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djverab [1.8K]
3 years ago
6

See the attachment below for the question.

Mathematics
2 answers:
kicyunya [14]3 years ago
6 0

Answer: Third option.

Step-by-step explanation:

We need to remember that:

a^m=a^n\\\\m=n

In this case, given this expression:

4^x=8^{( x- 1)}

We need to descompose 4 and 8 into their prime factors:

4=2*2=2^2

8=2*2*2=2^3

Rewriting the expression:

2^{2x}=2^{3(x - 1) }

Then:

2x = 3(x - 1)

Finally, applying Distributive property on the right side and solving for "x", we get:

2x=3x-3\\\\3=3x-2x\\\\x=3

tangare [24]3 years ago
5 0

Answer:

The correct answer is third option

x = 3

Step-by-step explanation:

It is given that,

4ˣ = 8⁽ˣ ⁻ ¹⁾

<u>To find the value of x</u>

4ˣ  = (2²)ˣ

8⁽ˣ ⁻ ¹⁾ = (2³)⁽ˣ ⁻ ¹⁾

4ˣ = 8⁽ˣ ⁻ ¹⁾

(2²)ˣ =  (2³)⁽ˣ ⁻ ¹⁾

2²ˣ = 2⁽³ˣ ⁻ ³⁾

2x = 3x - 3

3x - 2x = 3

x = 3

The correct answer is third option

x = 3

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2 years ago
Find the sixth term of the sequence 1/2, -3/8, 9/32
sukhopar [10]

Answer:

The sixth term is -243/2048 ⇒ answer B

Step-by-step explanation:

* Lets explain the geometric sequence

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)  

* General term (nth term) of a Geometric sequence:

# U1 = a  ,  U2  = ar  ,  U3  = ar²  ,  U4 = ar³  ,  U5 = ar^4

# Un = ar^(n-1), where a is the first term , r is the constant ratio

  between each two consecutive terms  and n is the position of the

  number in the sequence

- Ex: U5 = ar^4  ,  U7 = ar^6  ,  U10 = ar^9  ,  U12 = ar^11

- Lets solve the problem

∵ The sequence is 1/2 , -3/8 , 9/32

- Lets find the constant ratio r

∵ The first term is a = 1/2

∵ The second term is U2 = ar

∵ The second term  U2 = -3/8

∴ ar = -3/8

∴ 1/2 r = -3/8 ⇒ multiply both sides by 2

∴ r = -3/4

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∵ a = 1/2 and r = -3/4

∵ n = 6

∴ U6 = ar^5

∴ U6 = 1/2 (-3/4)^5 = 1/2 × -243/1024 = -243/2048

* The sixth term is -243/2048

8 0
3 years ago
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3 years ago
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Braving blizzard conditions on the planet Hoth, Luke Skywalker sets out at top speed in his snowspeeder for a rebel base 4800 mi
____ [38]

Answer:

v_top = 2400 mi/hr

v_w = 400 mi/h

Step-by-step explanation:

Given:

- Total distance D = 4800 mi

- Headwind journey time taken t_up= 3 hr

- Tailwind journey time taken t_down = 2 hr

Find:

Find the top speed of Luke's snow speeder and the speed of the wind.

Solution:

- The speed of Luke v_l is in stationary frame is given by:

                           v_l = v_w + v_l/w

Where,

           v_w: Wind speed

           v_l/w: Luke speed relative to wind.

- The top speed is attained on his returned journey with tail wind. We will use distance time relationship to calculate as follows:

                         v_top = D / t_down

                         v_top = 4800 / 2

                        v_top = v_down = 2400 mi/hr

- Similarly his speed on his journey up with head wind was v_up:

                         v_up = D / t_up

                         v_up = 4800 / 3

                        v_up = 1600 mi/hr    

- Now use the frame relations to find the wind speed v_w:

                         v_down = v_w + v_l/w

                         v_up = -v_w + v_l/w    

- Solve equations simultaneously:

                         2400 =  v_w + v_l/w

                         1600 =  -v_w + v_l/w

                         4000 = 2*v_l/w

                         v_l/w = 2000 mi/h

                         v_w = 400 mi/h

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lianna [129]

Answer:

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Step-by-step explanation:

You would distribute first.

− ( x + 3 ) − 2 ( 4x − 3 ) → -x − 3 − 8x + 6

(If you see a negative sign in front of a parenthesis without a number, its usually a negative 1)

From there, you would combine like terms.

-x − 3 − 8x + 6 → -9x + 3

8 0
3 years ago
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