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4 years ago

Which expression represents the prime factorization of 243?

Mathematics

2 answers:

Kobotan [32]4 years ago

5 0

Answer:

Below in bold.

Step-by-step explanation:

Dividing by primes:

3 ) 243

3 ) 81

3 ) 27

3) 9

So the prime factors of 243 are 3 * 3 * 3 * 3 * 3 or 3^5.

Anika [276]4 years ago

4 0

Answer:

$\boxed{3^5}$

Step-by-step explanation:

<em>Hey there!</em>

Look at the image below↓

By looking at the image we can tell the PR expression is $3^5$ .

<em>Hope this helps :)</em>

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Note that the right triangles with sides equal to 5, 12, 13 and 9, 12, 13 both have a side equal to 12. using this fact find the

kondor19780726 [428]

There is a mistake 9,12,13 is not a right triangle. but 9,12,15 is. IF you use this triangle instead, then the area of the 13,14,15 triangle is the sum of the area of the other two triangles.

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4 years ago

Anely and Sandra get paid per project. Anely is paid a project fee of $40 plus $11.50 per hour. Brenda is paid a project fee of

alexdok [17]

Answer:

$68 to hire and 28.25 per hour to hire both

Step-by-step explanation:

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3 years ago

Kim finds a 1-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and rem

True [87]

Answer:

3/5

Step-by-step explanation:

We want to find the fraction of the original branch that remains, so we will assume a length of the branch in order to make our calculation easier.

Since Kim marks it off in thirds and fifths, let's find the least common multiple of 3 & 5.

Least common multiple of 3 & 5 is 15.

Thus,let's make the length of the branch to be 15-meter long.

Now, if the branch is 15 m long, considering the markings of thirds and fifths, the branch would be cut at:

3, 5, 6, 9, 10, 12 meters.

We are told that She then breaks the branch along all the markings and removes one piece of every distinct length. Thus;

Distinct lengths are;

3 metres

5 - 3 = 2 metres

10 - 9 = 1 meter

Total she removes = 3 + 2 + 1 = 6 meters.

Total remaining is;

15 - 6 = 9 meters

Expressing this as a fraction of the original branch gives:

9/15

Divide both numerator and denominator by 3 to get; 3/5

7 0

3 years ago

Line segment NY has endpoints N(-11, 5) and Y(3,-3).

777dan777 [17]

Given:

Line segment NY has endpoints N(-11, 5) and Y(3,-3).

To find:

The equation of the perpendicular bisector of NY.

Solution:

Midpoint point of NY is

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$Midpoint=\left(\dfrac{-11+3}{2},\dfrac{5-3}{2}\right)$

$Midpoint=\left(\dfrac{-8}{2},\dfrac{2}{2}\right)$

$Midpoint=\left(-4,1\right)$

Slope of lines NY is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{-3-5}{3-(-11)}$

$m=\dfrac{-8}{14}$

$m=\dfrac{-4}{7}$

Product of slopes of two perpendicular lines is -1. So,

$m_1\times \dfrac{-4}{7}=-1$

$m_1=\dfrac{7}{4}$

The perpendicular bisector of NY passes through (-4,1) with slope $\dfrac{7}{4}$ . So, the equation of perpendicular bisector of NY is

$y-y_1=m_1(x-x_1)$

$y-1=\dfrac{7}{4}(x-(-4))$

$y-1=\dfrac{7}{4}(x+4)$

$y-1=\dfrac{7}{4}x+7$

Add 1 on both sides.

$y=\dfrac{7}{4}x+8$

Therefore, the equation of perpendicular bisector of NY is $y=\dfrac{7}{4}x+8$ .

6 0

3 years ago

The diameter of the circle is 6 miles. What is the area of the circle? Use 3.14 for II.

Marysya12 [62]

Answer:

28.26 miles

Step-by-step explanation:

Area= pi times radius squared

diameter is twice the radius so 6÷2=3miles

3 miles is the radius

So A= 3.14 × 3²

= 28.26

6 0

3 years ago

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