What is a general rule for simplifying expressions like x^a .x^b? where does this rule
comes from

Answers

Answer 1
So, x^a*x^b would simplify to x^(a+b)

As for the proof of this,
Given that addition, subtraction, multiplication, and division are already known and don’t need to be proved, we know:

x^a = x*x*x… (a times)
x^b = x*x*x… (b times)

If we were to multiply these two expressions together, we’d simply get:

x^a*x^b = x*x*x… (a+b times)

And thus, that is why

x^a*x^b = x^(a+b)

Related Questions

Li believes that the graph shows a direct variation.
do +
LI
Why is Li incorrect in saying that the graph shows a direct variation?

Answers

Answer:

b. or 2. When the x-value is 0, the y-value is 1.

Step-by-step explanation:

welcome bestie <3.

The Earth rotates at a unit rate of
.25 degrees per minute. How much
does the earth rotate in half of an
hour?

Answers

Answer:

it will rotate 7.5 degrees

Step-by-step explanation:

12 1/2, 3 3/4 what is the distance between the two

Answers

Answer:

Estimate the following (by rounding off to nearest hundred (a)6,941 (b)6,320 (c) 416 (d)126 (e)109 (f)202 (g) 146 (h)7,699 (I)8,311 (j)986

Step-by-step explanation:

Answer: 8 3/4

Explanation:
12 1/2 can be written as 12 2/4. One way of solving this problem is to convert each value into an improper fraction and then subtract.

12 2/4 = 50/4
3 3/4 = 15/4

50/4 - 15/4 = 35/4
35/4 can be simplified into 8 3/4

why is this an impossible sequence to solve?
3x + 1 ?

thanks​

Answers

Answer:

[tex]T(x)=\begin{cases}\frac{3x+1}{2} & x\text{ is odd} \\ \frac{x}{2} & x\text{ is even}\end{cases} \\ for \: instance \: start \: with \: 7 \: \\ which \: is \: an \: odd \: number \\ \frac{21 + 1}{2} = \frac{22}{2} = 11 \\ 11 \: is \: odd \\ \frac{11 + 1}{2} = 6\\ 6 \: is \: even \\ \frac{6}{2} = 3 \\ 3\: is \: odd \\ \frac{9 + 1}{2} = 5 \: \\ 5 \: is \: odd\\ \frac{15 + 1}{2} = 8 \\ 8 \: is \: even \\ \frac{8}{2} = 4 \\ 4 \: is \: even \\ \frac{4}{2} = 2 \: then \: 1 \\ [/tex]

Step-by-step explanation:

Can we connect to 1 for all numbers?

A general proof for a simple pattern seems almost impossible, probably a new branch of mathematics maybe needed to tackle this conjecture...

Tìm ma trận X thỏa:1264X315

Answers

pogpogii mooooooooooo

T(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was released. The average rate of change in T(d) for the interval d = 4 and d = 10 is 0. Which statement must be true?The same number of tickets was sold on the fourth day and tenth day.No tickets were sold on the fourth day and tenth day.Fewer tickets were sold on the fourth day than on the tenth day.More tickets were sold on the fourth day than on the tenth day.

Answers

Answer:

The same number of tickets was sold on the fourth day and tenth day.

Step-by-step explanation:

Given, T(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was  released.

The average rate of change in a function with respect to the independent variable gives the value of change in a particular period.

If average rate of change in T(d) for the interval d = 4 and d = 10 is  is 0 , that means nothing has been changed in the number of tickets sold on 4th day and 10th day after the film release.

Hence, the correct statement is "The same number of tickets was sold on the fourth day and tenth day."

Answer:

In simpler terms, for the edge answer;

A. The same number of tickets was sold on the fourth day and tenth day.

- _ -   long answers scare me...

Step-by-step explanation:

edg- answers ;p

Define the function
3
g(x) = x^3+ x
. If
f(x) = g^-1(x)
and
f(2) = 1
what is the value of
f'(2)
?

Answers

Given that

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

the inverse [tex]g^{-1}(x)[/tex] is such that

[tex]g\left(g^{-1}(x)\right) = g^{-1}(x)^3 + g^{-1}(x) = x[/tex]

or

[tex]g\left(f(x)\right) = f(x)^3 + f(x) = x[/tex]

Differentiating both sides using the chain rule gives

[tex]3f(x)^2f'(x) + f'(x) = 1 \\\\ f'(x) \left(3f(x)^2+1\right) = 1 \\\\ f'(x) = \dfrac1{3f(x)^2+1}[/tex]

Then the derivative of f at 2 is

[tex]f'(2) = \dfrac1{3f(2)^2+1} = \boxed{\dfrac14}[/tex]

A large tank is partially filled with a solution. The tank has a faucet that allows solution to enter the tank at a rate of 16 3/4 liters per minute. The tank also has a drain that allows solution to leave the tank at a rate of 19 4/5 liters per minute. (a) What expression represents the change in volume of solution in the tank in 1 minute? (b) Simplify and give your answer as a simplified mixed number. (c) What is the change in volume of the solution after 10 minutes? Show necessary work. Give your answer as a simplified mixed number.

Answers

The change in volume per minute and the total change in the volume of the solution after 10 minutes will be [tex] - 3 \frac {1}{20} \: litres [/tex] and [tex]- 30 \frac {1}{2} \: litres [/tex] respectively.

Entry rate = [tex] 16 \frac{3}{4} [/tex] per minute

Discharge rate = [tex] 19 \frac{4}{5} [/tex] per minute

Change in the volume of solution in the tank per minute can be calculated thus :

Change in volume = (Entry rate - Discharge rate) × time

[tex] 16 \frac{3}{4} - 19 \frac{4}{5} = \frac{67}{4} - \frac{99}{5} = \frac{(335 - 396)}{20} = \frac{-61}{20} = - 3\frac{1}{20} \: litres \: per \: minute [/tex]

The total change in the volume of solution in the tank after 10 minutes can be calculated thus :

Change in volume per minute × time

[tex] - \frac{61}{20} \times 10 = - \frac{610}{20} = - 30 \frac {1}{2} \: litres [/tex]

Therefore, the solution in the tank decreases by [tex] 30 \frac {1}{2} \: litres [/tex] after 10 minutes

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NEED HELP FOR REAL 69 points!!!!!!!!!!!!!! ASAP
The physicist from the last problem lets the particle fall another 100 times, and finds that the average travel time is now 16 sec. Remember that when running the simulation many times it took 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. What does she conclude and why?

Answers

It concludes that newtons laws of motion are at work

simplify the expression 6y-2y(x+1)​

Answers

Answer:

2. 4y-2xy

Step-by-step explanation:

6y-2y(x+1)=6y-2xy-2y

=4y-2xy

five times x equals one

Answers

Answer:

x=0.2

Step-by-step explanation:

1 / 5 = 0.2

therefore

5 x 0.2 = 1

Match the following equation to the correct situation 30%(b − 25) = 30%b − 7.5

Answers

Answer:

vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvfvgvgggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg

Step-by-step explanation:

Which equation in standard form has a graph that passes through the point (15,3) and has a slope of ¼?

Answers

Answer:

2y - 9x - 40 = 0

Step-by-step explanation: i already done the test

2. At the gym, Alex spends 24 minutes doing
resistance training for every 30 minutes
spent doing cardio exercises, Carisa spends
15 minutes on resistance for every
20 minutes on cardio, and Manuel spends
14 minutes on resistance for every
15 minutes on cardio. Which person has the
greatest ratio of minutes spent on resistance
to minutes spent on cardio? (Example 2)
Alex
Resistance (min)
Cardio (min)
Carisa
Resistance (min)
Cardio (min)
Manuel
Resistance (min)
Cardio (min)

Answers

Answer:

Manuel

Step-by-step explanation:

You should set up a proportion graph first such as r:c where r is the amount of minutes spent on resistance and c is the amount of minutes spent on cardio.

Alex's ratio: 24:30

Carisa's ratio: 15:20

Manuel's ratio: 14:15

Now you have to find the lowest common multiple (lcm) of the cardio minutes. Their lcm is 60. Now the ratios look like this:

Alex's ratio: 48:60

Carisa's ratio: 45:60

Manuel's ratio: 56:60

The ratio with the highest first number is considered larger. In this case its Manuel since he has the number 56.


The value of coin A is twice the value of coin B. Together, the total value of the two coins is $30.00 What is the value of each coin?

Answers

Answer: Coin A is $20, coin B is $10

Explanation:

A + B = $30

B = $10

$10 x 2 = $20

A = $20

$20 + $10 = $30

Calculus, derivatives. Please help! Show work, if possible. Thanks! :)

Answers

Answer:

y=-x+pi/3+sqrt(3)/2

Step-by-step explanation:

*I assume you are asking for help on part a because the other question is a calculator question.*

We want to find tangent line to y=2sin(x)cos(x) at x=pi/3.

First I prefer to use y=sin(2x). (Double angle identity: sin(2x)=2sin(x)cos(x) .)

Differentiate using chain rule:

y'=2cos(2x)

y' gives us the slope for any tangent along our curve.

So at x=pi/3, the slope is 2cos(2×pi/3)=2cos(2pi/3)=2(-1/2)=-1.

We also need to know a point our line to find the equation of our line.

At x=pi/3, y=sin(2×pi/3)=sin(2pi/3)=sqrt(3)/2.

So a point on our line is (pi/3, sqrt(3)/2).

So by point-slope form of a line we have

y-y1=m(x-x1)

y-sqrt(3)/2=-1(x-pi/3)

Distribute:

y-sqrt(3)/2=-x+pi/3

Add sqrt(3)/2 on both sides:

y=-x+pi/3+sqrt(3)/2

Answer:

y= -x+(pi/3)+(sqrt3)/2

Step-by-step explanation:

The given is y=2sin(x)*cos(x)

to take the derivative we will need to use the constant rule (which says when taking the derivative of any constant multiplied by an expression you take the derivative of the function and multiply it by the constant) and the multiplication rule to get

y'=2(sin(x)*-sin(x)+cos(x)*cos(x))

this would simplify to be

y'=-2sin^2(x)+2cos^2(x)

We then substitute in the given x value to find the slope of the tangent line at that point and get

-2sin^2(pi/3)+2cos^2(pi/3)

which simplifies to

-2*3/4+2*1/4

which is -1

Since we have the slope we need to find the y value to go with the original x so that we have a point to use in point slope form. When we substitute pi/3 into the given equation we get (sqrt 3)/2 and have the point (pi/3, sqrt3/2)

now we write the point slope form equation

y-(sqrt3)/2= -(x-pi/3)

y-(sqrt 3)/2 = -x+pi/3

y= -x+pi/3+(sqrt3)/2

you could simplify the last two terms, but I think it is simplest to understand this way.

For b, enter both equations into graphing software or a calculator

What is 39,800,000 in scientific notation?

Answers

Answer:

3.98 x 10 to the power of 5

Step-by-step explanation:

Mark me brainleist if this is correct!

The middle school is purchasing shoes for its basketball team. The cost of
each pair of shoes is $42. The total cost, t,is proportional to s,the number
of pairs of shoes ordered. Which of the following equations models this
proportional relationship? *

Answers

Answer:

9s = 378t      

is the same as  (9 x 42)   etc...

Step-by-step explanation:

I don't have the choice of answers of what is being said as proportional but an example is here below of what numbers are multiples of 42 and therefore found its proportion this way.

10s = 420t       (10 x 42)

9s = 378t         (9 x 42)   etc...

8s = 336t

7s = 294t

6s = 252t

5s = 210t    (5 x 42)

4s = 168t    etc....

Find the measure of D
E
3x
2x

A
B
С

Answers

Answer:

2x+3x+x= 180

6x= 180

x=180/6=30

<DBE = 3x = 3*30 = 90

Step-by-step explanation:

Pls mark as brainliest

¿Cuántas hipotenusa tiene el triangulo rectángulo?

Answers

Answer:

Step-by-step explanation:

Only one hypotenuse and it lies opposite to the right angle.

**The domain of f(x) = 3x + 2 is
{-1 in the range?

Answers

Answer:

Yes

Step-by-step explanation:

Graph this function on your calculator and you will see an upwards graph, if the range (y), -1 can be mapped on the graph, it is within the range.

I dont know how to do this Please explain!!!

Answers

Using the idea that similar triangles are proportional, we can solve this problem fairly easily using a proportion. It is always best to try to draw a picture if possible, as it may increase your understanding of the problem! I have attached an image of the situation.

Proportion: The woman's distance from the laser / the woman's height = the lamp post's distance from the laser / the lamp post's height

2.1 / 1.8 = 4.5 / x

8.1 = 2.1x

x = 3.9m

Hope this helps!! :)

a jacket is on sale for $170. this is 80% of the regular price. what is the regular price

Answers

Answer:

$212.5

Step-by-step explanation:

x= 100*170/80

x= 17000/80

x= 212.5

7. Mao counts by fives to 30. Alana counts by tens
to 40. Who will say more numbers? Explain.

Answers

Answer:

Mao will say more numbers.

Step-by-step explanation:

Think about it like this, 5x6=30 Mao will be saying 6 numbers

10x4=40... Alana will be saying 4 numbers.

3409/14 with decimal

Answers

Answer:

243.5

Step-by-step explanation:

3409/14 times 7/7

By the way i divided both numerator and denominator by 77 because of gcf

Reduce

487/2

243.5

Solve for x:
(x + 4) (x - 3) = 0
A. x = -4 and x = 3
B. x= -1 and x = 12
C. x= 1 and x = -12
D. X= 4 and x = -3

Answers

Answer:

answer is A x = -4 and x = 3

Step-by-step explanation:

-4 , 3

switch the signs

Answer:

The answer is "A."

Step-by-step explanation:

x+4=0. x-3=0

x=0-4. x=0+3

x= -4. x= 3

x = -4 and x = 3

Micah is saving to buy a new guitar and every month is putting $45 from his paycheck into his savings
account. He has already saved $120. How many more months will it take before he has enough to buy
the guitar if it costs $415?

Answers

Answer:

6.5555 months

Step-by-step explanation:

$415-$120= $295

Micah will need $295 from his paycheck earnings to be able to afford the guitar.

$295/$45= 6.5555months

what is the psychology of a middle school student compared to a elementary compared to a high school compared to a college how does the brain change

Answers

Our brain's capacity increases day by day with respect to our growth of our bodyAs older the student be the sharper theirs brain becomes.A middle school student has a less equipped brain capable to handle their studies.But a hugh school student has more sharper brain than the middle school student.

Jordan has completed 5/8 of his homework assignment. What is the decimal equivalent of the amount of the assignment he has completed?

Answers

5.8 I think if I’m wrong sorry

Answer:Try to see what you have to do and see if you have to divide and add subtract and multiply

Step-by-step explanation:

26-14-(-6)+(-7)-11

Please help

Answers

[tex] = 26 - 14 - ( - 6) + ( - 7) - 11 \\ = 26 - 14 + 6 - 7 - 11 \\ = 26 + 6 - 14 - 7 - 11 \\ = 32 - 14 - 7 - 11 \\ = 0[/tex]

Answer:

0

Step-by-step explanation:

G

E

M

D

A

S

26 - 14 - (-6) + (-7) - 11

26 - 14 = 12

12 - (-6) + (-7) - 11

12 - 1 = 11

11 - 11 = 0

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