Which of the following is the correct factorization of the polynomial below?
Answers
Answer:
C
Step-by-step explanation:
p³ - 216q³ ← is a difference of cubes and factors in general as
a³ - b³ = (a - b)(a² + ab + b²) , then
p³ - 216q³
= p³ - (6q)³
= (p - 6q)(p² + 6pq + 36q²) → C
Answer:
C. (p - 6q)(p² + 6pq + 36q²)
Step-by-step explanation:
Equation at the end of step 1
[tex](p^{3} ) - (2^{3} 3^{3} q^{3} )[/tex]
Trying to factor as a Difference of Cubes:
Factoring: p^3 - 216q^3
Theory: A difference of two perfect cubes, a^3 - b^3 can be factored into
(a-b) • (a^2 +ab +b^2)
Proof: [tex](a-b)(a^{2} +ab+b^{2} ) =[/tex]
[tex]a^{3} + a^{2} b+ab^{2} -ba^{2} -b^{2} a-b^{3} =[/tex]
[tex]a^{3} +(a^{2} b-ba^{2} )+(ab^{2} -b^{2} a)-b^{3} =[/tex]
[tex]a^{3} +0+0-b^{3} =[/tex]
[tex]a^{3} -b^{3}[/tex]
Check: 216 is the cube of 6
Check: p^3 is the cube of p^1
Check: q^3 is the cube of q^1
Factorization is:
[tex](p-6q)(p^{2} + 6pq+36q^{2} )[/tex]
Trying to factor a multi variable polynomial :
Factoring: p^2 + 6pq + 36q^2
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Final Result:
(p - 6q)(p² + 6pq + 36q²)
Related Questions
Please answer correctly! I will mark you as Brainliest!
Answers
Answer:
i got 616 for the answer good luck!!
Step-by-step explanation:
Answer:
B.) 205.3³
Step-by-step explanation:
Volume = (length·width·height) divided by 3
⬇
V = (lwh)/3
⬇
V = (11·7·8)/3 ≈ 205.33333
⬇
205.3³
Enter the correct letter to match each summation expression with the property or formula. N Σ i=1 cai is equal to . A n(n + 1)(2n + 1) 6 n Σ i=1 i is equal to . B n(n + 1) 2 n Σ i=1 c is equal to . C c n Σ i=1 ai n Σ i=1 i3 is equal to . D cn n Σ i=1 i2 is equal to
Answers
Answer:
[tex]\sum\limits_{i=1}^{n} c \cdot a_i \ is \ equal \ to \ c = \ c \cdot \sum\limits_{i=1}^{n} a_i[/tex]
[tex]\sum\limits_{i=1}^{n} i \ is \ equal \ to \ b = \dfrac{n \cdot (n + 1)}{2}[/tex]
[tex]\sum\limits_{i=1}^{n} c \ is \ equal \ to \ d = c \cdot n[/tex]
[tex]\sum\limits_{i=1}^{n} i^3 \ is \ equal \ to \ e = \left [ \dfrac{n \cdot (n + 1)}{2} \right]^2[/tex]
[tex]\sum\limits_{i=1}^{n} i^2 \ is \ equal \ to \ a = \dfrac{n \cdot (n + 1) \cdot (2 \cdot n + 1)}{6}[/tex]
Step-by-step explanation:
1) The sum of a series of the cubes of numbers 'i' is given as follows;
Sₙ = n/2 × (1st term + Last term)
∴ Sₙ = n/2 × (1 + n) = n·(n + 1)/2
It can be shown that the sum of a series of the cubes of numbers 'i²' is given as follows;
Sₙ = (n·(n + 1)·(2·n + 1))/6
It can be also be shown that the sum of a series of the cubes of numbers 'i³' is given as follows;
Sₙ = (n·(n + 1)/2)²
Therefore, we have;
[tex]\sum\limits_{i=1}^{n} c \cdot a_i= c \cdot \sum\limits_{i=1}^{n} a_i = c[/tex]
[tex]\sum\limits_{i=1}^{n} i = \dfrac{n \cdot (n + 1)}{2} = b[/tex]
[tex]\sum\limits_{i=1}^{n} c = c \cdot n = d[/tex]
[tex]\sum\limits_{i=1}^{n} i^3 = \left [ \dfrac{n \cdot (n + 1)}{2} \right]^2 = e[/tex]
[tex]\sum\limits_{i=1}^{n} i^2 = \dfrac{n \cdot (n + 1) \cdot (2 \cdot n + 1)}{6} = a[/tex].
Answer:
c, b, d, e, a
Step-by-step explanation:
simplify (3x^2 y^5)^4
Answers
Answer:
Step-by-step explanation:
Equation is below
Step 1
(3x^2 y^5)^4
Step 2
(3x^2 y^5)^4 Simplify
81x^8y^20
Step 3
81x^8y^20 check
Answer
81x^8y^20
Hope this helped
Which 2 coins equals 30 cents when one is not a nickel?
Answers
Answer:
nickel and a quarter
Step-by-step explanation:
One is a nickel, the other is NOT a nickel... it is a quarter.
A rectangular prism has a length of 1 yards, a width of 2) yards, and a height of 4 yards.
Enter the volume of the prism as a mixed number in simplest form in the box.
Answers
Answer:
8
Step-by-step explanation:
2*1*4=8
Need the answers for 4-8
Answers
Answer:
hope this helps you out ask me if you need more help
Think of an example of an externality and its effects on the third party.
Answers
Answer:
Negative consumption externalities. When certain goods are consumed, such as demerit goods, negative effects can arise on third parties. Common example include cigarette smoking, which can create passive smoking, drinking excessive alcohol, which can spoil a night out for others, and noise pollution.
What is the base, perimeter of base, and height of this figure? No links pls or I will report u!
Answers
which number line best represents the solution to the inequality 3.3w - 9 > -22.27
Plz answer hurry
Answers
Answer:
Step-by-step explanation:
The answer would be (G)
The value of w is greater than -4 which will best represent the inequality 3.3w - 9 > -22.27 on number line.
What is a number line?Number lines are simple, visual pictures of how the values of numbers increase and decrease.
Given an inequality 3.3w - 9 > -22.27
On solving, we get,
3.3w - 9 > -22.27
3.3w > -22.27 + 9
3.3w > -13.27
w > -4
Hence, the value of w is greater than -4 which will best represent the inequality 3.3w - 9 > -22.27 on number line.
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Help me please an thanks
Answers
Answer:
4.6
Step-by-step explanation:
2^2+x^2=5^2
4+x^2=25
x^2=25-4
x^2=21
x=square root 21
x=4.58=4.6
can someone please help
find slope/rate of change
a. 1/3
b. 3
c. 30
d. 10
Answers
Without properly working spark plugs, a vehicle will not run. For a specific vehicle, the spark plugs are supposed to have a gap between 3.9mm and 4.3mm. Any spark plugs with gaps larger or smaller than this will fail inspection and be discarded. At the factory, the machine that sets the gap follows a normal distribution with a mean of 4.1mm and standard deviation of 0.075mm. What is the probability that a randomly selected spark plug passes inspection
Answers
Answer:
The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.
P(3.9≤X≤4.3) = 0.9922
Step-by-step explanation:
Step(i):-
Given that the mean of the Normal distribution = 4.1mm
Given that the standard deviation of the Normal distribution = 0.0075mm
Let 'X' be the random variable in a normal distribution
Given that X₁ = 3.9mm
[tex]Z_{1} = \frac{X_{1} -mean}{S.D}[/tex]
[tex]Z_{1} = \frac{3.9 -4.1}{0.075} = -2.666[/tex]
Given that X₂ = 4.3mm
[tex]Z_{2} = \frac{X_{2} -mean}{S.D}[/tex]
[tex]Z_{1} = \frac{4.3 -4.1}{0.075} = 2.666[/tex]
Step(ii):-
The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.
P(3.9≤X≤4.3) = P(-2.666≤Z≤2.666)
= P(Z≤2.666)-P(Z≤-2.666)
= 0.5 +A(2.666) - (0.5-A(2.666)
= 2 × A(2.666)
= 2×0.4961
= 0.9922
Final answer:-
The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.
P(3.9≤X≤4.3) = 0.9922
Marsha deposited $7,500 into a savings account 5 years ago. The simple interest rate is 3%. How much money did Marsha earn in interest? What would be her new account balance?
Answers
they made $1125 and the new balance is $8625
Answer:
earned in intrest would be 450.
Step-by-step explanation:
i did the assingment
can someone help with this (please) :D
Answers
Answer:
i think the answer to this question is 2.461
Step-by-step explanation:
For a semicircle, the total perimeter includes half of the circumference + the diameter.
The half circumference is given by 2 pi r / 2
So the perimeter of 19.02 = 2pi r/ 2 + 2r
(WILL GIVE BRAINLIEST) Find the total surface area of the figure shown.
ANSWER CHOICES:
319.30 yd^2
284.60 yd^2
249.60 yd^2
270.30 yd^2
Answers
Yea
HELP ASAP
Two birds sit at the top of two different trees. The distance between the first bird and a birdwatcher on the ground is 32 feet. The distance between the birdwatcher and the second bird is 45 feet.
A triangle is created from point Bird Watcher, point First Bird, and point Second Bird. Angle First Bird is a right angle, and angle Second Bird measures x degrees.
What is the angle measure, or angle of depression, between this bird and the birdwatcher? Round your answer to the nearest tenth.
35.4°
44.7°
45.3°
54.6°
Answers
Answer:
The correct angle is 45.3°
Step-by-step explanation:
Since the opposite side of the angle is 32 feet, and the hypotenuse of the right triangle is 45 feet, you would know that the sine of x° is equivalent to [tex]\frac{32}{45}[/tex]. To find the value of x, take the arcsin of both sides and you'll get that [tex]x = arcsin(\frac{32}{45})[/tex] ⇒ [tex]x[/tex] ≈ 45.3°.
In this diagram, ABAC – AEDF. If the area of ABAC = 24 in2, what is the area of AEDF? D À E 2 in F В 4 in С Area AEDF = [?] in2 please I need help
Answers
Answer: 6
Step-by-step explanation:
The area of the triangle EDF is 6 in².
What are similar triangles?Two triangles are said to be similar if their corresponding angles are congruent, and their corresponding sides are in equal ratios.
Given that, two triangles are similar, ABC and EDF,
We know that, the area of two similar triangles implies that if two triangles are similar to each other, the ratio of their areas will be proportional to the square of their corresponding side ratios.
Therefore,
ar(ΔABC)/ar(ΔEDF) = (2/4)²
24/ar(ΔEDF) = 1/4
ar(ΔEDF) = 6
Hence, the area of the triangle EDF is 6 in².
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Very easy answer but does any one know what C is
Answers
Answer:
Step-by-step explanation:
they want you to recognize that it's a linear relationship
i need help with thil real quick please
Answers
Answer:
AED 18.85
Step-by-step explanation:
Given that:
Radius, r = 1cm
Length = height, h = 12
Cost per cm³ = AED0.50
VOLUME OF CYLINDER = pi * r² * h
Volume = 3.14 * 1² * 12
Volume = 37.699 cm³
Cost per cm³ = AED 0.5
TOTAL COST :
AED 0.5 * 37.699
= AED 18.849
= AED 18.85
1. The range of guest on New Year's Eve was 15>
2. About 50% of Thanksgiving dinners had 17 or more people.
3. Everyone had at least one guest over for dinner at Thanksgiving.
4. The IQR of Thanksgiving dinner was 20.
5. The median number of people at New Years' Eve dinner was 15.
6. Three-fourths of New Years' Eve dinners had five or more people.
Answers
Answer:
1.False
2. True
3.) True
4. False
5.) False
6.) True
Step-by-step explanation:
1.)
Range = maximum - minimum
New year's eve :
Maximum = 22 ; minimum = 3
Range = 22 - 3 = 19
2.)
Median for Thanksgiving = 17
50% up to 17 ;hence the remaining 50% is also 17 and above
4.)
IQR for Thanksgiving
Q3 - Q1
23 - 12 = 11
5.)
The median number of people at new year's eve for dinner was 7 (line in between the box)
6.)
3/4th of new year eve's dinner = Q3 = 15
1/4 = Q1 ; have up to 5 people
Therefore ; the remaining (1 - 1/4) = 3/4 have 5 and above
Answer:
1.False
2. True
3.) True
4. False
5.) False
6.) True
Step-by-step explanation:
Which solid has the top, side, and front views given
please help me I’m
In an exam!
Answers
Answer:
I. most probably
Hope it helps!!!
Step-by-step explanation:
A chocolate company makes dark chocolate bars. The quality control department of the company has found that the weights of the chocolate bars follow a normal distribution, with a mean of 85 grams and standard deviation of 1.2 grams. To ensure a consistent product, the company has a policy to reject any chocolate bars weighing less than 82.6 grams or more than 87.4 grams. Approximately what percent of chocolate bars are rejected?
a. 0.12%
b. 0.15%
c. 0.30%
d. 2.50%
e. 5.00%
Answers
WHAT IS 4/5 DIVIDED BY 8?
I WOULD GIVE YOU A POINTS
Answers
Answer:
1/10
Step-by-step explanation:
Answer: 0.1
Step-by-step explanation:
The box and whisker plots represent the number of minutes spent by users on two different social media groups. Which THREE statements are correct when comparing the plots?
A) The median time for users of Group B is 40 minutes.
B) Group B has greater median value than Group A.
C) The data for Group B varies slightly more than Group A.
D) The spread of the data for Group A is 25 minutes.
E) The spread of the data for Group A is 40 minutes.
Answers
Answer:
A, C, and D
Step-by-step explanation:
PLEASE HELP MEEEEEE!!! BRAINLIEST WILL BE GIVEN! NO LINKS!
Answers
Answer:
Step-by-step explanation:
it's like this Loving , 62.90 / 330 = 0.1906...
so she paying about 19 cents per mile :)
Find the value of y that makes the equation y = 8 – 2x true, when x = 3. A. 2 B. 5 C. 6 D. 8
Answers
Answer:
so first you would find out the whole equation after you plug in x and it would be
y=8-6
y=2
so the answer is A. 2
The value of y is 2.
The correct option is (A).
What is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
Given equation is: y = 8 – 2x.
So, when x=3
y= 8-2*3
=8-6
= 2.
Hence, the answer is A. 2
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Easy points you know it’s easy points
Answers
Answer:
98 ft²
Step-by-step explanation:
Answer:
98 ft²
Step-by-step explanation:
Want points
find the value of y. 120° y = ?°
Answers
Answer:
240
Step-by-step explanation:
360 minus 120 degree give 240 degree
Answer: 60
Step-by-step explanation:
120/2= 60
Help with this pleeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeease lol
Answers
Answer:
6- D
4- A
3- A
Step-by-step explanation:
Answer:
6. = D
4. = A
Step-by-step explanation:
6. 2(2.5)= 5
4(2.5)= 10
6(2.5) =15
9(2.5) is not 21 its 22.5
4. 125÷5 = 25
help asap pls, thank u
Answers
Answer:
1243.4 [tex]cm^{3}[/tex]
Step-by-step explanation: