Look at the arithmetic pattern shown here.

Select the Hint button to view a hint.

Using the variable n for the term, describe the sequence.

First, raise the denominator (27) to the power of 1:

3^-(x-2) = 1/27^1

Next, use the negative exponent rule that is represented by the equation of 1/b^n = b^-n and then move 27 to the numerator:

3^-(x-2) = 27^-1

Rearrange the term so that both equations have the same base:

3^-(x-2) = 3^-3

Now when noticing how this has been completed, it is noticed that since both of these equations have the same bases, the only thing left to do is have the exponents equal one another. For now, ignore the bases and focus only on the two sets of exponents -(x - 2) and (-3). Lets make a new equation with only the exponents:

-(x - 2) = -3

Next, add the distributive property on the left side of the equation to remove the - sign outside (Note: Double negatives equal positive)

-x + 2 = -3

Subtract 2 from both sides:

-x = -5

Finally, it is asking for positive x not negative, so divide both sides by -1:

x = 5

So, the answer is A which is 5.

If 3-(x - 2) = 1/27 then the value of x is a) 5.

To solve for x, we'll follow these steps:

1. Distribute:

Distribute the negative sign into the parentheses:  

3 - (x - 2) = 1/27

3 - x + 2 = 1/27

Simplify:

5 - x = 1/27

2. Isolate x:

To solve for x, we need to get it alone on one side of the equation. Subtract 5 from both sides:

5 - x - 5 = 1/27 - 5

-x = -134/27

3. Multiply by -1:

To solve for x, multiply both sides by -1 to isolate x:

-1 * -x = -1 * -134/27

x = 134/27

4. Simplify:

[tex]x = \approx 4.9629[/tex]

Since none of the given options exactly match the calculated value, we can see that option a) 5 is the closest answer.

However, the precise solution is a fraction between 4 and 5, so none of the provided options is an exact match.

In summary, while none of the given options is an exact solution, the closest answer is a) 5.

To know more about Equation here

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Complete Question

Choose the correct answer from the given options:

If 3-(x - 2) = 1/27, what is the value of x?

a) 5

b) 3

c) -1

d) -5

Step-by-step explanation:

the answer is in the image above

Answer:

3w + x/z + y

That is simplest form

Answer:divided the total buy 9 and if I’m reading correctly the total is two

Step-by-step explanation:

Answer:

18.......................

Answer:

-1

---------------------

Answer:

2nd power is 121

3rd power is 1331

Step-by-step explanation:

LOL

Answer:

The x-intercept is 8.

Step-by-step explanation:

To find the x-intercept, set y = 0 and solve for x

x + 4y = 8

x + 4(0) = 8

x + 0 = 8

x = 8                        The x-intercept is 8

Answer:

6

Step-by-step explanation:

why because when you work this out 6,957÷7 your answer will be 993.8571...

so you take the hole number of the decimal and multiply it by 7 the answer should be subtracted from 6,957

Answer:

You will need 32 ounces

Step-by-step explanation:

2 pounds x 16 = 32 ounces

300 cal / 3 oz = x / 32 oz

(300 * 32) / 3 = 3,200 calories

Answer:

Amal and Ji rent the same amount of per hour but Amal had a starting fee of $75

Step-by-step explanation:

Answer:

£22.8

Step-by-step explanation:

Akeem bought a used video game for $38. Later, he sold it for 40% less than he paid.

First, find

40% of £38

=£15.2

Then, find the price of which he sold the video game for...

£38 – £15.2

= £22.8

Hope this helped you- have a good day bro cya)

Answer:

8.6 meters

Step-by-step explanation:

a² + b² = c²    means        leg² + leg² = hypotenuse ²

5² + 7² = hypotenuse²

25 + 49 = hypotenuse²

74 = hypotenuse ²

[tex]\sqrt{74}[/tex] = hypotenuse

8.6 = hypotenuse

Answer:

area of trapezium:

a+b divided by 2, times by the height.

so its 8+20=28.

28/2=14.

14*14=196.

area=196

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

edge2020

Answer:

20

40

60

80

Step-by-step explanation:

The ratios have to be equal so:

1/3 = x/60 Then use cross multiplication

3x = 60

x = 20

Second one

1/3 = x/120

3x = 120

x = 40

Third One

1/3 = x/180

3x = 180

x = 60

Fourth One

1/3 = x/240

3x = 240

x = 80

Answer:

x < - 4

Step-by-step explanation:

- 5 - 3x > 2(10 + 2x) + 3 ← distribute parenthesis and simplify right side

- 5 - 3x > 20 + 4x + 3

- 5 - 3x > 4x + 23 ( add 3x to both sides )

- 5 > 7x + 23 ( subtract 23 from both sides )

- 28 > 7x ( divide both sides by 7 )

- 4 > x , that is

x < - 4

I think it's 0.075 inch per year

Answer:

Your answer is C. or 0.075 inches per year.

Step-by-step explanation:

251-248 = 3 ( To figure out how much it grew )

2005 -1965 = 40   ( To figure out how long it took )

3/40 = 0.075

Answer:

1. True

2. False

3. False

4. True

5. False

Step-by-step explanation:

Answer:

Step-by-step explanation:

1-  False

2- true

3- false

4- true

5-  true

Answer:

300.104

Step-by-step explanation:

3x100=300

1x(1/10)=0.1

4x(1/1,000)=0.004

300+0.1+0.004=300.104

The function is increasing where the slope is positive. The slope is positive from 4 to infinity.

Hope this helps!! :)

Answer:

2:4

3:6

4:8

Step-by-step explanation:

Answer:

Angle of elevation= 180- (20- 55)

180- 75

105°

D.

because the number have 3

Step-by-step explanation:

A+B+C = 30

A = 4C

B = A+3

=> 4C+4C+3+C = 30

9C + 3 = 30

9C = 30-3

9C = 27

C = 3

Therefore, the age of Cindy is 3 years old

(option D)

Answer:

y = 4

Step-by-step explanation:

The three lines means those segments are equal

4y+8 = 24

Subtract 8 from each side

4y+8-8 = 24-8

4y = 16

Divide each side by 4

4y/4 = 16/4

y = 4

Answer:

x = 19

y = 10

Step-by-step explanation:

3x - 5y - 7 = 0

x = 2k - 1

y = k

3x - 5y = 7

x = 2y - 1

3 * (2y - 1) - 5y = 7

6y - 3 - 5y = 7

6y - 5y = 10

y = 10

x = 2 * 10 - 1

x = 19

Given info:

Compound Interest = Rs.1290

Rate of Interest = 15% p.a

Time = 2 years

[tex] \dag{\underline{\boxed{\sf{C.I = P \bigg(1 + \dfrac{R}{100} \bigg)^{n} - 1}}}}[/tex]

Where

C.I = Compound Interest

P = Principle

R = Rate of Interest

N = Time

[tex]\textsf{ \underline{Solution-}}\\[/tex]

Here

C.I = Rs.1290

R = 15%

N = 2 years

Principle = ?

Now,Calculating the sum (Principle) borrowed by Rachna

[tex] \quad{: \implies{\sf{C.I = \Bigg[P \bigg(1 + \dfrac{R}{100} \bigg)^{n} - 1 \Bigg]}}}[/tex]

Substituting the given values

[tex]\quad{: \implies{\sf{1290 = \Bigg[P \bigg(1 + \dfrac{15}{100} \bigg)^{2} - 1 \Bigg]}}}[/tex]

[tex]\quad{: \implies{\sf{1290 = \Bigg[P \bigg(\dfrac{(1 \times 100) + 15}{100} \bigg)^{2} - 1 \Bigg]}}}[/tex]

[tex]\quad{: \implies{\sf{1290 = \Bigg[P \bigg(\dfrac{115}{100} \bigg)^{2} - 1 \Bigg]}}}[/tex]

[tex]\quad{: \implies{\sf{1290 = \Bigg[P \bigg(\dfrac{115}{100} \times \dfrac{115}{100} \bigg) - 1 \Bigg]}}}[/tex]

[tex]\quad{: \implies{\sf{1290 = \Bigg[P \bigg(\dfrac{13225}{10000} \bigg) - 1 \Bigg]}}}[/tex]

[tex]\quad{: \implies{\sf{1290 = \Bigg[P \bigg( \cancel{\dfrac{13225}{10000}} \bigg) - 1 \Bigg]}}}[/tex]

[tex]\quad{: \implies{\sf{1290 = \Bigg[P \bigg({1.3225 - 1} \bigg) \Bigg]}}}[/tex]

[tex]\quad{: \implies{\sf{1290 = P \times {0.3225}}}}[/tex]

[tex]\quad{: \implies{\sf{\dfrac{1290}{0.3225} = P}}}[/tex]

[tex]\quad{: \implies{\sf{\dfrac{1290 \times 1000}{0.3225 \times 1000} = P}}}[/tex]

[tex]\quad{: \implies{\sf{\dfrac{12900000}{3225} = P}}}[/tex]

[tex]\quad{: \implies{\sf{\cancel{\dfrac{12900000}{3225}} = P}}}[/tex]

[tex]\quad{: \implies{\sf{Rs.4000 = P}}}[/tex]

[tex]\quad{\dag{\underline{\boxed{\tt{\blue{Principle} = \purple{Rs.4000 }}}}}}[/tex]

[tex]\begin{gathered}\end{gathered}[/tex]

Hence,

The sum (Principle) is Rs.4000.

Answer:

(x + 2) (x - 2)

Step-by-step explanation:

Given the quadratic expression,  x² - 4:

Use the Difference of squares factoring formula:

u² - v² = (u + v)(u - v)

Determine what are possible factors that could have a product of -4:

Since -2 × 2 = -4, these can be used as factors.

Therefore, the factors of the quadratic expression, x² - 4 are:

(x + 2) (x - 2)