Express the terms of the following sequence by giving an explicit formula.

9, 12 15, 18, 21

A. u(n) = n + 3, where n = 1, 2, 3, 4, . . .
B. u(n) = 6 + 3n, where n = 1, 2, 3, 4, . . .
C. u(n) = 3 + n, where n = 1, 2, 3, 4 . . .
D. u(n) = 3n, where n = 1, 2, 3, 4, . . .

Step-by-step explanation:

a1/a2=b1/b2=c1/c2

-7=p=qx+1

p= -7 ,qx+1= -7

p= -7 ,q= -6/x

Answer:

[tex]\frac{7^2}{p^8 \cdot q^9}[/tex]

Step-by-step explanation:

[tex]\frac{p^{-8}}{7^{-2}} \cdot q^{-9} = \frac{\frac{1}{p^8}}{\frac{1}{7^2}} \cdot \frac{1}{q^9} = \frac{7^2}{p^8 \cdot q^9}[/tex] by the definition of negative exponents: [tex]a^{-b} = \frac{1}{a^b}[/tex] for all [tex]a,b[/tex] so long as [tex]a\ne 0[/tex].

The value of the exponential equation is A = 7²q⁹ / p⁸

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

A = p⁻⁸ / 7⁻² ( q ) ⁻⁹   be equation (1)

On simplifying the equation , we get

A = 7² ( q ) ⁹ / p⁸

Therefore , the value of A is 7²q⁹ / p⁸

Hence , the exponential equation is A = 7²q⁹ / p⁸

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Answer:

If solving for X. (didn't know if you were solving for X or Y.

x=2y-12

x=5y-15

Step-by-step explanation:

x-2y=-12

+2y on both sides

x=2y-12

x-5y=-15

+5y on both sides

x=5y-15

Answer:

x = -10

y = 1

Step-by-step explanation:

x - 5y = -15

x - 2y = -12

__________--

-3y = -3

y = -3/-3

y = 1

x - 2y = -12

x - 2(1) = -12

x - 2 = -12

x = -12 + 2

x = -10

Answer:

alternate interior angles are always congruent.

Step-by-step explanation:

- Consecutive [Same-side] exterior angles are always supplementary.

- Consecutive [Same-side] interior angles are always supplementary.

- Corresponding angles are always congruent.

I am joyous to assist you anytime.

Answer:

B

Step-by-step explanation:

If a transversal intersects two parallel lines, then alternate interior angles are congruent. If a transversal intersects two parallel lines, then same-side interior angles are supplementary. ... If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel.

Answer:

-1/3

Step-by-step explanation:

slope = rise/run = -1/3

Answer:

35

Step-by-step explanation:

180-145=35

The total of 3 angles is 180 degrees

Answer:

x=35°

Step-by-step explanation:

45°+100°+x=180°{sum of angle of triangle}

145+x=180

x=180-145

x=35°

hope it helps.

Answer:

1. 37

2. 50

3. 50

4. 40

Step-by-step explanation:

hope I helped!!

Answer:

A) 29

Step-by-step explanation:

Step 1: Find angle G

Since Sin(θ) = Opposite over Hypotenuse:

[tex]sin^{-1} ( 58 / (52+52) )[/tex] = θ

θ = 33.896°

Now repeat for just the smaller triangle:

[tex]sin(33.896) = Opposite/Hypotenuse\\sin(33.896) = Opposite/52\\Opposite = sin(33.896) * 52\\Opposite = 29[/tex]

9514 1404 393

Answer:

  (5, -8)

Step-by-step explanation:

Reflection over the y-axis negates the x-coordinate. Translation down 3 subtracts 3 from the y-coordinate. The resulting transformation is ...

  (x, y) ⇒ (-x, y-3)

  (-5, -5) ⇒ (5, -8)

The coordinates of the final point are (5, -8).

Answer:

Greater than.

1 1/27 or 28/27.

Step-by-step explanation:

You're multiplying more than 2/3, so it is greater than.

2/3 x 1 5/9 is the same as 2/3 x 14/9. The answer to this is 28/27. Simplify to a mixed number which is 1 1/27.

Hope it helps!

Answer:

2/3 is less than and the answer is 28/27 = 1  1/27 = 2/3 x 1  5/9

Step-by-step explanation:

2/3 x 1  5/9 = 28/27 = 2/3 x 14/9 = 1  1/27

2/3  ≤ 28/27 = 1  5/9

Answer:

4.5

Step-by-step explanation:

Answer:

3:2

Step-by-step explanation:

to write a ratio, we can do ?:? in order. for example, 5 big shops to 10 small shops would be 5:10 (we are going to simplify it later) You always have to put the ratio numbers in order like they are in the question. In this case, small bones : big bones. We get 9:6. We can then divide both sides by a common factor, in this case 3. The end result is 3:2. Hope this helps!

Answer:

Greta will be earning 3.6/h more at her new job.

Step-by-step explanation:

To find the difference subract Greta‘s salary from her current job from Greta’s salary from her future job.

To find Greta’s salary (numerator) at her future job divide her current weekly salary ($729) by 45h then multiply that answer (16.2) by the increase in salary 10% or 1.1. You should end up with $17.82- this is your numerator. To find the denominator divide her current hours (45h) by 45 then multiply that answer (1) by 0.9 which is the 10% decrease in hours. Now you have a fraction ($17.82/0.9) then multiply that fraction by 1.1/1.1 to get the denominator to 1 hour so you can subtract the fractions. You should end up with $19.8/h.

Now subtract Greta’s current salary ($16.2/h)- you just take the numbers from the first part before you increase or decrease- from her future salary ($19.8/h), you will end up with 3.6/h.

I was challenged to write this in a single equation:

[((($729\45h)x1.1)/((45h\45)x0.9))x1.1/1.1]-[($729\45h)/(45h\45)]

=$3.6/h

/ means a fraction bar

\ means division

Also I am just a student so please tell me if you find any mistakes I could fix or any suggestions to make this a better explanation, and if you have any questions ask away.

Answer:

y = 2

Step-by-step explanation:

y varies inversely with x setup is:

y = k/x

7 = [tex]\frac{k}{2/3}[/tex]  (find 'k')

k = 7/1 · 2/3

k = 14/3

use what you know about 'k' and 'x' to solve for 'y'

y = 14/3 ÷ 7/3  (remember to multiply by the reciprocal when dividing fractions)

y = 14/3 · 3/7

y = 2

Answer:

Here’s what I got.

Hope it helps.

Answer:

[tex]\frac{12}{5}[/tex]

Answer:

[tex]8.3125[/tex]pounds

Step-by-step explanation:

We are given that

Density of ethyl acetate at 25 degrees =[tex]0.902g/ml[/tex]

We have to find the number of pounds in 133 ounces weigh.

To find the number of pounds in 133 ounces we will use unitary method

By using unitary method

We know that

1 ounce=0.0625 pounds

133 ounce=[tex]133\times 0.0625[/tex]pounds

133 ounce=[tex]8.3125[/tex]pounds

Hence,8.3125 pounds would 133 ounces weigh.

Midpoint formula:

[tex](\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2})[/tex]

So,

(-2 + 8 / 2 , 6 + 0 / 2)

(6 / 2 , 6 / 2)

(3, 3)

Midpoint coordinate: (3, 3)

Answer:

Graph D

Step-by-step explanation:

Graph D shows (0,4) because the x coordinate is 0, and then the y coordinate is 4 so you move up 4.

The graph D shows the point R(0, 4).

Given are four graphs we need to determine which graph shows the point R(0, 4),

A point R(0, 4) is represented in a Cartesian coordinate system as a point located at x = 0 and y = 4.

The graph that shows this point is a vertical line passing through the y-axis at 4. It is a line parallel to the x-axis, intersecting it at y = 4 and extending infinitely in both directions.

Visually, the graph of the point R(0, 4) would be a single point on the y-axis at y = 4.

Hence the graph D shows the point R(0, 4).

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Answer:

The value of the opposite number are B negative 1 over 4

Answer:

[tex]Growth\ Rate = 0.2000[/tex] --- Year 1 to 2

[tex]Growth\ Rate = 0.3333[/tex] --- Year 2 to 3

[tex]Growth\ Rate = 0.0625[/tex] --- Year 3 to 4

[tex]Average\ Growth\ Rate = 19.86\%[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{cc}{Year\ 1} & {100} & {Year\ 2} & {120} & {Year\ 3} & {160} & {Year\ 4} & {170} \ \end{array}[/tex]

Solving (a): Growth Rates between each year

For Year 1 to 2.

[tex]Growth\ Rate = \frac{Year\ 2 - Year\ 1}{Year\ 1}[/tex]

[tex]Growth\ Rate = \frac{120-100}{100}[/tex]

[tex]Growth\ Rate = \frac{20}{100}[/tex]

[tex]Growth\ Rate = 0.2000[/tex]

For Year 2 to 3.

[tex]Growth\ Rate = \frac{Year\ 3 - Year\ 2}{Year\ 2}[/tex]

[tex]Growth\ Rate = \frac{160-120}{120}[/tex]

[tex]Growth\ Rate = \frac{40}{120}[/tex]

[tex]Growth\ Rate = 0.3333[/tex]

For Year 3 to 4.

[tex]Growth\ Rate = \frac{Year\ 4 - Year\ 3}{Year\ 3}[/tex]

[tex]Growth\ Rate = \frac{170-160}{160}[/tex]

[tex]Growth\ Rate = \frac{10}{160}[/tex]

[tex]Growth\ Rate = 0.0625[/tex]

Solving (b): The average growth rate

This is calculated as by calculating the mean value of the growth rates in (a)

[tex]Average\ Growth\ Rate = \frac{1}{3}(0.2000 + 0.3333 + 0.0625)[/tex]

[tex]Average\ Growth\ Rate = \frac{1}{3}(0.5958)[/tex]

[tex]Average\ Growth\ Rate = \frac{1}{3}*0.5958[/tex]

[tex]Average\ Growth\ Rate = 0.1986[/tex]

Convert to percentage

[tex]Average\ Growth\ Rate = 0.1986 * 100\%[/tex]

[tex]Average\ Growth\ Rate = 19.86\%[/tex]

Answer:

The probability is 0.609

Step-by-step explanation:

Out of 46 times that the experiment was performed:

A orange chew was selected 5 times.

A apple chew was selected 23 times.

A lime chew was selected 18 times.

We can find the relative frequency of each one of them as the quotient between the number of times that a particular chew was selected, and the total number of chews.

Then for the orange ones we have a relative frequency (that can be thought as the probability) of:

Po = 5/46

For apple we get:

Pa = 23/46

For Lime we get:

Pl = 18/46

We want to find the probability that the next chew Kylie removes from the bag will be a flavor other than lime (so this is equal to the probability of getting orange plus the probability of getting apple):

P = Po + Pa = 5/46 + 23/46 = 0.609

Answer:

0.61

Step-by-step explanation:

Kylie has a bag that contains orange chews, apple chews, and lime chews. She performs an experiment. Kylie randomly removes a chew from the bag, records the result, and returns the chew to the bag. Kylie performs the experiment 46 times. The results are shown below:

A orange chew was selected 5 times.

A apple chew was selected 23 times.

A lime chew was selected 18 times.

Based on these results, express the probability that the next chew Kylie removes from the bag will be a flavor other than lime as a decimal to the nearest hundredth.

The experiment occured 46 times, a flavor other than lime was selected 5+23=28 times.

Probability the next chew will be a flavor other than lime:

\frac{\color{steelblue}{28}}{\color{indianred}{46}}=

46

28

​

=

\,\,0.608695...

0.608695...

\approx

≈

\,\,0.61

0.61

Answer:

Round off to closest value.

Step-by-step explanation:

In order to remove the requirement for change, every time the client buys a product for $0.20 the random number that lies between 0 and 1 would be produced also the same would be rounded to the closest value i.e. 0 or 1. In the case when 0 arise so the customer would not have to pay any amount but if 1 arise so the customer have to pay $1. So this type of method would remove the requirement for a minor change

Answer:

[tex]x=2.3\text{ only }[/tex]

Step-by-step explanation:

We are given the second derivative:

[tex]g^\prime^\prime(x)=0.1x^5-0.29x^4-0.694x^3+1.9136x^2[/tex]

And we want to find the values for -3 < x < 4 in which the graph of g has a point of inflection where the concavity changes from concave up to down.

First, recall that inflection points occur whenever g''(x) = 0 or is undefined.

And that:

Graphing the function (please refer below for the graph), we can see that g''(x) has an inflection point at x = -2.6, 0, 2.3, and 3.2.

If g''(x) changes from concave up to concave down, the values before and after that inflection point must be positive and then negative.

We can see that g''(x) is only positive for the values before the inflection points at x = 0 and x = 2.3.

However, for values after the inflection points, only x = 2.3 becomes negative.

Therefore, since at x = 2.3, the graph changes from positive to negative, this is where the graph of g changes from concave up to concave down.

Notes:

For the point x = 0, the graph stayed positive both before and after x = 0.

Therefore, g does not have an inflection point at x = 0.

Answer:

[tex]Proof~that~(a+x)^n=a^n(1+\frac{x}{a})^n\\R.H.S. = a^n(1+\frac{x}{a})^n = [a(1+\frac{x}{a})]^n [a^nb^n=(ab)^n] \\~~~~~~~~~~~= (a+x)^n =L.H.S. ~proved[/tex]

Answer:

£4414.20

Step-by-step explanation:

Find out how much is 1% of the money invested in his bank account.

100% = 2100

1% = 2100 ÷ 100 = 21

Find out 5.1% which is his interest that he receives every year.

5.1% = 21 x 5.1 = 107.1

Find out how much he receives including interest every year.

2100 + 107.1 = 2207.1

Find out how much he will have after 2 years.

2207.1 x 2 = 4414.2

You do not need to estimate as there isn't an estimated for nearest penny as it has been estimated for you.

Answer:

x = π/4, 5π/4

Step-by-step explanation:

sin(x) - 2 = cos(x) - 2

sin(x) = cos(x)

x = π/4, 5π/4