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Jet001 [13]
3 years ago
14

One of the factors of x³ - 27 is x - 3. What is the other factor?

Mathematics
1 answer:
Oksi-84 [34.3K]3 years ago
6 0

Answer:

We know that, a³ - b³ = (a - b)(a² + ab + b²)

Now,

  • x³ - 27
  • (x)³ - (3)³
  • (x - 3)(x² + 3x + 9)

Therefore,

  • <u>(x² + 3x + 9)</u> is the other factor.
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Answer:

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3 years ago
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Maria takes guitar lessons that last 4/5 of an hour. She had 4 lessons last week. What is the total number of hours Maria spent
Mazyrski [523]

192 minutes or 3 hours and 12 minutes

an hour is 60 minutes and 60 divided by five is 12 so i multiplied 12 by 4, which is 48 and multiplied 48 by 4 and i got my answer

4 0
2 years ago
Find the sixth term of the sequence 1/2, -3/8, 9/32
sukhopar [10]

Answer:

The sixth term is -243/2048 ⇒ answer B

Step-by-step explanation:

* Lets explain the geometric sequence

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)  

* General term (nth term) of a Geometric sequence:

# U1 = a  ,  U2  = ar  ,  U3  = ar²  ,  U4 = ar³  ,  U5 = ar^4

# Un = ar^(n-1), where a is the first term , r is the constant ratio

  between each two consecutive terms  and n is the position of the

  number in the sequence

- Ex: U5 = ar^4  ,  U7 = ar^6  ,  U10 = ar^9  ,  U12 = ar^11

- Lets solve the problem

∵ The sequence is 1/2 , -3/8 , 9/32

- Lets find the constant ratio r

∵ The first term is a = 1/2

∵ The second term is U2 = ar

∵ The second term  U2 = -3/8

∴ ar = -3/8

∴ 1/2 r = -3/8 ⇒ multiply both sides by 2

∴ r = -3/4

- Lets find the sixth term

∵ a = 1/2 and r = -3/4

∵ n = 6

∴ U6 = ar^5

∴ U6 = 1/2 (-3/4)^5 = 1/2 × -243/1024 = -243/2048

* The sixth term is -243/2048

8 0
3 years ago
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I need help with this problem, if anyone could help ASAP, that would be much appreciated. In the figure below, mROP = 125° Find
VARVARA [1.3K]

Answer:

mRP = 125°

mQS = 125°

mPQR = 235°

mRPQ = 305°

Step-by-step explanation:

Given that

  • mROP = 125°
  • ∠ROP is a central angle

Then:

  • measure of arc RP, mRP = mROP = 125°

Given that

  • ∠QOS and ∠ROP are vertical angles

Then:

  • mQOS = mROP = 125°
  • measure of arc QS, mQS = mROP = 125°

Given that

  • ∠QOR and ∠SOP are vertical angles

Then:

  • mQOR = mSOP

Given that

  • The addition of all central angles of a circle is 360°

Then:

mQOS + mROP + mQOR + mSOP = 360°

250° + 2mQOR = 360°

mQOR = (360°- 250°)/2

mQOR = mSOP = 55°

And (QOR and SOP are central angles):

  • measure of arc QR, mQR = mQOR = 55°
  • measure of arc SP, mSP = mSOP = 55°

Finally:

measure of arc PQR, mPQR = mQOR + mSOP + mQOS = 55° + 55° + 125° = 235°

measure of arc RPQ, mRPQ = mROP + mSOP + mQOS = 125° + 55° + 125° = 305°

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Haylie and Justin went camping with their families for 7 days. They each took their own bottles of water. Haylie drank 6 bottles
trasher [3.6K]

Haylie took 48 bottles of water on the trip.

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