[tex]5^{3x}-5^{3x-1}=4[/tex] In the following equation, solve for x (to two decimal places if necessary) and write all the steps until the final answer.

Answers

Answer 1

Answer:

[tex]x = \frac{1}{3} [/tex]

or x = 0.33

Step-by-step explanation:

[tex] {5}^{3x} - {5}^{3x - 1} = 4 \\ \\ \implies{5}^{3x} - {5}^{3x} . {5}^{ - 1} = 4 \\ \\ \implies{5}^{3x}(1 - {5}^{ - 1} )= 4 \\ \\ \implies{5}^{3x} \bigg(1 - \frac{1}{5} \bigg)= 4 \\ \\ \implies{5}^{3x} \bigg(\frac{5 - 1}{5} \bigg)= 4 \\ \\ \implies{5}^{3x} \times \frac{4}{5} = 4 \\ \\ \implies{5}^{3x} = 4 \times\frac{5}{4} \\ \\ \implies{5}^{3x} =5 \\ \\ \implies \: 3x = 1 \\ \\ \huge \implies \: x = \frac{1}{3} \\\\ \huge \implies \: x = 0.33[/tex]


Related Questions

The movement
Find the Least Common Denominator. Then, express each fraction using the Least Common Denominator.
7/10 and 5/6

Answers

Answer:

LCM of 7/10- 70

LCM of 5/6- 30

Step-by-step explanation:

Solution:

To find the Least common denominator (LCD) of 7/10 and 5/6, we need to find the Least common multiple of 10 and 6.

I found the LCM through division method. Refer to image attached~

We can tell that:

The LCM is 2 x 3 x 5, which when simplified, we obtain 30. The LCD is 30.

Now, let's multiply the denominators and the numerators such that 30 is the denominator in both fractions.

=> 7/10 = 7 x 3/10 x 3 = 21/30=> 5/6 = 5 x 5/6 x 5 = 25/30

The fractions are:

21/30 and 25/30



What is the value of u?

Answers

Answer:

W/m²K                  by-step explanation:

An equation of the circle with center (h, k) and radius r is (−ℎ)^2+(−)^2=^2

Answers

Answer:

An equation of the circle with center (h, k) and radius r:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Step-by-step explanation:

Not sure what you need to find out but,

An equation of the circle with center (h, k) and radius r:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

The person who started Educational system ,was really educated?

If you have any doubt in maths you can ask ?

Answers

Answer:

me plase me me please meeee

Answer:

Education is started when humans arose in the world.

Step-by-step explanation:

I am unable to understand the laws of sin cosin tan cot sec etc

Here are all the ways to make 5 except for one. Which one is missing?

5 + 0 = 5
2 + 3 = 5
4 + 1 = 5
3 + 2 = 5
0 + 5 = 5

Answers

Answer:

1 + 4 = 5

Step-by-step explanation:

You did duplicates of all numbers, other than that one! :)

Hope this helps!!

1. When you add the fractions 5/8, 3/16 and 11/32 the answer is _____________ *

Answers

Answer:

37/32

Step-by-step explanation:

5/8 + 3/16 + 11/32 = 37/32

Answer:

1.15625 or 1 and 5/32

Step-by-step explanation:

Result

5/8 + 3/16

= 13/16

Result in decimals: 0.8125

Calculation steps:

5/8 + 3/16 =  

5 × 2

8 × 2

+

3

16

=  

10

16

+

3

16

=  

10 + 3/16 =  13/ 16

The next  step would be:

home / math / fraction calculator

Fraction Calculator

Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.

Result

13

16

+

11

32

=

37

32

=

1 5

32

Result in decimals: 1.15625

Calculation steps:

13

16

+

11

32

=  

13 × 2

16 × 2

+

11

32

=  

26

32

+

11

32

=  

26 + 11

32

=  

37

32

=  

1 5

32

Hope this helps! Have a nice day!

Please give brainliest when possible!

:3

heather ate 3/6 of a box of cookies. Melody ate 3/5, who ate
more?

Answers

Answer:

Melody

Step-by-step explanation:

3/6 = 0.5

3/5 = 0.6

i.e. If it has the same numerator but different denominator the one with the smaller denominator will be bigger  

Answer: Melody ate more.

Step-by-step explanation:

So, it would be Melody who ate more because

Over here:

Heather: ate 3 OUT of 6

Melody: ate 3 OUT of 5

Melody ate more because if you count up to 5 theres two cookies left, while Heather had 3 cookies left.

Hope this answers your question!

Jen traveled from Boston to Cape Cod at 60 mph. On her way back, the
traffic was bad and her return trip took 3 times as long. What was Jen's
average speed on the round trip?

Answers

Jen's average speed on the round trip will be 20mph

Distance and sped

The formula for calculating speed is expressed as:

Speed = Distance/Time

d = st

Let the time taken on Jen's way to Cape Cod  be "t"

The time taken back to Boston will be t + 3

d1 = 60t
d2 = 60(t+3)

Since he traveled the same distance to and fro, hence;

Average speed = 60/3

Average speed  = 20mph

Hence Jen's average speed on the round trip will be 20mph

Learn more on speed here: https://brainly.com/question/4931057

Answer:

30 mph

Step-by-step explanation:

This Is due tomorrow I really need the help, please make the answer short and simple

Answers

Answer:

Step-by-step explanation:

21.019=d

21.019+4=25.019 ft of rope

25.019x.45=11.26

He willpay $11.26 for the rope

.The Tigers scored nine times fewer points than the Eagles. The Tigers
scored 18 points. How many points did the Eagles score

Answers

Answer:

2

Step-by-step explanation:

18/9=2

its 9 times fewer than 18

Give an example using the subject of time to describe how to number patterns are related. go math 5th grade 563 9.5

Answers

Answer:

they are related by numbers

A birch tree that is 4 ft tall grows at a rate of 1 ft per year. A larch tree that is 6 ft tall grows at a rate of 0.5 ft per year.

Let the variable t represent time in years and let the variable h represent height in feet.

In how many years will the trees be the same height?

Which system of equations can be used to solve this problem?




{h=1+4th=0.5+6t

{h=4+th=6+0.5t

{h=5th=6.5t

{h=4−th=6−0.5t

Answers

Answer:

h=1+4th=0.5+6t

Step-by-step explanation:

you have to multiply t and h by four and 1 separately

Answer:

H=4+t

H=6+0.5t

Step-by-step explanation:

Took the test the other answer is wrong.

What is the percent difference in height between a building that is 600 feet tall and a tree that is 72

Answers

Answer:

730%

Step-by-step explanation:

600 - 72 = 528

528/72 = 7.3

7.3 * 100 = 730%

Brainliest if correct

Answers

Answer:

y=3

Step-by-step explanation:

We can solve this using substitution (substitute 4 for x)...

4+y=7

Subtract 4 from both sides

y=3

Answer:

y = 3

Step-by-step explanation:

x + y = 7

x = 4

4 + y = 7

y = 7 - 4

y = 3

Solve for b.
b
-1 = 5
4
b = 1

Answers

Answer:

B= 16

b/4 - -1 =5 is the same as b/4 + 1 = 5

b/4 + 1 = 5

- 1 both sides

b/4 = 4

x 4 both sides

b=16

16/4 - -1 =5

4 + 1 = 5

- - Means add

+ + Means add

- + Means take away or minus

Hope this helps!

[tex] \frac{b}{4} - ( - 1) = 5 \\ \\ \frac{b}{4} + 1 = 5 \\ \\ \frac{b}{4} = 5 - 1 \\ \\ \frac{b}{4} = 4 \\ \\ b = \frac{4}{4} \\ \\ b = 1.[/tex]

The value of b is 1 .

How many gallons of 35% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of 40%
alcohol solution?

There needs to be____
gallons of 35 % alcohol solution and____
gallons of 50 % solution.

Answers

Answer:

There needs to be   6     gallons of 35 % alcohol solution

and    3     gallons of 50 % solution.

======================================================

Explanation:

x = number of gallons of the 35% solution

y = number of gallons of the 50% solution

The two amounts must add to 9 gallons, so x+y = 9

This solves to y = 9-x

Since we want 9 gallons of 40% alcohol solution, this means we want 0.40*9 = 3.6 gallons of pure alcohol.

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

0.35x = amount of pure alcohol from the first batch

0.50y = amount of pure alcohol from the second batch

0.35x+0.50y = total amount of pure alcohol

Set that expression equal to the 3.6 figure calculated earlier (the total amount of pure alcohol we're after) and we get this equation

0.35x+0.50y = 3.6

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

Next, we replace y with 9-x and then solve for x.

0.35x+0.50y = 3.6

0.35x+0.50(9-x) = 3.6

0.35x+4.5-0.50x = 3.6

-0.15x+4.5 = 3.6

-0.15x = 3.6-4.5

-0.15x = -0.9

x = -0.9/(-0.15)

x = 6

We'll need 6 gallons of the 35% solution

Use this x value to find y

y = 9-x

y = 9-6

y = 3

We'll also need 3 gallons of the 50% solution

The residents of the city voted on whether to raise property taxes. The ratio of yes votes to no votes was 8 to 5. If there was 11,648 total votes, how many yes votes were there?

Answers

7168 yes votes

11,648/13=896
8(896)=7168 yes
5(896)=4480 no

can someone help me please ​

Answers

Answer:

  a) 1.2 seconds

  b) 50 bpm

Step-by-step explanation:

a)

The period is the value of t that makes the angle be 2π:

  5πt/3 = 2π

  t = 3(2π)/(5π) = 6/5

The period of the function is 6/5 = 1.2 seconds.

__

b)

The number of beats per minute is ...

  (1 beat)/(1.2 s) × (60 s)/(1 min) = 60/1.2 beats/min = 50 beats/min

the diameter of the circle X is 12 centimeters. The diameter of the circle Y is 8 centimeters.
Which measurement is closest to the difference between the circumference of circle X and the circumference of circle Y in centimeters.

Answers

Answer:

20

Step-by-step explanation:

All you do add because it is with even numbers

Pllllease help mmmme

Answers

Answer:

21/38

0.553

Step-by-step explanation:

There are 63 married males out of the total 114 males.

So the fraction is 63/114. That is simplified into 21/38

Then divide 38 by 21 to get the decimal form.

38÷21=0.55263...

Solve the compound inequality x + 6 > 4 and 3x + 5 < 5

Answers

Answer:

[tex]x + 6 > 4 \\ x > 4 - 6 \\ x > - 2 \\ and \\ 3x + 5 < 5 \\ 3x < 5 - 5 \\ 3x < 0 \\ \frac{3x}{3} < \frac{0}{3} \\ x < 0 \\ therefore \\ - 2 < x < 0 [/tex]

if you are going 55 miles per hour how long will it be til you go 70 miles

Answers

Answer

time = 60 miles / (55 miles/hour) = (60/55) (miles/(miles/hour)) = 1.09 hour

Step-by-step explanation:

Speed = distance / time

A bit of algebra will get you the formula

time = distance/speed

Answer:

15sec if its a lamboghihi

Step-by-step explanation:

Which shows how to find the x-coordinate of the point that will divide AB into a 2:3 ratio using the formula x=(a/a+b)(x2-x1)+x1?

Answers

Let,

A = x1 = 2B = x2 = 3

Now, Plug in the values in the formula

[tex] \boxed{ \sf \multimap \: x = ( \frac{a}{a + b})( x_{2} - x_{1}) + x_{1} }[/tex]

[tex] \tt\nRightarrow \: x = ( \frac{2}{2 + 3} )( - 3 - 2) + 2[/tex]

[tex] \bf \Rrightarrow \: x = (\frac{2}{5} )( - 3 - 2) + 2[/tex]

Therefore, Option C is the correct choice!!~

i need help woth this quadratics questions, confused, i think the answer is 24 but the answer key says 34​

Answers

Answer:

then it's 34... sometimes I have a hard time understanding a math problem and I feel that... I suggest using Math*way without the (*) it helped me a lot through high school and college check it out see if you like it

Step-by-step explanation:

given g(x)=5x+3, find g(4)

Answers

Answer:

g(4) = 23

Step-by-step explanation:

g(x)=5x+3, find g(4)

g(4) = 5(4) + 3

g(4) = 20 + 3

g(4) = 23

Hope that helps!

Answer:

[tex] \boxed{g(4) \: is \: 23}[/tex]

Step-by-step explanation:

given :

g(x) = 5x + 3

find g(4)

Answer :

substitute 4 into the equation of function

[tex] g(x) = 5x + 3[/tex]

[tex]g(4) = 5(4) + 3[/tex]

[tex]g(4) = 20 + 3[/tex]

[tex]g(4) = 23[/tex]

The decrease in the worth of Kenzie's car can be represented by the function m(t)=23,000(0.97)t, where t is the time in years, and m is the car's value in dollars.

What is the average rate of change of the car's value in dollars per year (rounded to the nearest dollar) during the first 4 years Kenzie owns it?


660

2638

−2638

−660

Answers

Answer:

-660

Step-by-step explanation:

calculate the measure of each angle. find X

Answers

Solution:

Note that:

4x - 27 = 3x + 4 (Vertically opposite angles)

Using the equation (4x - 27 = 3x + 4), solve for x.

4x - 27 = 3x + 4=> -3x + 4x - 27 = 3x + 4 - 3x=> x - 27 = 4=> x - 27 + 27 = 4 + 27=> x = 31

The measure of x is 31.

Finding x

(4x-27)°=(3x+4)° [Vertically Opposite angles]

Solve for X ~

[tex] \bf4x - 27 = 3x + 4[/tex]

[tex] \bf \: 4x - 3x = 4 + 27[/tex]

[tex] \boxed{ \bf \: x = 31}[/tex]

Now, Finding each angle⤵️

[tex] \tt \: ∠1 = 2x + 21 \\ \tt \: = 2 \times 31 + 21 \\ \tt \: ∠1= 83 \degree[/tex]

[tex] \tt \: ∠2 = 4x + 27\\ \tt \: = 4\times 31 - 27 \\ \tt \: ∠2= 97 \degree[/tex]

[tex] \tt \: ∠3 = 3x + 4 \\ \tt \: = 3\times 31 + 4 \\ \tt \: ∠3= 97 \degree[/tex]

answer both questions and get 20 points and brainliest ​

Answers

Answer:

item 30.

d. 1 ½ as we can see the difference between the each x value is 2 and y value is more of 1 and 2.

items 31.

a. ⅖ as similar to upper question the difference between each x value is 2 and y value is 5 so ⅖

A real estate broker sold your house for $189,000 The broker's commission was 4.5% of the selling price. How much would you get for the house after the commission is paid ?

Answers

Answer: $180,495 is the take-home after the broker's commission.

Step-by-step explanation:

Write the trinomial as a square of a binomial or as an expression opposite to a square of a binomial: -1 + 4a -4a^2

Answers

Answer:

-(1 - 2a)^2

Step-by-step explanation:

-1 + 4a - 4a^2

= -[1^2 - 2*1*(2a) + (2a)^2]

= -(1 - 2a)^2

Answer:

Step-by-step explanation:

Begin by taking out the minus

-(4a^2 - 4a + 1)     The answer is the square root of the 1st and 3rd terms.

√4a^2 = 2a

√1 = 1                    Since middle term is minus, one of 2a or 1 must also be minus

Usually the one is made minus.

That leaves you with a perfect square

- (2a - 1)^2   There are more ways than 1 to write this, but I think this is the clearest answer

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