Tell whether the statement is always, sometimes, or never true. The LCM of two different prime numbers is their product.

-4，2

Step-by-step explanation:

find the average of the x coordinates and y coordinates

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:

156

Step-by-step explanation:

just plug in the x and y values

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:

the answerrrrrrr is

356.85

Answer:

input: $200,5% Output: 10

Step-by-step explanation:

Answer:

I think its D

Step-by-step explanation:

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

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:

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

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

Answer:

4=q+13

or, 4 - 13 = q

or, -9=q

q = -9

Answer:

The answer is C

Step-by-step explanation:

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:

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

Step-by-step explanation:

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:

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:

Step-by-step explanation:

5^2=.25

1^2=1

-1^2=-1

Answer:

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

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:

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

[tex] - 5m \: + \:10 \: > 25 \\ or \: - 5m > 25 - 10 \\ or \: - 5m > 15 \\ or \: m > \frac{15}{ - 5 } \\ or \: m \: > - 3[/tex]

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:

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:

Step-by-step explanation:

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:

Addition

it's PEMDAS

First you would solve whats in the ( )

Then you would use division

Third you would use addition

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:

Step-by-step explanation:

a) 3 x 5

b) 15 Celcius