2x)

Multiply each side by 2

12*2 = 2*1/2 (5x^2 - 2x)

24 = 5x^2 - 2x

Subtract 24 from each side

24-24 = 5x^2 - 2x-24

0 = 5x^2 - 2x-24

Answer:

See below

Step-by-step explanation:

a.  here you are to multiply the two functions together:

[tex](3x-1)(2x^{2} )=6x^{3}-2x^{2}[/tex]

b.  here you are to subtract g from f:

[tex](3x-1)-(2x^{2})=-2x^{2}+3x-1[/tex]

c.  here you are to compose g into f.  In other words, pick up the whole g function and plug it into f wherever you see an x:

[tex]3(2x^{2} )-1=6x^{2} -1[/tex]

d.  here you are compose f into g.  In other words, pick up the whole f function and plug it into g wherever you see an x:

[tex]2(3x-1)^2[/tex]

You now have to FOIL out the (3x-1) like so:

[tex]2[(3x-1)(3x-1)][/tex]

which gives you

[tex]2(9x^{2} -6x+1)[/tex]

Distribute in the 2 and you'll end up with the answer:

[tex]18x^{2} -12x+2[/tex]

answer: right

reason: because you are talking about the x axis so if you go left that would be a negative and you cant go up and down bc that's the y axis so the only way to go is right

hope this helped

[tex]\vec u[/tex] starts at (1, 1) and ends at (-4, 3), so it's pointing in the same direction as the vector

[tex](-4, 3)-(1,1)=(-5,2)[/tex]

This vector terminates in the second quadrant, so its direction is

[tex]\pi+\tan^{-1}\left(-\dfrac25\right)\,\mathrm{rad}\approx158.2^\circ=(180-158.2)^\circ\,\text{N of W}=21.8^\circ\text{N of W}[/tex]

Answer:

C. 21.8 degrees N of W

Step-by-step explanation:

got it right on edge :)

Answer:

  (d)  $1120.70

Step-by-step explanation:

You want the total of deposited checks as shown on the deposit slip.

The total value of checks is shown on the line "Subtotal." This is amount of the deposited checks. The same deposit slip shows a withdrawal of $80 cash, so the net deposit is $80 less than that subtotal.

Vera deposited $1120.70 in checks, choice D.

The correct total amount of all checks Vera deposited is $664.30, and the deposit ticket reflects a subtotal of $1040.70, which includes both checks and cash. Therefore, option (b) $664.30 is the accurate representation of the total amount of all checks.

To determine the total amount of all checks Vera deposited, we need to add the amounts of the individual checks listed on the deposit ticket.

1. Check #184: $138.09

2. Check #308: $312.15

3. Check #298: $214.14

Adding these amounts: $138.09 + $312.15 + $214.14 = $664.38

Therefore, the correct answer is option (b) $664.30. This represents the total amount of all checks Vera deposited. The deposit ticket indicates the subtotal of checks as $1120.70, but this includes the cash amount received as well. To find the total amount of all checks, we subtract the cash amount received, which is $80.00, from the subtotal: $1120.70 - $80.00 = $1040.70.

Given:

Problem-solving:

Let us prepare the leading terms, constant terms, and the coefficients of the polynomial are being asked.

[tex]\boxed{ \ 7x^5 + bx^4 + cx^3 + dx^2 + ex + 6 \ }[/tex]

Now we make the first polynomial, for example:

Thus, the result is [tex]\boxed{\boxed{ \ 7x^5 + 3x^4 - 2x^3 + 2x^2 - 5x + 6 \ }}[/tex]

Then we make the second polynomial as an alternative. For example:

Thus, the polynomial is [tex]\boxed{\boxed{ \ 7x^5 - 6x^4 + 4x^2 + 6 \ }}[/tex]

Of course, you can form another polynomial using the procedure above. Try to vary the coefficients.

Notes:

Let us rephrase the following definitions.

For example, consider the polynomial [tex]\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }[/tex]

A polynomial is said to be in standard form if the terms are written in descending order of degree. For example:

Keywords: a polynomial of the 5th degree, a leading coefficient of 7, a constant term of 6, a monomial, terms, the leading coefficient, constant, in a standard form, rational function, whole number power, integer

A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6 could take the form of 'f(x) = 7x^5 + 6'. The other coefficients (b, c, d, e) can be any real numbers, but for simplicity, they can be set to zero in this instance.

The student's question relates to constructing a polynomial of the 5th degree with specific characteristics in the field of Mathematics, specifically in algebra. One can present such a polynomial with the general form:

f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f

Where the leading coefficient a is 7 and the constant term f is 6. In this case, since the only information provided is the leading coefficient and the constant term, and not any constraints on the other coefficients (b, c, d, e), they can be any real numbers, including zero. Thus, one example of a polynomial fitting these constraints is:

f(x) = 7x^5 + 0x^4 + 0x^3 + 0x^2 + 0x + 6

To simplify the algebra and make calculations easier, one can eliminate terms wherever possible, which in this example has been executed by setting the coefficients of x^4, x^3, x^2, and x to zero. After forming any polynomial, it is also important to check the answer to ensure that it matches the given criteria, which in this case it does.

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Answer:

12

Step-by-step explanation:

If square 1's area is 25, that must mean its side is 5

If square 2's area is 16, that must mean its side is 4

Since it looks like its going in order, square 3's side is 3, and since there's 4 sides to a square, the perimeter is 12.

Answer:

12 units²

Step-by-step explanation:

4^2+b^2=5^2

b=25-16

b^2=9

b=√9

b=3

there are 4 sides in a square so 3•4=12

Answer:

see explanation

Step-by-step explanation:

A

If the sequence is arithmetic then the common difference d is

d = t - 4 = 9 -t, that is

t - 4 = 9 - t ( add t to both sides )

2t - 4 = 9 ( add 4 to both sides )

2t = 13 ( divide both sides by 2 )

t = [tex]\frac{13}{2}[/tex] = 6 [tex]\frac{1}{2}[/tex]

----------------------------------------------------------------------

B

If the sequence is geometric then the common ratio r is

r = [tex]\frac{t}{4}[/tex] = [tex]\frac{9}{t}[/tex] ( cross- multiply )

t² = 36 ( take the square root of both sides )

t = [tex]\sqrt{36}[/tex] = 6

A: If the sequence is arithmetic, what is the value of t is 6.5.

B: If the sequence is geometric, what is the value of t is 6.

If the sequence is arithmetic then the common difference d is,

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms are the same.

d = t - 4

d= 9 -t,

that is,

t - 4 = 9 - t ( add t to both sides )

2t - 4 = 9 ( add 4 to both sides )

2t = 13 ( divide both sides by 2 )

t =[tex]\frac{13}{2}[/tex]  = 6.5

If the sequence is geometric then the common ratio r is

r = [tex]\frac{t}{4} =\frac{9}{t}[/tex] =  ( cross- multiply )

t² = 36 ( take the square root of both sides )

t =  [tex]\sqrt{36}[/tex]= 6

Therefore we get,

A: If the sequence is arithmetic, what is the value of t is 6.5.

B: If the sequence is geometric, what is the value of t is 6

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Answer:

[tex]\frac{8}{81}[/tex]

Step-by-step explanation:

Since the sequence is geometric there is a common ratio r between consecutive terms.

r = [tex]\frac{1}{3}[/tex] ÷ [tex]\frac{1}{2}[/tex]

  = [tex]\frac{1}{3}[/tex] × [tex]\frac{2}{1}[/tex] = [tex]\frac{2}{3}[/tex]

Multiplying [tex]\frac{4}{27}[/tex] by r gives the next term in the sequence

[tex]\frac{4}{27}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{8}{81}[/tex]

Answer:

Step-by-step explanation:

the answer is 27%.

Answer:

27 %

Step-by-step explanation:

To find the percentage of which her net income is her rent payment you do

[tex]\frac{200}{740}[/tex] × 100 = 27.027027027

Answer:

$38.00

Step-by-step explanation:

You purchase 4 large pizzas.

Each one costs $9.50

Total expenditure on pizza = $9.50 × 4 = $38.00

4 times 9.50 would be 38. So you will have to spend $38.00