All categories

2 years ago

Can I have some help please And please make sure it's right

Mathematics

1 answer:

ElenaW [278]2 years ago

6 0

Answer: OPTION C.

Step-by-step explanation:

According to the Quotient of powers Property, if you divide two numbers whose base is the same, you must rewrite the base and subtract the exponents. Observe:

$\frac{a^m}{a^n}=a^{(m-n)}$

Notice that "a" is the base and "m" and "n" are the exponents.

Therefore, knowing this property, you can solve the exercise.

Given the following expression:

$\frac{3^{15}}{3^3}$

You can notice that the base 3 is in the numerator and in the denominator, then you must apply the Quotient of powers Property and subtract the exponents.

You get that the result is:

$=3^{(15-3)}=3^{12}$

You might be interested in

An astronomical unit (AU) is the average distance between Earth and the sun. One AU is equal to approximately 150,000,000 km. As

Dimas [21]

Using scientific notation, it is found that the measure of one astronomical unit in kilometers is $1.5 \times 10^8$

A number in <em>scientific notation</em> is given by:

$a \times 10^b$

In which $a \in [1, 10)$

To realize the conversion from decimal to scientific notation, b is the number of decimal places the comma moves, being positive if to the left, negative if to the right.

In this problem, 1 AU = 150,000,000 km.

The comma has to move 8 places to the right, hence $b = 8$

Then, the measure is: $1.5 \times 10^8$

For more on scientific notation, you can check brainly.com/question/16394306

5 0

2 years ago

Alvin wants to know what his average paddling rate was for a canoe trip to a campsite. On the way there it took him 8 hours agai

Marizza181 [45]

let

r--------> Alvin's average paddling rate in km/hour

y -------> speed of the current in km/hour

we know that

speed= distance/time ------> solve for distance

distance=speed*time

to Campsite against the current

speed=r-y-----> speed=(r-3)

time=8 hours

distance=(r-3)*8------> equation 2

From Campsite with the current

speed=r+y-----> speed=(r+3)

time=3 hours

distance=(r+3)*3------> equation 1

equate equation 1 and equation 2-----> because is the same distance

(r+3)*3=(r-3)*8----> 3r+9=8r-24----> 8r-3r=24+9-----> 5r=33----> r=6.6 km/hour

therefore

the answer is

Alvin's average paddling rate is 6.6 km/hour

7 0

3 years ago

Find all the solutions of sin x + cos x = 1 in the interval [0, 2pie).

Mashcka [7]

Answer:

X = 0, π/2 in the interval [0, 2pi).

Step-by-step explanation:

Use the auxiliary angle method:

R sin(x + a) = Rsin x cos a + Rcos x sin a = 1

sin x + cos x = 1

Comparing coefficients:

R cos a = 1 and R sin a = 1, so

tan a = R sin a / R cos a = 1

So a = π/4 radians.

Also R^2(sin^2 a + cos^2 a) = 1^2 + 1^2 = 2

Therefore R = √2.

So √2 sin (x +π/4 = 1

sin x + π/4 = 1/√2

x + π/4 = π/4

x = 0 radians

Also

x = 0 + π/2 = π/2.

8 0

2 years ago

A garrison of 120 people had provisions for 30 days. If 20 people leave the garrison after 10 days, how long does the remaining

stiv31 [10]

Answer:

24 days

total units = 120* 30 = 3600

used after 10 days = 120*10 = 1200

remaining units after 10 days = 3600-1200 = 2400

2400/100 people = 24 days that the provisions will last

Step-by-step explanation:

6 0

2 years ago

Solve y = f(x) = (2x+1)^1/2<br><br> & g(x) = x-1

snow_lady [41]

Answer:

f(x) = $x = \frac{y^{2} - 1}{2}$

g(x) = 1

Step-by-step explanation:

y = (2x + 1)^1/2

$y^{2} = 2x + 1$

$y^{2} - 1 = 2x$

$\frac{y^{2} - 1}{2} = x$

y = x - 1

y + 1 = x

8 0

3 years ago