Answers
Step-by-step explanation:
Part A: [tex]u^6[/tex] can be written as the square of u³, or [tex](u^3)^2[/tex]. Similarly, [tex]v^6=(v^3)^2[/tex]. Hence, we can write this as a difference of two squares by writing it as
[tex](u^3)^2-(v^3)^2[/tex]
Part B:
Difference of Two SquaresWe can first factor a difference of two squares a² - b² into (a+b)(a-b). Here, a would be u³ and b would be v³.
[tex](u^3+v^3)(u^3-v^3)[/tex]
Sum and Difference of Two CubesWe can factor this further by the use of two special formulas to factor a sum of two cubes and a difference of two cubes. These formulas are as follows:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)\\a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
Since u³ + v³ is a sum of two cubes, let's rewrite it.
[tex]u^3+v^3=(u+v)(u^2-uv+v^2)[/tex]
Since u³ - v³ is a difference of two cubes, we can rewrite it as well.
[tex]u^3-v^3=(u-v)(u^2+uv+v^2)[/tex]
Now, let's multiply them together again to get the final factored form.
[tex]u^6-v^6=(u+v)(u^2-uv+v^2)(u-v)(u^2+uv+v^2)[/tex]
Part C:
If we want to factor [tex]x^6-1[/tex] completely, we can just see that x to the sixth power is just [tex]x^6[/tex] and 1 to the sixth power is just 1. Hence, x can substitute for u and 1 can substitute for v.
[tex]x^6-1=(x+1)(x^2-x(1)+1^2)(x-1)(x^2+x(1)+1^2)\\x^6-1=(x+1)(x^2-x+1)(x-1)(x^2+x+1)[/tex]
We can repeat this for [tex]x^6-64[/tex], as 64 is just 2 to the sixth power.
[tex]x^6-64=(x+2)(x^2-x(2)+2^2)(x-2)(x^2+x(2)+2^2)\\x^6-64=(x+2)(x^2-2x+4)(x-2)(x^2+2x+4)[/tex]
Related Questions
Determine the measure of the indicated angle in the following triangle:
Answers
Answer:
Θ ≈ 58°
Step-by-step explanation:
using the Cosine Rule in the triangle
cosΘ = [tex]\frac{80^2+60^2-70^2}{2(80)(60)}[/tex] = [tex]\frac{64000+3600-4900}{9600}[/tex] = [tex]\frac{5100}{9600}[/tex] = [tex]\frac{51}{96}[/tex] , then
Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{51}{96}[/tex] ) ≈ 58° ( to the nearest degree )
- What is the value of x in the figure
(5x)
140
Answers
Answer:
Step-by-step explanation:
5x = 140
= x = 140/5
= x = 28
Consider the given set of numbers 70, 81, 91, 83, 88, and 55. A new number equal to a 12% increase in the median of this set is added to the list. What percentage larger is the mean of the new list in comparison with the original
Answers
New mean is 2.53% larger than the original mean.
What is mean?
Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.
We can find the percentage larger is the mean of the new list in comparison with the original as shown below:
Given, set of number 55, 70, 81, 83, 88, 91
Median= (81+83)/2
= 164/2
= 82
Mean = (55+70+81+83+88+91)/6
= 468/6
= 78
New value which is added = 82*1.12
= 91.84
New Mean = (55+70+81+83+88+91+91.84)/7
= 559.84/7
= 79.97
Increase in mean = 79.97-78
=1.97
increase percentage (1.97/78) *100
= 2.53%
Hence, new mean is 2.53% larger than the original mean.
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Sarah has just opened her own nail salon. Based on experience, she knows that her daily profit, P, can be modelled by = −122 + 168 − 510, where x is the number of clients per day. How many clients should she book each day to maximize her profit?
Answers
Answer:
Step-by-step explanation:
p=-12x^2 + 168 - 510
isolate the varible by diveding each side by factors that dont conatin the varible
x= square root of -p+342/3/2
x= - square root of -p+ 342/3/2
I hope this has helped if you need any clarfcation just ask
The fatal crash rate of teenage drivers 16 years of age is nearly twice as high at night. Select one: True False
Answers
TRUE
The fatal accident rate for young drivers aged 16 to 19 is about four times higher than at night. Two or more passengers of the same age triple the risk of a fatal accident driving a teenager.
An accident in which someone dies. Synonyms: Accident. Type: Collateral damage.
Of the collisions between cars, angled collisions are the most deadly (about 8,000 in 2020). The interactive chart also shows the estimated number of fatalities, injuries, casualties, and all accidents in different types of car accidents.
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Please help me ASAP!! I really appreciate it
Answers
Answer:
a = -1
Step-by-step explanation:
1. Subtract [tex]\frac{2}{3}[/tex] from both sides.
[tex]6a=-\frac{16}{3} - \frac{2}{3}[/tex]
2. Solve the side after the equal sign.
[tex]6a=-6[/tex]
3. Divide 6 from both sides.
[tex]a=-1[/tex]
4. Hope this helped!
[tex]:)[/tex]
The line l cuts the y-axis at (0, 5). l also passes through the point (2, 1). find the equation of the line which is parallel to l and which passes through the point (3, 0).
Answers
Answer: [tex]y=-2x+6[/tex]
Step-by-step explanation:
The slope of line l is
[tex]\frac{5-1}{0-2}=-2[/tex]
Since parallel lines have the same slope, the slope of the line we need to find is -2.
Substituting into point-slope form,
[tex]y=-2(x-3)\\\\y=-2x+6[/tex]
PLEASE HELP
If two lines are perpendicular, then the lines intersect to form four right angles that are 180° each.
False O True
Answers
Answer:
False
Step-by-step explanation:
[If two lines are perpendicular, then the lines intersect to form four right angles] It's true up till here, but a right angle is 90 degrees, not 180 degrees
PLEASE I NEED HELP ON THIS QUESTION
Answers
Answer:
Option c is the correct answer
Step-by-step explanation:
distance of satrun - distance of jupiter
The following graph shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013
Answers
A journalist's statement about this piece of information after analyzing the data could be (a) the owner made a mistake because the rate is constant
How to determine the Journalist statement about this piece of information after analyzing the data?From the question, we have the following highlights:
Year = 2008 to 2013 (this represents the domain)Owner's claim: Production increased at an exponential rateFrom the graph attached to the question, we can see that the graph that shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013 is a linear graph
This is so because the points on the graph are connected by a straight line.
Linear graphs have constant rate
Hence, a journalist's statement about this piece of information after analyzing the data could be (a) the owner made a mistake because the rate is constant
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Complete question
The following graph shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013. The owner of the sugar mill said in an interview that the production increased at an exponential rate since the inauguration. What would a journalist say about this piece of information after analyzing the data?
Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of cosines, what is the measure of angle C? Round your answer to the nearest whole number, if necessary.
A=29
C=24
B=101
Answers
The measure of angle C is obtained as 35 degrees
What is the angle C?Give that;
b^2 = a^2 + c^2 - 2ac Cos B
a = 29
c = 24
B = 101 degrees
b^2 = (29)^2 + (24)^2 - [2 * 29 * 24 cos 101]
b^2 = 841 + 576 + 266
b = 41 cm
Now;
b/sinB = c/sinC
bsinC = csinB
sinC = csinB/b
sinC = 24 * sin 101/41
C = sin-1(24 * sin 101/41)
C = 35 degrees
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Which letter has point symmetry?
Answers
Answer:
Letters A, M, and T
Step-by-step explanation:
All of these letters have a point of symmetry.
Answer: m
Step-by-step explanation:
Find the surface area of the prism. Round to the nearest tenth if necessary.
Answers
The surface area of the prism is 544 mm²
How to determine the surface area
The formula is given thus;
SA=2B+ph
Where
B = area of the base
p = perimeter of the base
h = height
B = 1/2 h(b1+b2)
B = [tex]\frac{1}{2} * 8 * (17 + 9)[/tex]
B = 108 mm²
Perimeter = sum of length of sides
Perimeter = 17 + 9 + 15
Perimeter = 41 mm
Surface area = 2 ( 108 ) + 41 ( 8)
Surface area = 216 + 328
Surface area = 544 mm²
Thus, the surface area of the prism is 544 mm²
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A farmer claims that the average mass of an apple grown in his orchard is 100g. To test this claim, he measures the mass of 150 apples that are grown in his orchard and determines the average mass per apple to be 98g. The results are calculated to be statistically significant at the 0.01 level. What is the correct interpretation of this calculation
Answers
The data is significant at a significance level of 0.01 indicating that the average mass of apples in a farmer's orchard differs from 100g to a level of 0.01. Option C is correct.
Given as the farmer states that the average mass of an apple grown in his orchard is 100g, he measures the mass of 150 apples grown in his orchard and finds that the average mass per apple is 98g and the results are calculated as statistically significant at the 0.01 level.
The null hypothesis is:
H₀ = 100
Because of the farmer's claim.
The alternative hypothesis is:
H₁ ≠ 100
The alternative hypothesis tests the farmer's claim at a level of significance. Results are calculated as statistically significant at the 0.01 level.
This means that at the 0.01 level, the null hypothesis is rejected, i.e. H the average mass of the farmer's orchard differs from 100. Since it is significant at the 0.01 level, it will be significant at the 0.05, 0.1 and increasing levels.
Thus, at the significance level of 0.01, the average mass of apples grown in the farmer's orchard differs by 100 g. The correct answer is therefore given by option C.
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Solve for x: -8 < 3x +1 < 13
Answers
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-8 < 3x+1 < 13 }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-8+-1 < 3x+1+-1 < 13+-1 \ (Add \ -1 \ to \ all \ parts) }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{-9}{3} < \frac{3x}{3} < \frac{12}{3} \ (Divide \ all \ parts \ by \ 3) }} \end{gathered}$}[/tex]
[tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-3 < x < 4 }} \end{gathered}$} }}[/tex]
Luiza wants to go on a popular talent TV show. In order to be accepted, her audition must get at least 60%
positive votes from the people in the crowd. She was afraid she will not get enough votes, so she made a
video of her act and showed it to 60 random people from the crowd before the show. 50% of the people
said they would vote for her.
Let's test the hypothesis that the actual percentage of positive votes among the crowd is 60% versus the
alternative that the actual percentage is lower than that.
The table below sums up the results of 1000 simulations, each simulating a sample of 60 votes, assuming
there are 60% positive votes.
According to the simulations, what is the probability of getting a sample with 50% positive votes or less?
Let's agree that if the observed outcome has a probability less than 1% under the tested hypothesis, we
will reject the hypothesis.
What should we conclude regarding the hypothesis?
Choose 1 answer:
We cannot reject the hypothesis.
We should reject the hypothesis.
Answers
We cannot reject the null hypothesis as the p value is less than 0.01.
How to illustrate the hypothesis?From the information given, Luiza wants to go on a popular talent TV show and in order to be accepted, her audition must get at least 60% positive votes from the people in the crowd.
The observed outcome also has a probability less than 1% under the tested hypothesis. Based on the information, the test statistic will be - 1.58.
After this, this will be checked under the standard normal distribution table where the p value will be 0.0571.
Based on this information, we cannot reject the null hypothesis as the p value is less than 0.01.
In conclusion, the correct option is that we cannot reject the hypothesis.
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By using a number line, arrange each of the each of the following in descending order (a) 4 29upon 33, -2.365,5.5,-3 upon 4 (b) 5 upon 8,-8, 10 1 upon 2 , 5.855, - 2π
Answers
The arrangement of the numbers in descending order (largest to smallest) are as follows;
a). 5.5, 4, 29/33, -3/4, -2.365b). 10, 5.855, 5/8, 1/2 -2π, -8What is the arrangement of the numbers in descending order in each case?It follows from convention that the positive numbers are larger than negative numbers and hence, should appear before negative numbers when the arrangement is in descending order.
Consequently, the numbers can be evaluated and arranged as in the answer above with positive numbers increasing rightwards and negative numbers decreasing leftward of 0 on the number line.
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what is the measure of the largest side of an isosceles acute, if one side is 36
Answers
The measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.
What is an isosceles triangle?A triangle with two sides and angles of equal length and degrees is an isosceles triangle.
Acute Triangle:-
A triangle whose all angels are greater than and less than 90° i.e., all angels are acute is called an acute triangle.
Therefore, all the three angles are less than 90 degrees and two angles are equal.
If one angle is 36 degrees, the other two angles will be 72 degrees each.
If the two angles are 36 degrees each, the last angle will be 108 degrees. 108 degrees is greater than 90 degrees..
Therefore, the angles will be 36°, 36° and 72°.
Hence, the measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.
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Phone chargers in a store are priced $19, $18, $15, $17, $19, $12, $19, and $15.
What display would best show the measures of variation?
(ignore my answer. i didn't mean to click)
Answers
The display that would best show the measures of variation of the given prices is; B: Box and Whisker Plot
What is the importance of Box and Whisker Plot?We are given the prices of Phone chargers in a store as;
$19, $18, $15, $17, $19, $12, $19, and $15.
Now, since we want to determine the display that would best show the measures of variation, the best display would be a box and whisker plot. This is because Box and Whisker plots are a great chart to use when showing the distribution of data points across a selected measure. These box and whisker plots display ranges within variables measured.
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24. A dealer paid 72 cents for a fountain pen listed at 90 cents. What was the rate of discount allowed him? (A) 5% (B) 2% (C) 8% (D) 20%
Answers
Answer:
20%
Step-by-step explanation:
To find the percentage of change find the difference between the two numbers, divide by the original number, then multiply by 100.
Find difference
90-72=18
Divide difference by original
18/90=0.2
Multiply by 100
0.2*100=20
Can someone help mw please :)
Answers
Solve for m.
[tex] \frac{5}{4 - m} = \frac{ - 3}{m + 2}[/tex]
A. [tex] - \frac{11}{3} [/tex]
B. [tex] - 11[/tex]
C. [tex] - \frac{7}{3} [/tex]
D. [tex] - 3[/tex]
Answers
Hello,
[tex] \frac{5}{4 - m} = \frac{ - 3}{2 + m} [/tex]
[tex]5(2 + m) = - 3(4 - m)[/tex]
[tex]10 + 5m = - 12 + 3m[/tex]
[tex]5m - 3m = - 12 - 10[/tex]
[tex]2m = - 22[/tex]
[tex]m = \frac{ - 22}{2} [/tex]
[tex]m = - 11[/tex]
→ Answer B
Variable m cannot be equal to any of the values −2,4 as division by zero is undefined. Multiply both sides of the equation by (m − 4)(m + 2), the lowest common denominator of 4−m,m + 2.
−(2 + m) ×5 = (m −4 )( −3 )To find the opposite of 2+m, find the opposite of each term.
(−2 −m) ×5 = ( m−4 )( −3 )Use the distributive property to multiply −2−m by 5.
−10 −5m = ( m−4 )( −3 )Use the distributive property to multiply m−4 by −3.
−10 −5m =−3m + 12Add 3m to both sides.
−10 − 5m + 3m =12Combine −5m and 3m to get −2m.
−10 −2m = 12Add 10 to both sides.
−2m = 12 + 10Add 12 and 10 to get 2.
−2m = 22Divide both sides by −2.
m = 22 / -2Divide 22 by −2 to get −11.
m = −11Therefore, the correct option is "B".
WILL GIVE BRAINLEST!!!!
Find the measure for the unknown angle.
Answers
The measure for the unknown angle is 65 degrees.
What is the measure for the unknown angle?
The two perpendicular lines form a right angle. A right angle would always have a value of 90 degrees.
In order to determine the unknown angle, subtract 25 degrees from 90 degrees.
90 - 25 = 65 degrees
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The graph below represents which type of power function of the form y = kx'?
Direct Variation with an odd r-value & a positive k-value
O Direct Variation with an even r-value & a positive k-value
Inverse Variation with an odd r-value & a negative k-value
O Inverse Variation with an even r-value & a positive k-value
Answers
The graph represents the type of power function of the form y = kx in the form of D. Inverse Variation with an even r-value & a positive k-value.
How to illustrate the graph?It should be noted that a graph simply means a diagrammatic representation of a particular thing.
Here, the function of the for y = kx is illustrated in the graph.
This is an inverse variation with an even r-value and a positive k-value.
In conclusion, the correct option is D.
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Determine whether the following sequence is geometric. If so, find the common ratio.
1,5,25,125,….
Answers
Answer:
Yes,
Common ratio = 5.
Step-by-step explanation:
If its geometric it will have a common ratio.
5/1 = 5
25/5 = 5
125/25 = 5
So its geometric with commo ratio 5.
The manager of a food store noted that for every 20 persons who visit the store, they sell 6 burgers at $2.35 each, 8 aerated drinks at $1.60 each, and 4 pack of fries at $ 2.00 each. To the nearest cent, what is the average (arithmetic mean) amount of sales per person who comes in?
Answers
JJ decided to leave a tip that is 15% of the original price for his meal. How much should he leave as tip for the $5.50 cheeseburger and $2.50 milkshake? Express you answer to the hundreaths place.
Answers
If JJ decided to leave a tip that is 15% of the original price for his meal, he should leave $1.2 as tip for the $5.50 cheeseburger and $2.50 milkshake.
How to calculate discount?According to this question, JJ bought a $5.50 cheeseburger and a $2.50 milkshake.
This means that in total, JJ purchased $5.50 + $2.50 = $8 worth of meal.
If he decided to leave a tip that is 15% of the original price of his meal, hence,
15/100 × $8 = $1.2
Therefore, if JJ decided to leave a tip that is 15% of the original price for his meal, he should leave $1.2 as tip for the $5.50 cheeseburger and $2.50 milkshake.
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Suppose the daily customer volume at a call center has a normal distribution with mean 4,900 and standard deviation 700. What is the probability that the call center will get fewer than 4,400 calls in a day
Answers
The probability that the call center will get fewer calls than 440 is 0.26115.
Given mean of 4900 and standard deviation of 700.
We have to calculate the probability that the call center will get fewer than 4400 calls.
Probability lies between 0 and 1.
μ=4900
σ=700
We can apply z as well as t statistics because the sample size is not given.
We are applying z statistics.
P(X<4400)=0.5-P(4400<X<4900)
z=X-μ/σ
where μ= mean
σ=standard deviation
z=4400-4900/700
=-500/700
=-0.71
p value of -0.71 is 0.23885.
So the p value of calls less than 4400 is 0.5-0.23885=0.26115.
Hence the probability that the call center will get calls less than 440 is 0.26115.
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12 / (2+1) + 6 * 2 please help me and include steps i am not sure where to go or this
Answers
Answer:
12 / (2+1) + 6 * 2 = 16 (The answer is 16)
Step-by-step explanation:
Step 1: Calculate within parentheses ( 2 + 1 ) : 3
= 12/3 + 6 * 2
Step 2: Multiply and divide (left to right) 12/3 : 4
= 4 + 6 * 2
Step 3: Multiply and divide (left to right) 6 * 2 : 12
= 4 + 12
Step 4: Add and subtract (left to right) 4 + 12 : 16
= 16
Hope this helps out!
The product of the proper positive integer factors of $n$ can be written as $n^{(ax b)/c}$, where $x$ is the number of positive divisors $n$ has, $c$ is a positive integer, and the greatest common factor of the three integers $a$, $b$, and $c$ is $1$. What is $a b c$
Answers
The value of a + b + c based on the product formula is 8.
How to calculate the value?From the information given, the product of the proper divisor is illustrated.
Based on the information, the addition of the symbols will be:
= a + b + c
= 3 + 3 + 2
= 8
In conclusion, the correct option is 8.
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