1st term in sequence is 6-4th term is -6, the 8th term is -22 write a function that can be used to find the nth term of the sequence

2x + 16 = 5

2x = -11

x = -5.5

y = 5

(-5.5,5)

Final answer:

The solution to the system of equations y=5 and y=2x+16 is found using substitution, yielding the solution (-5.5, 5).

Explanation:

To solve the system of equations y=5 and y=2x+16, we can use the method of substitution. Since the first equation directly gives us the value of y, we can substitute y = 5 into the second equation to find the corresponding value of x. Doing so, we have 5 = 2x + 16. To solve for x, we subtract 16 from both sides to get -11 = 2x, and then divide both sides by 2 to find that x = -5.5. Thus, the solution to the system is (-5.5, 5).

I am attaching an image with explanation. I added in red labels like

(STEP NUMBER) <value in inches>

The STEP helps you follow the sequence of deductions, starting from dividing 24 by 4 to get "(1) 6 in" and so on from there. Lmk if there's something unclear.

The length is 9"

Final answer:

To evaluate (f ∘ g)(4), we substitute the value of g(4) into f(x) which gives us 22.

Explanation:

To find (f ∘ g)(4), we need to first evaluate g(4) and then plug that value into f(x). Given that g(4) = 8 and f(8) = 22, we can substitute 8 into f(x) as follows:

(f ∘ g)(4) = f(g(4))

(f ∘ g)(4) = f(8)

(f ∘ g)(4) = 22

Answer:

3.6 miles

Step-by-step explanation:

For a trip of x miles, there are x-0.5 miles of it that are "additional", which makes (x-0.5)/0.1 additional tenths.

Then the charges (in dollars) are ...

... 3.50 + 0.30(x -0.5)/0.1

Adding a tip of $2 and requiring the total be less than $15 gives ...

... 3.50 + 0.30(x -0.5) + 2.00 ≤ 15.00

... 5.50 + 3(x - 0.5) ≤ 15.00 . . . . simplify a bit

... 4.00 +3x ≤ 15.00 . . . . . . . . . . simplify more

... 3x ≤ 11.00 . . . . . . subtract 4.00

... x ≤ 3.667 . . . . . . divide by 3

Miles are measured in tenths. We cannot go 3.7 miles on $15, but we can go 3.6 miles.

B

A(6) = 2500 × [tex]e^{(0.05(6))}[/tex] = 2500 × [tex]e^{0.3}[/tex] = $3, 374.65

My investment amount will be 3374.65 rupees after 6 years.

So, option B is the correct answer.

What is Euler's number ?

A(t) [tex] = p {e}^{rt} [/tex] is known as Euler's number.

A is the desired amount per account/price/population/etc. equal

P is the principal or amount you start with.

e is a particular irrational number that is approximately 2.718. Just as pi is a concrete irrational number, so is e. The Euler number is often used as a title for e. Just as pi is an infinite non-repeating decimal, so is e. And just as many people use 3.14 to approximate pi, some use 2.718 for e. However, using the special π button on the calculator gives a more accurate answer than 3.14, and using the e button on the calculator is more accurate than using 2.718.

r is a rate written as a decimal, not a percentage.

t is time.

Let's say you have a population of bacteria that is constantly growing at a rate of 15% per hour. If there were 40 bacteria at the beginning of the experiment, how many bacteria will there be after 8 hours?

A is the amount after 8 hours, it's unknown, so I'll just use the variable A.

P initially has 40 bacteria.

e I use the “e” button on my calculator.

r is the hourly rate of 15%, I write it as 0.15

t is time, in this case 8 hours.

A = 40•e^(0.15•8)

A = 132.8, you need to round down because you haven't reached the next whole number of bacteria.

132 bacteria after 8 hours.

Here given,invest amount is $2,500 and rate of interest is 5% and total time period is 6 years.

Here we need to use continuous function A(t)[tex] = p {e}^{rt} [/tex]

Where P is principal,r rate of interest is interest and t is time.

Now,

[tex]p = 2500 \\ r = 5\% = 0.05\\ t = 6 \: years[/tex]

So,after 6 years the amount become ,A(6)

= [tex]2500 \times {e}^{0.05 \times 6} \\ = 2500 \times {e}^{0.3} [/tex]

[tex] = 2500 \times 1.34986 \\ = 3374.65[/tex]

Therefore,my investment amount will be 3374.65 rupees after 6 years.

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-110 = 13 + 3(4h -6) . . . . . . given

-110 = 13 + 12h -18 . . . . . . . eliminate parentheses using the distributive property

-110 = 12h -5 . . . . . . . . . . . . collect terms

-105 = 12h . . . . . . . . . . . . . . add 5 to both sides of the equation

-105/12 = h = -8.75

______

There are many ways you can solve this. Another is to undo the operations done to h. The variable h is ...

When you undo these, you do it in reverse order:

-110 -13 = 3(4h -6) . . . . subtract 13

-123/3 = 4h -6 . . . . . . . divide by 3

-41 +6 = 4h . . . . . . . . . .add 6

-35/4 = h . . . . . . . . . . . divide by 4

h = -8.75

x = 10

[tex]\frac{x-2}{4}[/tex] = 2 ( multiply both sides by 4 to eliminate fraction )

x - 2 = 4 × 2 = 8 ( add 2 to both sides )

x - 2 + 2 = 8 + 2

x = 10

I will interpret and evaluate your expression following order of operations rules strictly.  6*5 (multiplication) and 3*3*3 / 3 (division) must be done first, before subtraction.  Then we have 30 - 9, or 21.  If you truly meant 3*3*3, why not write that as 3^3?

Answer:

a = 4.762203156

Step-by-step explanation:

Given:

ab^4 = 12 and a^5b^5 = 7776

Making the equations a subject of a;

a = 12/b^4 and a^5 = 7776/b^5

Finding fifth root on both sides of equation two;

a = [tex]\sqrt[5]{7776}[/tex]/b

You will get a = 6/b

Equating the two equations;

12/b^4 = 6/b

Multiplying both sides by b^4 gives:

b = [tex]\sqrt[3]{2}[/tex] = 1.25992105

We had that a = 12/b^4 so;

a = 12/1.25992105^4 = 12/2.5198421 = 4.762203156

Answer:

I'd say you need to be more specific.

Step-by-step explanation:

"Different" doesn't tell you much.

Consider the equations ...

These equations are "different", but they are dependent.

_____

I'd mentally (or actually) put the equations in the same form and compare the coefficients of x and y. If they have different ratios, the system is independent and consistent.

If they have the same ratio, the system will not have a single solution. Whether there is no solution or an infinite number of solutions depends on the constant, which I would examine next.

The system above can be put in the form

In both cases, the ratio of the x coefficient to the y coefficient is 2/-1 = 4/-2 = -2. This means the lines are at least parallel, if not identical. The numbers in the second equation are all 2 times the numbers in the first equation, so the equations are dependent, and there are an infinite number of solutions. (Both describe the same line.)

If the second equation were 4x -2y = 1, then the two equations would be describing parallel lines, so they would be called inconsistent.

the mode of the data is 4.

mode is the number repeats in the data set the most.

Answer:

6782

Step-by-step explanation:

x = 15

since the figures are similar then the ratios of corresponding sides are equal

[tex]\frac{x}{6}[/tex] = [tex]\frac{20}{8}[/tex] ( cross- multiply )

8x = 6 × 20 = 120 ( divide both sides by 8 )

x = 15

See the attached picture:

the answer is 6/1 and 6/1 simply divide and put the answer over one                      

I believe that the answer is C, I don't know if it is addition or multiplication, but if is is addition, it would be 146, C

(1)

substitute y = 3 into the other equation

3 = 2x + 3 ( subtract 3 from both sides )

0 = 2x → x = 0

solution : (x, y) → (0, 3 )

(2)

substitute y = x into the other equation

x = 2x - 5 ( subtract x and add 5 to both sides )

5 = x then y = x so y = 5

solution : (x, y) → (5, 5 )

(3)

substitute y = - 6 into the other equation

- 6 = 4x + 10 ( subtract 10 from both sides )

- 16 = 4x ( divide both sides by 4 )

x = - 4

solution : (x, y) = (- 4, - 6 )

A graph quickly shows the solution to be ...

... A. x=3 and y=-10

_____

There are a couple of different strategies you can employ to eliminate possibilities.

1. Since the equations involve fractions, you can look only at answers that deal well with the fractions. That is, look for x-values that are multiples of 3 and y-values that are multiples of 5. Right away, this suggests you are not interested in choices B and C.

2. You can look at the general nature of the equations to see where the lines lie on a graph. It can be handy to know that intercept form is ...

... x/a + y/b = 1

where a and b are the x- and y-intercepts, respectively. That is, you can divide by the constant on the right (or just pay attention to its sign) to check the signs of the intercepts. For the first equation, the intercepts are both negative. Hence there cannot be any 1st-quadrant solutions. (That line never goes through the first quadrant—eliminating choices C and D.)

Likewise, the intercepts for the second equation are both positive, so it will never go through the third quadrant—eliminating choice B.

x < -  [tex]\frac{13}{7}[/tex]

add [tex]\frac{4}{7}[/tex] to both sides

- 3x > [tex]\frac{4}{7}[/tex] + [tex]\frac{35}{7}[/tex]

- 3x > [tex]\frac{39}{7}[/tex] ( divide both sides by - 3 )

note that when we divide/ multiply by a negative quantity we must reverse the inequality symbol

x < - [tex]\frac{13}{7}[/tex]

This would just be 7 1/5 + 3/5 since the negative sign gets distributed and makes (-3/5) into a positive number.

From there you have basic math and you get 7 4/5.

The subtraction of the given expression will be [tex]7\dfrac{4}{5}[/tex].

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The subtraction will be calculated as:-

[tex]=7\dfrac{1}{5}-(-\dfrac{3}{5})[/tex]

[tex]= \dfrac{36}{5}+\dfrac{3}{5}\\\\\\= \dfrac{39}{5}\\\\\\= 7\dfrac{4}{5}[/tex]

Therefore subtraction of the given expression will be [tex]7\dfrac{4}{5}[/tex].

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Answer:

b = 24

d = 10

f = 32

g = 34

h = 46

Step-by-step explanation:

From the given table we find that students who are in band = 48

So 24 + b = 48

b = 48 - 24

b = 24

Total students who do not play sports = h

And h = students in band + students not in band

h = b + 22

h = 24 + 22 = 46

h = 46

Total students who play sports and who do not play sports = 80

g + h = 80

g + 46 = 80

g = 80 - 46 = 34

g = 34

Total students who are not in band and not in band = 80

48 + f = 80

f = 80 - 48

f = 32

Students who are not in Band but either play sports or do not play sports = f

d + 22 = f

d + 22 = 32

d = 32 - 22 = 10

d = 10

Using the change of subject, the values of the alphabet b, d, f g, h calculated from the table are 24, 10, 32, 34, and 46 respectively.

To find b :

24 + b = total

24 + b = 48

b = 48 - 24

b = 24

To find h :

b + 22 = total

b + 22 = h

24 + 22 = 46

h = 46

To find g :

g + h = 80

g + 46 = 80

g = 80 - 46

g = 34

To find d :

24 + d = g

24 + d = 34

d = 34 - 24

d = 10

To find f :

d + 22 = f

10 + 22 = f

f = 32

Therefore, the values of b, d, f g, h are 24, 10, 32, 34, and 46 respectively.

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Total of fees: 1,000 + 4,900 = 5,900

You are told the APR is the total fees divided by the amount financed, so divide the total fees by the amount financed:

5,900 / 83,098.59 = 0.71

0.71 x 100 = 7.1% APR.

The answer is B.

Answer: about 0.0432 or 4.32%

Step-by-step explanation:

Given : A bag of marbles contains 7 red, 5 blue, 4 green, and 2 yellow marbles.

Total marbles = 7+5+4+2=18

Let R : Event of getting first marble as red .

Y= Event of getting second marble as yellow.

Jon selects a marble, replaces it, then selects another marble.

⇒Both events are independent .

Probability of getting first marble as red = [tex]P(R)=\dfrac{\text{Number of red marbles}}{\text{Total marbles}}[/tex]

[tex]\\\\=\dfrac{7}{18}[/tex]

Probability of getting second marble as yellow = [tex]P(Y)=\dfrac{\text{Number of yellow marbles}}{\text{Total marbles}}[/tex]

[tex]\\\\=\dfrac{2}{18}[/tex]

Now, the probability that Jon selects a red marble and then a yellow marble :

[tex]P(R)\times P(Y)=\dfrac{7}{18}\times\dfrac{2}{18}\approx0.0432=4.32\%[/tex]  [ ∵ Event R and Y are independent .]

Hence, the probability that Jon selects a red marble and then a yellow marble is about 0.0432 or 4.32%.

When you are given the side length and apothem of a regular polygon and asked for area, you are expected to use the formula

... A = (1/2)Pa

where P is the perimeter of the polygon, "a" is the apothem, and A is the area.

The only additional information you need is that a decagon has 10 sides, so its perimeter is 10×3.2 inches = 32 inches.

The area is ...

... A = (1/2)(32 in)(5 in)

... A = 80 in²

_____

Sometimes the dimensions of a problem like this don't quite add up. The geometry of a regular polygon means that the apothem can be found from the side length and vice versa. In this case, the side length of 3.2 inches means the apothem is about 4.92 inches; or the apothem of 5 inches means the side length is about 3.25 inches. Either way, the area is slightly different from that computed using the given numbers.

This is why I say you're expected to use the above formula. (You're not expected to think about it too much.)

There is no way to factor this so i would assume the answer is no solution.

(5^5) / (5^8)  

1 / 5^3

The answer is 1 / (5^3)

[tex]\sqrt{5}=2.23607, \sqrt{13}=3.60555, \sqrt{21}=4.58258, \sqrt{38}=6.16441[/tex]

These are all approximate decimal versions of the given numbers' square roots. If you need help rounding the decimals to a certain number of digits, let me know.

I hope this helps :)

h(6) = 8

reading vertically from x = 6 , we get , horizontally that y = 8

See this solution/explanation (answer is '7 meters'):

1. According to the condition 'y' means the height, and 'x' - the length from the start of the lift hill.

2. The phrase 'height of 343 meters' means y=343.

3. From the another side y=x³. If to substitute 343 instead of 'y': 343=x³, - it is possible to find the value of 'x'.

x=7 [m] - how far from the start of the lift hill...

top left choice is correct. 0.002 g is 10^(-3) time the approximate number of seed in the jar 4*10^4 (40000) = 10

Separate the equation like this:

(4x2) (10^-3 x 10^4)

Then multiply the first and add the powers:

Final Answer: 8 x 10^1

hope that helps :)