how to solve 9x-2 × 27x=3
[tex] { {9}^{} }^{ x - 2 } .27 {}^{x} = 3[/tex]


Answers

Answer 1

Answer:

x = 1

Step-by-step explanation:

Using the rules of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

Note that 9 = 3² and 27 = 3³ , thus

[tex]9^{x-2}[/tex] × [tex]27^{x}[/tex]

= [tex](3^2)^{x-2}[/tex] × [tex](3^3)^{x}[/tex]

= [tex]3^{2x-4}[/tex] × [tex]3^{3x}[/tex]

= [tex]3^{(2x-4+3x)}[/tex]

= [tex]3^{5x-4}[/tex] , then

[tex]3^{5x-4}[/tex] = [tex]3^{1}[/tex]

Since the bases on both sides are equal, equate the exponents

5x - 4 = 1 ( add 4 to both sides )

5x = 5 ( divide both sides by 5 )

x = 1


Related Questions

In the figure below, 7 || m. Find x

Answers

Answer:

80

Step-by-step explanation:

If a piggy bank consists of quarters and dimes.

There are 4 more dimes than quarters and the total

value of all the coins is $4.60. How many quarters

and dimes are there in the bank?

Answers

Answer:

There are 12 quarters and 16 dimes

Step-by-step explanation:

Firstly, we need to know that a quarter is worth $0.25 while a dime is worth $0.10

There are 4 more dimes than quarters;

So if there are x quarters, there are x + 4 dimes

From the question we can get;

0.25(x) + 0.1(x + 4) = 4.6

0.25x + 0.1x + 0.4 = 4.6

0.35x = 4.6-0.4

0.35x = 4.2

x = 4.2/0.35

x = 12

X + 4 = 12 + 4 = 16

4 4/5 What decimal should the digital scale​ show?

Answers

Answer: 4.8

Hope this helped!

A 2-column table with 6 rows. Column 1 is labeled Tables with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled Chairs with entries 6, 12, 18, 24, 30, 36. Rachel is setting up for her birthday. Rachel wants to put the same number of chairs around each table. How many chairs will Rachel place around each table at her birthday party?

Answers

Answer:

A 2-column table with 6 rows. Column 1 is labeled Tables with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled Chairs with entries 6, 12, 18, 24, 30, 36.

Rachel is setting up for her birthday. Rachel wants to put the same number of chairs around each table. How many chairs will Rachel place around each table at her birthday party?

✔ 6

Step-by-step explanation:

got it right on edge

4 , 15 , 30 , 49 , 72 , 99 , 130 what is the nth term would really appreciate help

Answers

Answer:

30 i think

Step-by-step explanation:

Please help I have no idea what the answer is

Answers

Answer:

x = 25

Step-by-step explanation:

Answer:

x= 25

Step-by-step explanation:

Add 2 given sides then subtract 180

2,000,000 + 900,000 + 50,000 + 4,000 + 100 + 60 + 1 in standard form?

Answers

Answer:

2,954,151

Step-by-step explanation:

Answer:

2954161

Step-by-step explanation:

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve.
-2/5x-9<9/10

Answers

did you ever figure out the answer? if not i can help

I WILL GIVE BRAINLIEST AND POINTS HELP PLEASE!!!!!!!

Answers

Answer:

Step-by-step explanation:

263

273

237

267

627

623

673

637

327

367

763

723

I dunno anymore. 12

What is 4+3?
Giving points back to the community!

Answers

Answer:

10004

Step-by-step explanation:

Write the equation of the line that passes through the points (5,0) and (-6, -1).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.

Answers

Answer:

The equation in point-slope form is: [tex]\mathbf{y=\frac{1}{11}x-\frac{5}{11} }[/tex]

Step-by-step explanation:

We need to find equation of line in point slope form that passes through points (5,0) and (-6, -1).

The general equation of point slope form is: [tex]\mathbf{y-y_1=m(x-x_1)}[/tex]

where m is the slope of line.

We need to know Slope m

Finding Slope m

Finding Slope m using formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

We have [tex]x_1=5, y_1=0, x_2=-6 \ and \ y_2=-1[/tex]

Putting values and finding slope

[tex]Slope=\frac{-1-0}{-6-(5)}\\Slope=\frac{-1}{-6-5}\\Slope=\frac{-1}{-11}\\Slope=\frac{1}{11}[/tex]

So , slope m is: [tex]\mathbf{m=\frac{1}{11}}[/tex]

Using point (5,0) and slope m =1/22 the equation of point-slope form is:

[tex]y-y_1=m(x-x_1)\\y-0=\frac{1}{11} (x-5)\\y=\frac{1}{11}x-\frac{5}{11}[/tex]

So, the equation in point-slope form is: [tex]\mathbf{y=\frac{1}{11}x-\frac{5}{11} }[/tex]

Enter the ordered pair for the vertices for (Ry-axis ○ T(2, 0))(QRST).

Answers

Answer:

The answer is:

[tex]Q' = (-3, 3)\\\\R' = (-5, -3)\\\\S' = (-2, -2)\\\\T' = (0, 1)\\\\[/tex]

Step-by-step explanation:

All vertices of its quadrilateral were co-ordinated;  

[tex]T(-2, 1), \ Q(1, 3), \ S(0, -2), \ R(3, -3)[/tex] Therefore, we first undertake the operation correct: [tex]T(2, 0) \ QRST[/tex], there;

[tex]T(2, 0) \ QRST[/tex] [tex]\to T(-2 + 2, 1), \ Q(1 + 2, 3), \ S(0 + 2, -2), \ R(3 + 2, -3)[/tex]

[tex]T(2, 0) \ QRST[/tex][tex]\to T(0, 1), \ Q(3, 3), \ S(2, -2), \ R(5, -3)[/tex]

A preimage (x, y) will be the image in the next phase R-y-axis reflecting mostly on the y-axis (-x, y)  and we've got it;  

R y-axis [tex](T(0, 1), \ Q(3, 3), \ S(2, -2), \ R(5, -3)) = \ T'(0, 1), \ Q'(-3, 3), \ S'(-2, -2), \ R'(-5, -3)[/tex]From which we get [tex](Ry-axis \ T(2, 0)) \ (QRST = T'(0, 1), \ Q'(-3, 3), \ S'(-2, -2),\ R'(-5,-3).[/tex]

What is the y-intercept of the line 7x - 5y = 35

Answers

Answer:

(0,-7) is the answer

Bank A offers to pay you 3.5% annual interest if you deposit $500 for one year. Bank B will pay you 1.25% annual interest if you deposit $600 for one year. Which bank do you think will pay more to deposit your money over the course of a year?

Answers

The answer would be:
Bank A

Explanation:
Bank A gives 3.5% which is already more and you only have to pay a deposit of $500 for one year which is less than bank B.

I hope this helped :)

An athlete runs 1 mile in 5 minutes 52 seconds. What is her/his average speed in feet per second!

Answers

Answer: The answer is B 12

Step-by-step explanation:

571 x ?
I don’t know
what I’m doing wrong !

Please answer this the way it’s shown thanks

Answers

Answer:

5

571

x 38

---------

4,568 <------571×

+3,213x <------571x

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

36,698

What’s this in standard form it’s in photos

Answers

Answer: 600+10+7+0.9+0.002

Can someone tell me the answers for all 10 questions

Answers

Answer:

18x+8

-48x-24

4x+5

-48x-18

6x-16

30x-10

-24x+8

30x-10

10x-2

-9x+6

The answeres are in ordered so you dont get comfused.

I hope this help you! :)

Which of the following describes the correct first step in solving the equation 2x - 7 = 5?

Answers

Answer:

Adding 7 to both sides of the equal sign

Step-by-step explanation:

Choose the division equation that represents the fraction shown 1/7

Answers

Answer:

1÷7 is the answer

The answer is 69420

What percent of 160 is 24?

Answers

Answer:

i think its 38.4 but im not 100% sure

Answer:

15

Step-by-step explanation:

what is the gcf of 12 and 8

Answers

The answer is 4 hope this helps

Can someone really help me pls

Answers

Answer:

7 units down

Step-by-step explanation:

it goes from 0 as intercept to -7

Answer:

in my opinion I would say your answer should be -7

8 Find RT.
R
Р
S
15x - 17
23- 6
Q
T

Answers

Answer:

RT = 86

Step-by-step explanation:

23x - 6 = 2(15x - 17)

23x - 6 = 30x - 34

23x - 30x = - 34 + 6

-7x = -28 |÷(-7)

x = 4

RT = 23x - 6 = 23 × 4 - 6 = 92 - 6 = 86

4.2z + 3.8z simplify the expression ​(Use the operation symbols in the math palette as needed. Simplify your answer. Use whole numbers or decimals for any numbers in the​ expression.)

Answers

Answer:

8z

Step-by-step explanation:

Since these are like terms, add the numbers together and then put the z on.

Identify the slope of each of the following equations.
(a) y = 4/5x + 3
(b) y = -x + 1
(c) y = 2x
And what is the y-intercept of equation (c)?

Answers

Answer:

Please see the explanation.

Step-by-step explanation:

As we know that the slope-intercept form of the equation is

[tex]y=mx+b[/tex]

where m is the slopeb is the y-intercept

Now, comparing the given equations with the slope-intercept form

a) y = 4/5x + 3

Here:

m = 4/5

Therefore, the slope of the equation y = 4/5x + 3 is: m = 4/5

b) y = -x + 1

Here:

m = -1

Therefore, the slope of the equation y = -x + 1 is: m = -1

b) y = 2x

Here:

m = 2

y-intercept = b = 0       ∵ y = mx+b here b is the y-intercept

Therefore, the slope of the equation y = 2x is:

m = 2 and

y-intercept = b = 0

Lindsay joins a weight loss program that has a membership fee of $20 plus $15 per month. Her friend joined another program that has a fee of $40 and charges $10 per month. In how many months will Lindsay and her friend's cost be the same? 4 months 8 months 80 months O 20 months​

Answers

i’m pretty sure it is 4 months

Tom collects 20 crayons from his sister.
One of the crayons is the color red.
Find the percentage of crayons that are colored red in the bundle that Tom collected.

Answers

Answer:

5%

1 of the 20 crayons is red, so...

1/20 = 5% or 0.05

Answer: 5%

Step-by-step explanation:

Pumpkins at the pumpkin patch cost $3 for a small or $5 per large. On Saturday, they collected $105 and a total of 29 pumpkins sold. Create the two equations that would represent this system and type them in below: *

Answers

Let, number of small and big pumpkin are x and y.

So, mathematical equation is given by :

x + y = 29    ...1)

3x + 5y = 105     ...2)

Putting value of x from equation 1 to equation 2, we get :

[tex]3(29-y ) +5y=105\\\\2y = 18\\\\y = 9[/tex]

So, x = 20

Therefore, number of small and large pumpkins are 20 and 9 respectively.

Hence, this is the required solution.

a ship leaves port and travels 40 miles due north, then changes course to n35e and travels for 50 more miles

Answers

Answer:

Ok so the problem is what are we looking for how many miles was traveled? or what

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