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Answer:

5+9n

Step-by-step explanation:

Here, we notice that the series is in A.P. (Arithmetic Progression).

Therefore, first term a = 14

common difference d = 23 - 14 = 9

Therefore the nth term will be = a + [n -1] d

putting the values, we get

nth term = 14 + 9×[n-1]

= 14 + 9n - 9

= 5 + 9n

Answer:

-1152

Step-by-step explanation:

abc² the expression can be rewritten using the given values for each letter

(-3)*6*(-8)^2 now we find the second power of (-8) by multiplying it with itself

(-8)*(-8) = 64

(-3)*6*64 = -1152

An arithmetic progression is a sequence that has a common difference between consecutive terms.

Question 6:

The recursive function is given as:

[tex]f(0) = 19\\f(n) = f(n - 1) -6;[/tex]     for [tex]n \ge 1[/tex]

The definition of nth term is given as:

[tex]f(n) = 19 - 6n[/tex]  for [tex]n > 0[/tex]

A proof that the functions represent the same sequence is as follows:

Set [tex]n=1[/tex] in

[tex]f(0) = 19\\f(n) = f(n - 1) -6;[/tex]

[tex]f(1) = f(1 -1) - 6 = f(0) - 6[/tex]

[tex]f(1) = 19 - 6 = 13[/tex]

Set [tex]n = 2[/tex]

[tex]f(2) = f(2 -1) - 6 = f(1) - 6[/tex]

[tex]f(2) = 13 - 6 = 7[/tex]

Set [tex]n = 3[/tex]

[tex]f(3) = f(3 -1) - 6 = f(2) - 6[/tex]

[tex]f(3) = 7 - 6 = 1[/tex]

Write out the equations

[tex]f(1) = 19 - 6 = 13[/tex]

[tex]f(2) = 13 - 6 = 7[/tex]

[tex]f(3) = 7 - 6 = 1[/tex]

Rewrite as:

[tex]f(1) = 19 - 6 = 13[/tex]

[tex]f(2) = 19 - 6 - 6 = 7[/tex]

[tex]f(3) = 19 - 6 - 6 -6= 1[/tex]

Rewrite again as:

[tex]f(1) = 19 -6\times 1 = 13[/tex]

[tex]f(2) = 19 -6\times 2 = 7[/tex]

[tex]f(3) = 19 -6\times 3 = 1[/tex]

Replace the numbers in brackets with n

[tex]f(n) = 19 -6\times n[/tex]

[tex]f(n) = 19 -6n[/tex]

Hence, it is proved that

[tex]f(n) = 19 -6n[/tex] and

[tex]f(0) = 19\\f(n) = f(n - 1) -6;[/tex]  represents the same sequence

The definition I will choose for f(20) is:

[tex]f(20) = 19 - 6 \times 20[/tex]

This is gotten from [tex]f(n) = 19 -6n[/tex].

I choose the definition because it is faster to calculate f(20) directly, than using recursion

Question 7:

Given that:

[tex]T_1 = 20[/tex]

[tex]T_2 = 16[/tex]

First, we calculate the common difference

[tex]d = T_2 - T_1[/tex]

[tex]d = 16 - 20 =-4[/tex]

The 500th term is then calculated using the nth term of an arithmetic progression formula.

[tex]T_n = T_1 + (n - 1) \times d[/tex]

So, we have:

[tex]T_{500} = 20+ (500 - 1) \times -4[/tex]

[tex]T_{500} = 20+ 499 \times -4[/tex]

[tex]T_{500} = 20 -1996[/tex]

[tex]T_{500} = -1976[/tex]

Hence, the 500th term is -1976.

Read more about arithmetic progression at:

https://brainly.com/question/22445557

Answer:

-1.25 =x

Step-by-step explanation:

-5x + 10 = -13x

Add 5x to each side

-5x + 10+5x = -13x+5x

10 = -8x

Divide by -8

10/ -8 = -8x/-8

-5/4 =x

-1.25 =x

[tex]\red{\bigstar}[/tex] The Solution of the given equation is [tex]\large\leadsto\boxed{\rm\purple{x = \: - 1.25}}[/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ [tex]\sf - 5x + 10 = - 13x[/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ [tex]\sf - 5x + 10 + 13x = 0[/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ [tex]\sf 8x + 10 = 0[/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ [tex]\sf 8x = - 10[/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ [tex]\sf x = \dfrac{-10}{8}[/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

★ [tex]\bold\red{\large{x = - 1.25}}[/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

✯ Therefore, the the solution of the given equation is x = - 1.25

Answer:

Step-by-step explanation:

A) 71.578 < seventy-one and five hundred seventy-one thousandths

B) Seventy-one and five hundred seventy-one thousandths < 71.578

C) Seventy-one and five hundred seventy-one thousandths > 71.578

D) Seventy-one and five hundred seventy-one thousandths = 71.578

Answer:

√213 > 14(⅖) > 14.33

Step-by-step explanation:

√213 = 14.59

14(⅖) = 14.4

14.33 = 14.33

Smallest = 14.33

Greatest number = √213

Answer:

(1, 8 1/2)

(x1+x2)/2, (y1+y2)/2

2/2, 17/2

Step-by-step explanation:

Answer:

(1 , 8.5)

Step-by-step explanation:

[tex]( \frac{xa \: + \: xb}{2} ) \: ( \frac{ya \: + \: yb}{2} ) \\ ( \frac{4 \: + ( - 2)}{2}) \: ( \frac{16 \: + \: 1}{2} ) \\ ( \frac{2}{2} and \frac{17}{2} ) \\ midpoint \: of \: a \: line \: segment \: = \: (1 \: and \: 8.5)[/tex]

Answer:

input: $200,5% Output: 10

Step-by-step explanation:

Answer:

[tex] \frac{(3x - 2)}{5} = 2 \\ 3x - 2 = 10 \\ 3x = 2 + 10 \\ 3x = 12 \\ x = \frac{12}{3} \\ \boxed{x = 4}[/tex]

Answer:

1361 ft.

Explanation:

The circumference of the wheel times the number of rotations equals distance travelled

[tex]C = d\pi[/tex]

Answer:

Step-by-step explanation:

One rotation is same distance as:

Total distance traveled:

Convert inches to feet:

Answer:

Step-by-step explanation:

a) 3 x 5

b) 15 Celcius

Answer:

answer of your questions is: -2is not equal to 0. so may be this is distributive property

Answer:

4=q+13

or, 4 - 13 = q

or, -9=q

q = -9

Answer:

Ans is D

In the figure, you are given that the radius is 10 inch. So, diameter will be 10*2= 20 inch.

Now,

C=πd

= 3.14*20 inch

=62.8 inch

Answer:

y= 37.5

Step-by-step explanation:

x = 30°

180-30= 150

4x=150

x = 37.5

Answer:

Y = 40

Step-by-step explanation:

I do not understand that language but if it is asking what Y is equal to when x is equal to 30 degrees and EFG is a straight line.

1. 3Y + 2X = 180 (Straight angle)

2. X = 30 (given)

3. therefore 2X = 2x30

                          = 60

4. Therefore 3Y + 60 = 180

5. 3Y = 180 - 60

6. 3Y = 120

7. Y = 120/3

8. Y = 40

Answer:

Step-by-step explanation:

4x - 3 = 2x + 7

4x - 2x = 3 + 7

2x = 10

x = 5

and

2x + 6 = 7x -14

6 + 14 = 7x -2x

20 = 5x

4 = x

Answer:

x = 5

x = 4

Step-by-step explanation:

First one, move the constants and variables on seperate sides:

4x-3 = 2x+7

4x-2x = 7+3

2x = 10

x = 5

Second one, move the constants and variables on seperate sides:

2x+6 = 7x-14

2x-7x = -14-6

-5x = -20

x = 4

Answer:

The answer is C

Step-by-step explanation:

Answer:

d. h(x) = 4x + 48

Step-by-step explanation:

[tex]f(x) = \frac{1}{4} x - 12[/tex]

[tex]y = \frac{1}{4} x - 12[/tex]

[tex]x = \frac{1}{4} y - 12[/tex]

[tex] \frac{1}{4} y - 12 = x = 4( \frac{1}{4} y - 12) = 4x[/tex]

[tex]4 \times \frac{1}{4} y - 4 \times 12 = 4x[/tex]

[tex]y - 48 = 4x[/tex]

[tex]y = 4x + 48[/tex]

[tex]\boxed{\green{= h(x) = 4x + 48}}[/tex]

Answer:

Step-by-step explanation:The LCM of two or more prime numbers is equal to their product. ... Assume two prime numbers as two different variables and find their LCM using prime factorization of both the numbers.

Answer:

Each interior angle of a pentagon equals 108 degrees.

Therefore Angle U = 108 degrees.

The angle of the square is 90 degrees.

Therefore, Angle x = 360 - 108 -90 degrees = 162 degrees!

Step-by-step explanation:

Answer:

Addition

it's PEMDAS

First you would solve whats in the ( )

Then you would use division

Third you would use addition

the answerrrrrrr is

356.85

Answer:

Step-by-step explanation:

2(9t + 2) + 9 + 9 =

= 18t + 18 + 9 + 9 = 18t + 36 ← the end

Answer:

(-12, -20).

Step-by-step explanation:

A dilation of factor 4 moves (-3, 5) to (-3*4, 5*4) = the point (-12, 20).

A reflection  over  the x-axis is (x, y) ------> ( x, -y).

So ( -12, 20) goes to (-12, -20).

Answer:

I think its D

Step-by-step explanation:

Im not positively for sure. but i hope this helps you

Answer:

156

Step-by-step explanation:

just plug in the x and y values

Answer:

Option 3 is not true as already option 1 and 3 are contradictory..

Answer:4

Step-by-step explanation:

Obtuse means bigger than 90 degree angle which is the angle in the top both other angles are the same and smaller than 90 degrees so that makes them acute angles

Answer:

43/40x^3-5x^5+2

Step-by-step explanation: