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

Can someone help me please I will mark u brilliant

Answers

Answer:

I think the answer is option 3

Step-by-step explanation:

Answer: The box plot that represents this data is option 3.

Step-by-step explanation:

-2
у
5
4.75
4.5
4.25
1
2.

Answers

The answer is 2.456 to be exact

A cone and a cylinder have the same radius and height What would you need to do to the volume of the cone to find the volume of the cylinder? Multiply by 3 Divide by 3?​

Answers

You will use this formula V=πr2h to get the volume. R will be ur radius and h is height just put it in the calculator and you will get tour answer

look at pic 10 pts will mark brainilest pls

Answers

Answer: it look like you have to do 20*10=200 and 8*4=32 the 4 where I got it from is 10-6=4 so 200+32=232 this is what I think, sorry if it wrong.

Step-by-step explanation: Hope this help :D

what is the probability of rolling an even number with one roll of a number cube?

Answers

Answer:

50% or 1/2

Step-by-step explanation:

There is an even amount of even and odd numbers on a number cube, therefor it is split half and half, giving you 50%.

50% or 1/2

(i may be wrong but i had this for a hw problem)

Annabelle’s bicycle has a wheel radius of 13 inches. She places a sticker on the wheel so that its minimum height above the ground is 0.5 inches. When she rides her bicycle, the wheel completes 90 revolutions every minute. The sticker begins at its minimum height above the ground. Which equation models the height in inches of the sticker after x minutes? y = 0.5 sine (180 pi x) + 13 y = 12.5 sine (180 pi x) + 13 y = 0.5 sine (180 pi x minus StartFraction pi Over 2 EndFraction) + 13 y = 12.5 sine (180 pi x minus StartFraction pi over 2 EndFraction) + 13

Answers

Answer:

[tex]y=12.5 sin(180\pi x-\frac{\pi}{2})+13[/tex]

Step-by-step explanation:

In order to solve this we can start by drawing a sketch of the problem (see attached picture)

So fist, let's take the general form of a sinusoidal movement:

[tex]y=Asin(\omega x+\phi)+b[/tex]

where:

A= amplitude

[tex]\omega[/tex]= angular frequency

x= time

[tex]\phi[/tex] = horizontal shift

b= vertical shift.

In this case, the amplitude will be the maximum distance between the center of the wheel and the highest or lowest point of the trajectory, in this case:

A= 13in - 0.5in =12.5 in

The angular frequency is how many radians the wheel will turn in a minute, so we get:

[tex]\omega=\frac{90 rev}{min}*\frac{2\pi rad}{1 rev}[/tex]

[tex]\omega=180\pi rad/min[/tex]

Generally, the sin function will start at the center of the circular movement. In this case, since it starts on the lowest point, we can say that the graph moves right by [tex]\frac{\pi}{2} rad[/tex], so in this case:

[tex]\phi=-\frac{\pi}{2}[/tex]

and finally, the vertical shift is the distance between the center of the circular movement and the ground so in this case:

b=13in

so when putting it all together we get our equation to be:

 [tex]y=12.5 sin(180\pi x-\frac{\pi}{2})+13[/tex]

A coffee shop sells their coffee beans by the pound. The table below shows the cost, in dollars, for a pound of two different types of coffee. How much more is the cost for 1 1/3 pounds of Jimmy jitters beans than the cost for 1 1/3 pounds of Harry's Himalayan Beans?

Answers

Answer:

1 1/3 x 1/3 =234/6

Step-by-step explanation:

your mama

5. A set of 9 books has 5,487 pages.
Estimate the number of pages in
each book, if each book has the
same number of pages.

Answers

The answer would be 5487/9 since it says each book has the same number of pages

If the Math Olympiad Club consists of 13 students, how many different teams of 5 students can be formed for competitions?

Answers

Answer:

2 teams

Step-by-step explanation:

13 divided by 5 is 2.6, but you cannot split a person in half, so it would be two teams with a remainder of three people.

There are 1287 different teams of 5 students can be formed for competitions.

What is Combination?

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that;

The Math Olympiad Club consists of 13 students.

And, To form different teams of 5 students can be formed for competition.

Hence, We get;

Number of different teams of 5 students can be formed for competitions is,

⇒ ¹³ C ₅

⇒ 13! / 5! 8!

⇒ 1287

Thus, There are 1287 different teams of 5 students can be formed for competitions.

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PLEASE HURRY
A number cube will be rolled 100 times as part of an experiment. Which calculation would you use to predict the number of times a 4 will be rolled?

Answers

Answer:

C. (100)(1/6)

Step-by-step explanation:

This is based on the "number cube" being a regular 6-sided die. You have a 1 out of 6 chance of rolling a 4 each time you roll the die. So that chance times 100 rolls is your answer.

Cambridge slim ate 11 sausages in the first 6 minutes of a high stakes eating contest assuming that he conuitnes at the same pace how many sausgaes would he have eaten by the end of the 15 minute contest

Answers

60(seconds)x6(minutes)= 360 seconds. So 11 sausages in 360 seconds.
60(seconds)x15(minutes)= 900
(11/360)x900= 27,5 sausages

Fort his problem what is the correct answer?

Answers

Answer:

its b have  a nice day

Step-by-step explanation:

Answer:

I think its D.

Step-by-step explanation:

Find the measure of <5.
45 = [?]
699
45
Enter

Answers

Answer:

Step-by-step explanation:

Answer:

Solution given:

<5+69°=180°[co- interior angle]

<5=180°-69°=111°

<5=111°

Bryson is updating his computer. The amount of
time required for a complete update is 48 minutes. The
update is currently 40% complete. How much longer will it
take for the update to be complete?

Answers

Answer:

28.8 min

Step-by-step explanation:

48 x 40% = 19.2

48-19.2 = 28.8

Find the equation of the line shown.

Answers

answer: y = -1/4x + 2
explanation: line passes through y axis on 2, so 2 is your y-intercept. rise/run is ur slope, which is -1/4 .

The equation of the line shown in the graph in point-slope form passing through the points (4, 1) and (0, 2) is,

⇒ [tex]y - 1 = \frac{-1}{4} (x - 4)[/tex]

Given that,

Graph of the equation of the line shown in the image.

Use the formula,

The equation of a line in point-slope form passing through the points

[tex](x_1 , y_1)[/tex] and [tex](x_2 , y_2)[/tex] with slope m is defined as;

⇒ [tex]y - y_1 = m (x - x_1)[/tex]

Where, [tex]m = \frac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

Let us take two points on the graph, which are (4, 1) and (0, 2).

Here, [tex](x_1 , y_1) = (4, 1)[/tex]

And,  [tex](x_2 , y_2)= (0, 2)[/tex]

So, the slope of the line is,

[tex]m = \frac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

[tex]m = \frac{(2 - 1)}{(0-4)}[/tex]

[tex]m = \frac{1}{- 4}[/tex]

[tex]m = \frac{-1}{4}[/tex]

Therefore, the equation of the line with slope [tex]m = \frac{-1}{4}[/tex] is,

⇒ [tex]y - y_1 = m (x - x_1)[/tex]

⇒ [tex]y - 1 = \frac{-1}{4} (x - 4)[/tex]

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Mason wants to play with Maliyah's Doll House, but first he needs to stop at the clubhouse. If all
three stops are in the shape of a triangle, which of the following distances would NOT be an option?

Answers

Answer:

B, (6,8,14)

Step-by-step explanation:

6+8 is equal to 14, not greater than 14

If all three stops are in the shape of a triangle then the distances 6 8 14 would not be an option.

Let us Apply the triangle inequality to the options.

A)5+6>9

6+9>5

5+9>6

So the triangle is possible.

B) 6+8=14 while the condition is that the sum of any two sides in a triangle is always greater than the third side i.e 6+8 must be greater than 14.

So, the triangle is not possible.

Similarly, C and D are possible triangles.

Hence, out of the 4 options, the distances 6 8 14 would not be an option.

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Mason wants to play with Maliyah's Doll House, but first he needs to stop at the clubhouse. If all

three stops are in the shape of a triangle, which of the following distances would NOT be an option?

Answers :

5 6 9 city blocks

6 8 14

7 9 10

8 15 17

A right angled triangle has a second angle equal 24 degrees. The side adjacent to this angle is 3,7 metres long. How long are the hypotenuse and opposite sides? (3)​

Answers

Hypotenuse will be 4.05
Opposite will be 1.65

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Save & Eat
Question 1
Part A
Graph the equation y = -50% - 100 by going to your math tools and opening the Graph tool. Set the scale of the y-axis to range from -150 to 50, and
set the x-values to range from 5 to 10. Paste a screenshot of your graph in the answer field.
B IV X
Font Sizes
A-A-EZ
Characters used: 0/ 15000
Submit

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

5). Find the surface area.
3.6 yd
7 yd
3 yd
2 yd

Answers

15.6 . hope this helps

What is the perimeter, in feet, of a rectangle whose length is twice its width and whose width is 5 feet

Answers

9514 1404 393

Answer:

  30 ft

Step-by-step explanation:

The width is 5 ft. The length is twice that, so is 10 ft. The perimeter is given by the formula ...

  P = 2(L +W)

  P = 2(10 ft + 5 ft) = 2(15 ft)

  P = 30 ft

The perimeter of the rectangle is 30 feet.

Solve for x.
4x + 6
4x + 6
x = [?]

Answers

Answer:

21

Step-by-step explanation:

4x+6+4x+6=180

8x+12=180

8x=168

x=21

Answer:

X=21

Step-by-step explanation:

Well since its just a right angle you really gotta only solve for one since their their the same things.

4x+6=90

Solve the equation

x=21

Even if you do the two together with 180, same thing.

you pick a card at random 4,5,6,7 What is p(5)

Answers

Answer:

1/4

Step-by-step explanation:

probability of picking 5 is 1/4

the number of 5 in the set is 1 and the total is 4

hence 1/4

Answer:

1/4 or 25% chance

Step-by-step explanation:

There are 4 cards in total

There is only 1 5 card.

To find the probability of getting 5:

1/4 = 25%

Help on this math question. 25 points.

Answers

Answer:

the third one

Step-by-step explanation:

X=180-(67+52) this is the correct answer

a)How many vertices does it have?
(b) How many edges (lateral edges plus base edges) does it have?
(c)How many faces (lateral faces plus bases) does it have?

Answers

5 vertices

7 edges

5 faces

What happens when you add two numbers that are opposites?
Example:
[tex] - 33 + - 37[/tex]

Answers

-70
Some actually if it were y=mx+b then it would be the opposite. It would turn positive but I don’t think this one turns like that. I think it’s just -70

63°
13°
Choose the equation that best describes the image

Answers

Answer:

63degrees

Step-by-step explanation:

I cant see the picture well but i assume that is an angle and it is right before 90 degrees

Complete the square in the following quadratic equation

Answers

Answer:

x^2 + 2x = 1 = - 1

Step-by-step explanation:

x^2 + 2x + 3 = 1

x^2 + 2x + 3 - 2 = 1 - 2

x^2 + 2x + 1 = - 1

Lola has 3 feet of ribbon. She needs to cut the ribbon into equal 2-inch strips
2
How many 2-inch strips can she cut from the 3 feet of ribbon?
2
A
15
B
90
C
21
D
145

Answers

Answer:

18

Step-by-step explanation:

1 ft=12in

3ft=36in

divide 36 by 2 and you get 18

Truck A leaves station 1 at 9:00 a.m. and travels at the rate of 60 kph. After 2 hours, Truck B leaves the same station and travels in the same direction at the rate of 80 kph. At what time will Truck B overtake Truck A?

Answers

Answer: [tex]5:00\ PM[/tex]

Step-by-step explanation:

Given

Truck A speed is [tex]v_a=60\ kmph[/tex]

Truck B speed is [tex]v_b=80\ kmph[/tex]

Truck A leaves 2 hours before truck B

Distance traveled in the 2 hour

[tex]\Rightarrow 60\times 2=120\ km[/tex]

Suppose Truck B will catch truck A after t hours

[tex]\therefore 120+60t=80t[/tex]

[tex]\Rightarrow 120=20t\\\Rightarrow t=6\ hr[/tex]

Overtake time is [tex]9:00am +2+6=5:00\ PM[/tex]

Write out the first five terms of the sequence.

an = n - 5

Answers

Answer:

its A

Step-by-step explanation:

took the quiz

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