All categories

2 years ago

Write an explicit rule to represent the sequence:

Mathematics

2 answers:

alexgriva [62]2 years ago

6 0

$a_n=4n+16$

Lapatulllka [165]2 years ago

6 0

Answer:

Step-by-step explanation:

36-4=32

32-4=28

28-4=24

24-4=20

20+4=24

24+4=28

28+4=32

32+4=36

You might be interested in

Determine whether each expression is equivalent to 49^2t – 0.5.

vampirchik [111]

Answer:

None of the expression are equivalent to $49^{(2t - 0.5)}$

Step-by-step explanation:

Given

$49^{(2t - 0.5)}$

Required

Find its equivalents

We start by expanding the given expression

$49^{(2t - 0.5)}$

Expand 49

$(7^2)^{(2t - 0.5)}$

$7^2^{(2t - 0.5)}$

Using laws of indices: $(a^m)^n = a^{mn}$

$7^{(2*2t - 2*0.5)}$

$7^{(4t - 1)}$

This implies that; each of the following options A,B and C must be equivalent to $49^{(2t - 0.5)}$ or alternatively, $7^{(4t - 1)}$

A. $\frac{7^{2t}}{49^{0.5}}$

Using law of indices which states;

$a^{mn} = (a^m)^n$

Applying this law to the numerator; we have

$\frac{(7^{2})^{t}}{49^{0.5}}$

Expand expression in bracket

$\frac{(7 * 7)^{t}}{49^{0.5}}$

$\frac{49^{t}}{49^{0.5}}$

Also; Using law of indices which states;

$\frac{a^{m}}{a^n} = a^{m-n}$

$\frac{49^{t}}{49^{0.5}}$ becomes

$49^{t-0.5}}$

This is not equivalent to $49^{(2t - 0.5)}$

B. $\frac{49^{2t}}{7^{0.5}}$

Expand numerator

$\frac{(7*7)^{2t}}{7^{0.5}}$

$\frac{(7^2)^{2t}}{7^{0.5}}$

Using law of indices which states;

$(a^m)^n = a^{mn}$

Applying this law to the numerator; we have

$\frac{7^{2*2t}}{7^{0.5}}$

$\frac{7^{4t}}{7^{0.5}}$

Also; Using law of indices which states;

$\frac{a^{m}}{a^n} = a^{m-n}$

$\frac{7^{4t}}{7^{0.5}}$ = $7^{4t - 0.5}$

This is also not equivalent to $49^{(2t - 0.5)}$

C. $7^{2t}\ *\ 49^{0.5}$

$7^{2t}\ *\ (7^2)^{0.5}$

$7^{2t}\ *\ 7^{2*0.5}$

$7^{2t}\ *\ 7^{1}$

Using law of indices which states;

$a^m*a^n = a^{m+n}$

$7^{2t+ 1}$

This is also not equivalent to $49^{(2t - 0.5)}$

6 0

3 years ago

Is this right? you’re supposed to find FH

Rudik [331]

Answer:

FH=7

Step-by-step explanation:

If the whole thing FG is 22 and HG is 15 you subtract 22-15 and get 7

8 0

3 years ago

I need help with this problem

Arada [10]

Answer:

65.56°

Step-by-step explanation:

We know that if we take dot product of two vectors then it is equal to the product of magnitudes of the vectors and cosine of the angle between them

That is let p and q be any two vectors and A be the angle between them

So, p·q=|p|*|q|*cosA

⇒ $cosA=\frac{u.v}{|u||v|}$

Given u=-8i-3j and v=-8i+8j

$|u|=\sqrt{(-8)^{2}+ (-3)^{2}} =8.544$

$|v|=\sqrt{(-8)^{2}+ (8)^{2}} =11.3137$

let A be angle before u and v

therefore, $cosA=\frac{u.v}{|u||v|}=\frac{(-8)*(-8)+(-3)*(8)}{8.544*11.3137} =\frac{40}{96.664}$

⇒ $A=arccos(\frac{40}{96.664} )=arccos(0.4138 )=65.56$

Therefore angle between u and v is 65.56°

5 0

2 years ago

The 59th and 4th team of an Ap are - 61 and 64 respectively. Show that the common differences is - 2.5 and 23rd term is 16.5

Mnenie [13.5K]

Answer:

See answers below

Step-by-step explanation:

T59 = a+58d = -61

T4 = a+3d = 64.

Subtract

58d-3d = -61-64

-55d = -125

d =125/55

d = 25/11

Get a;

From 2

a+3d = 64

a+3(25/11) = 64

a = 64-75/11

a = 704-75/11

a = 629/11

T23 = a+22d

T23 = 629/11+22(25/11)

T23 = 1179/11

3 0

2 years ago

The midpoint of AB is (-4,-7) if the coordinates of A are (-7,-6) what are the coordinates of B

slava [35]

Answer:

(-1,-8)

Step-by-step explanation:

7 0

3 years ago