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[tex]\bf x^6-9x^4-81x^2+729\qquad \begin{cases} x^6=x^{2\cdot 3}\\ \qquad (x^2)^3\\ 729=9\cdot 9\cdot 9\\ \qquad 9^3\\ 81=9\cdot 9\\ \qquad 9^2 \end{cases}\\\\ -------------------------------\\\\[/tex]
[tex]\bf (x^6+729)-(9x^4+81x^2)\implies [(x^2)^3+9^3]-(9x^2x^2+9^2x^2) \\\\\\\ [\underline{(x^2+9)}(x^4-9x^2+9^2)]\ -\ [9x^2\underline{(x^2+9)}]\impliedby \begin{array}{llll} notice\ the\\ \textit{\underline{common factor}} \end{array} \\\\\\ (x^2+9)\ [(x^4\underline{-9x^2}+9^2)\underline{-9x^2}]\impliedby \textit{now we add \underline{these two}} \\\\\\[/tex]
[tex]\bf (x^2+9)\ [x^4-18x^2+9^2]\impliedby \begin{cases} \sqrt{x^4}=x^2\\ \sqrt{9^2}=9\\ 18x^2=2(x^2)(9)\\ thus\ a\\ \textit{perfect square trinomial} \end{cases} \\\\\\ (x^2+9)\ [(x^2)^2-18x^2+9^2] \\\\\\ (x^2+9)(x^2-9)^2\implies (x^2+9)(x^2-3^2)^2 \\\\\\ (x^2+9)\ [(x-3)(x+3)]^2\implies \boxed{(x^2+9)(x-3)^2(x+3)^2} \\\\\\ \textit{and I guess you could be redundant and use} \\\\\\ (x^2+9)(x-3)(x-3)(x+3)(x+3)[/tex]
Related Questions
Martin bought 30 shares of microsoft at the close price of $24.53. in a few years, martin sells all of his shares at $33.71. how much money did martin make?
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Answer:
Money that Martin make is $ 275.9
Step-by-step explanation:
Number of shares Martin Bought = 30
Cost Price of a share = $ 24.53
Total Cost price of all share = 30 × 24.53 = $ 735.9
Selling Price of a share = $ 33.71
Total Selling Price of all shares = 30 × 33.71 = $ 1011.3
Profit money that Martin make = 1011.3 - 735.9 = $ 275.9
Therefore, Money that Martin make is $ 275.9
4⋅10 6 4, dot, 10, start superscript, 6, end superscript is how many times as large as 1\cdot10^41⋅10 4 1, dot, 10, start superscript, 4, end superscript?
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The given problem is very confusing since it was copy pasted directly from the source so the equations look scrambled and plus it was one words. After my own translation, I believe the given numbers are:
4 ⋅ 10^6
and
1 ⋅ 10^4
The symbol ⋅ means that the two numbers are multiplied while the symbol ^ means an exponent of. Now we are asked to find how much the 1st number is larger than the 2nd number. To solve this, we simply have to divide the bigger number by the smaller number. Since 4 ⋅ 10^6 has bigger exponent than 1 ⋅ 10^4 then it is the bigger number.
Ratio = 4 ⋅ 10^6 / 1 ⋅ 10^4
Ratio = 4 ⋅ 10^2 = 400
Therefore 4 ⋅ 10^6 is 400 times bigger than 1 ⋅ 10^4.
Answer:
400 times
Having knowledge about potencies we will find that the final value will be greater than 400 times.
Recalling the properties of powers we find:
Multiplication of powers with the same base.Division of powers with the same base.Power of potency. Potency of a product.Quotient power.Then we can write the two given powers as:
[tex]4 *10^6\\1 * 10^4[/tex]
We know that we have a multiplication and a power, so solving for each of them, we find:
[tex]Ratio = 4 *10^6 / 1 * 10^4\\Ratio = 4 * 10^2 = 400[/tex]
See more about power at brainly.com/question/1618040
How smart are you? A lady walk in the store and steals $100 bill from the register without the owners knowledge. She comes back 5 mins later and buys $70 worth of goods with the $100 bill. The owner gives her $30 in change. How much did the owner lose?
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I included the value of the merchandise that she "purchased", so the owner lost $100 in total value.
think about it...she stole $ 100.....but then the $ 100 was given back to the store....so she basically exchanged the $ 100 for $ 70 worth of goods and $ 30 cash.
What are the solutions of the equation 9x^4 – 2x^2 – 7 = 0? Use u substitution to solve.
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Answer: x=-1, x=1
Compulsive hand washing often increases in frequency because it relieves feelings of anxiety. This best illustrates the impact of
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Solve for x:p=12-x/1000
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1000p=12-x
1000p-12=-x
x=12-1000p
Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a). x^2 – 3x + 6 and x-9
Part 1. Show all work using long division to divide your polynomial by the binomial.
Part 2. Show all work to evaluate f(a) using the function you created.
x – 9 = 0
x = 9
First take the original expression. x^2 - 3x + 6
Fill in the blanks.
9^2-3(9)+6
81-27+6
81-21
60
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x + 6
----------------------------
x - 9 | x² - 3x + 6
- x² - 9x
-------------------
6x + 6
- 6x - 54
--------------
60
There quotient is (x+6) with a quotient of 60.
Part 2. The steps shown are from the concept of Factor and Remainder Theorem. When you substitute x=a to the function, the answer could determine if x=a is a factor or not. If the answer is zero, then x=a is a factor. If not, the answer represents the remainder.
Therefore, x = 9 is not a factor of the given function. It yields a remainder of 60 which coincides with Part 1.
find the GCF 12, 18, 24
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18= 2*3*3
24= 2*2*2*3
The GCF would be equal to the product of all common multiples.
2*3=6
Final answer: 6
(a)at davidson's bike rentals, it costs $14 to rent a bike for 3 hours. how many dollars does it cost per hour of bike use?
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If 9<15mx-8<27, where m is a positive constant, what is the possible range of values of 8/3 -5mx?
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Divide the all by 3
3<5mx-8/3<9
After that times all by -1
-3<8/3-5mx<-9
The possible range of [tex]\dfrac{8}{3}-5mx[/tex] is:
(-9,-3) i.e. [tex]-9<\dfrac{8}{3}-5mx<-3[/tex]
Step-by-step explanation:We are given a set of inequalities of the form:
[tex]9<15mx-8<27[/tex]
Now when we divide all of the inequality by 3 we get that:
[tex]\dfrac{9}{3}<\dfrac{15mx}{3}-\dfrac{8}{3}<\dfrac{27}{3}\\\\i.e.\\\\3<5mx-\dfrac{8}{3}<9[/tex]
Now when we multiply the inequality by -1 then the sign of the inequality gets interchanged.
i.e.
[tex]-3>-(5mx-\dfrac{8}{3})>-9\\\\i.e.\\\\-3>\dfrac{8}{3}-5mx>-9[/tex]
i.e.
[tex]-9<\dfrac{8}{3}-5mx<-3[/tex]
Hence, the possible range of [tex]\dfrac{8}{3}-5mx[/tex] is:
(-9,-3) i.e. between -9 and -3 with -9 and -3 excluded from the range.
What two steps are necessary to put this equation into standard form?
x^2-3x+27=8x-3
A. Add 3 to both sides and subtract 8x from both sides.
B. add 3 to both sides and add 8x from both sides.
C. the equation is already in standard form.
D. Subtract 3 from sides and subtract 8x from both sides.
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+ 3 + 3
---------------------------
x² - 3x + 30 = 8x subtract 8x from both sides ⇒
- 8x - 8x
--------------------------
x² - 11x + 30 = 0 ← standard form
A. Add 3 to both sides and subtract 8x from both sides.
The variable Z is directly proportional to X, and inversely proportional to Y. When X is 10 and Y is 4, Z has the value 47.5.
What is the value of Z when X = 13, and Y = 10
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[tex]Z=k( \frac{X}{Y}),\\k=constant [/tex]
When X=10 and Y=4, Z=47.5.
Therefore
k(10/4) = 47.5
2.5k = 47.5
k = 19.
That is,
[tex]Z= \frac{19X}{Y} [/tex]
When X=13 and Y=10, obtain
Z = (19*13)/10 = 24.7
Answer: 24.7
What are the constants in the expression below? 12x -3.7 -8y +1/3
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In other words, the constants are -3.7 and 1/3
What is the projection of (4 4) onto (-7 3) open study?
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[tex]\vec{a} =4\vec{i} + 4\vec{j}[/tex]
[tex]\vec{b} = -7\vec{i}+3\vec{j}[/tex]
By definition, the projection of [tex]\vec{a}[/tex] onto [tex]\vec{b}[/tex] is
[tex]a_{b} = \vec{a} . \frac{\vec{b}}{|b|} [/tex]
[tex]\hat{b} = \frac{\vec{b}}{|b|} = \frac{1}{\sqrt{49+9}} (-7\vec{i}+3\vec{j})=(-7\vec{i}+3\vec{j})/\sqrt{58}[/tex]
Therefore
[tex]\vec{a} . \vec{b} = -28+12=-16[/tex]
[tex]a_{b} = -16/\sqrt{58} = -2.1[/tex]
Answer:
The projection of (4 4) onto (-7 3) is -2.1.
If EFGH is a parallelogram, then ___________________.
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Answer: The correct option is (B) It might be a rhombus.
Step-by-step explanation: Given that EFGH is a parallelogram. We are to select the correct statement for EFGH.
A PARALLELOGRAM is a quadrilateral whose opposite sides are parallel and equal, opposite angles are equal, the sum of the interior angles is 360 degree.
A RHOMBUS is a particular type of parallelogram, where all the sides are equal and diagonals bisect each other perpendicularly.
Therefore, we can say that every rhombus is a parallelogram, but every parallelogram is not a rhombus.
Therefore, the parallelogram EFGH might be a rhombus.
So, option (B) is correct.
In a certain set of numbers, 12.5 is 1.5 units of standard deviation above the mean, and 8.9 is 0.5 units of standard deviation below the mean. what is the mean of the set?
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12.5 is 1.5 units of standard deviation
So the value for the upper standard deviation would be:
12.5 - 1.5 = 11
8.9 is 0.5 units of standard deviation
So the value for the lower standard deviation would be:
8.9 + 0.5 = 9.4
So, the range of the standard deviation would be about 11 - 9.4 = 1.6 units. The mean would be located at the center of this range which is 0.8 from each of the values. Therefore, the mean would be 11-0.8 = 10.2.
Molly earns a rebate each month on her movie tickets and books. She earns $0.25 for each movie ticket and $2 for each book. Last month Molly purchased 4 movie tickets and earned $17. Part A: Create an equation that will determine the number of books she purchased. (3 points) Part B: Solve this equation justifying each step with an algebraic property of equality. (6 points) Part C: How many books did Molly purchase last month? (1 point)
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r(4,b)=0.25(4)+2b=17
1+2b=17 subtract 1 from both sides
2b=16 divide both sides by 2
b=8.
So Molly purchased 8 books last month.
Choose the equation of the horizontal line that passes through the point (-5,9).
Y= -5
Y= 9
X= -5
X= 9
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Answer: Y=9 Just because the guy above me said so.
Darien ordered soda for $2.75, a sandwich for $8.50, and a dessert for $3.85. Sales tax was $1.15. Use mental math to find the total amount of the bill. Explain
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Then I would add the 2.75. This would be 7.75.
Then add 7.75 + 8.50. To simplify this, you can add 7 + 8, then .75+ .50
Which would equal 15 + 1.25 + 16.25
This question is based on the mental math. Therefore, the total amount of bill is $16.25.
Given:
Darien ordered soda for $2.75, a sandwich for $8.50, and a dessert for $3.85. Sales tax was $1.15.
We need to determined the total amount of the bill.
Let start with the price of the dessert and the sales tax $3.85+ $1.15= $5.
Now, added 2.75 to $5 .
We get,
$2.75 + $5 = $ 7.75
Then, add 7.75 + 8.50.
We get,
= $16.25
Therefore, the total amount of bill is $16.25.
For further details, please prefer this link:
https://brainly.com/question/2017990
You have ten fewer quarters than dimes and 5 fewer nickles than quarters. The total value of the coins is $4.75. How many quarters, nickles, and dimes do you have?
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d = q + 10
n = q - 5
0.05(q - 5) + 0.10(q + 10) + 0.25q = 4.75
0.05q - 0.25 + 0.10q + 1 + 0.25q = 4.75
0.40q + 0.75 = 4.75
0.40q = 4.75 - 0.75
0.40q = 4
q = 4 / 0.40
q = 10 <=== quarters
d = q +10
d = 10 + 10
d = 20 <== dimes
n = q - 5
n = 10 - 5
n = 5 <== nickels
d=q+10 and n=q-5
.25q+.1d+.05n=4.75, then using d and n from above, this becomes:
.25q+.1(q+10)+.05(q-5)=4.75 perform indicated multiplications
.25q+.1q+1+.05q-.25=4.75 combine like terms
.4q+.75=4.75 subtract .75 from both sides
.4q=4 divide both sides by .4
q=10, since d=q+10 and n=q-5
d=20, n=5
So you have 10 quarters, 20 dimes, and 5 nickels.
What would you look for in a word problem that might indicate that you need to use an absolute value inequality?
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a group of college students are volunteering for help the homeless during spring break. They are putting the finishing touches on a house they built. Working alone, irina can paint a certain room in 4 hours. Paulo can paint the same room in 3 hours. write an equation that can be used to find how long it will take them working together to paint the room. how many hours will it take them to paint the room?
A.12 hours
B.1.71 hours
C.0.14 hours
D.3.5 hours
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Let us say that x is the total amount of time it will take if they work together.
From the given statement above, we know that the rate of Irina working alone is 1 job / 4 hours. While that of Paulo is 1 job / 3 hours. Where 1 job indicates to the job of completely painting the room. So adding the two rates would result in 1 job / x hours. Therefore:
1 / 4 + 1 / 3 = 1 / x
Multiplying both sides with 12 x:
(1 / 4 + 1 / 3 = 1 / x) 12 x
3 x + 4 x = 12
7 x = 12
x = 1.71 hours
So working together, they can paint the room for 1.71 hours.
Answer:
B
How do you factor the quadratic equation 36^2= 25
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Do you have the question typed correctly?
In a certain? country, the true probability of a baby being a girlgirl is 0.4640.464. among the next fivefive randomly selected births in the? country, what is the probability that at least one of them is a boyboy??
Answers
ⁿCₓ(p)ˣ(q)ⁿ⁻ˣ
P(girls) = 0.464 ; P(NO girls) = 1-0.464 = 0.536
Then:
p(girls) = 0.464
q(NO girls) = 0.536
n = 5
Probability(NO GIRLS) = ⁵C₀(0.464)⁰(0.536)⁵⁻⁰
⁵C₀ = 1; (0.464)⁰ = 1
Probability(NO GIRLS) = (0.536)⁵
Probability(NO GIRLS) = 0.04424
Probability(at LEAST one boy) = 1 - 0.04424 = 0.955
Final answer:
Calculate the probability of at least one boy being born among the next five randomly selected births in a country where the true probability of a baby being a girl is known.
Explanation:
The probability of at least one boy being born among the next five randomly selected births can be calculated by finding the probability of all girls being born and subtracting it from 1. This is known as the complement rule in probability.
Step-by-step calculation:
Find the probability of all births being girls: 0.4645 = 0.00532Subtract this from 1 to get the probability of at least one boy: 1 - 0.00532 = 0.99468
Therefore, the probability of at least one of the next five births being a boy in this country is approximately 0.99468 or 99.468%.
A gumball machine contains 230 gumballs of 5 different colors: 64 red, 22 blue, 32 orange, 26 green, and the rest white. The machine dispenser randomly selects one gumball. What is the probability that the gumball dispensed is white?
72/115 ≈ 63%
32/115 ≈ 28%
43/115 ≈ 37%
86/100 = 86%
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To solve for the number of white gumballs, you subtract all the other balls to the total.
Number of white balls = 230 - 64 red - 22 blue - 32 orange - 26 green
Number of white balls = 86
Thus,
Probability of white ball = 86/230 = 43/115 or 37%
Answer:
43/115 or 37%
Step-by-step explanation:
A bag contains 7 red marbles, 8 blue marbles, and 9 green marbles. What is the probability of choosing a blue marble when one marble is drawn?
Answers
The probability of choosing a blue marble from the bag is 1/3.
Explanation:The probability of choosing a blue marble can be calculated by dividing the number of blue marbles by the total number of marbles in the bag. In this case, there are 8 blue marbles out of a total of 7 + 8 + 9 = 24 marbles.
So, the probability of choosing a blue marble is:
P(Blue Marble) = Number of Blue Marbles / Total Number of Marbles = 8 / 24 = 1/3
Final answer:
The probability of choosing a blue marble when one marble is drawn from the bag is 1/3 or approximately 0.333.
Explanation:
To find the probability of choosing a blue marble when one marble is drawn from a bag, we need to determine the number of favorable outcomes (blue marbles) and divide it by the total number of possible outcomes (all the marbles).
In this case, there are 8 blue marbles out of a total of 7 red + 8 blue + 9 green = 24 marbles. So the probability of choosing a blue marble is 8/24, which simplifies to 1/3 or approximately 0.333.
Therefore, the probability of choosing a blue marble when one marble is drawn is 1/3 or approximately 0.333.
Answer for lady stole 100 from owner she bought 70 dollars worth of products and got back 30 how much did the owner lose
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Answer: The total loss incurred by the store owner is 100$.
At first look, the answer might seem to be 200$ or 130$, but that's not the correct one. The explanation is below:
The lady stole 100$ from the owner therefore loss incurred is 100$.
The lady went back to the store and:
Step 1 - The lady hands back the 100$ to the store owner. Loss incurred is back to 0$.
Step 2 - The store owner hands over merchandise worth 70$. Loss Incurred is now 70$.
Step 3 - The store owner hands over 30$ worth of change. Loss Incurred is (70 + 30)$ = 100$
in order to use a normal distribution to calculate confidence intervals for p, what conditions on np and nq need to be satisfied? Select one: a. n and q must be integers b. n must be positive c. np>10 and nq<0 d. np and nq must be > 5
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Final answer:
To use normal distribution for calculating confidence intervals for proportion p, both np and nq must be greater than or equal to 5.
Explanation:
In order to use a normal distribution to calculate confidence intervals for a population proportion p, the conditions on np and nq need to be such that both np ≥ 5 and nq ≥ 5. These conditions are necessary because they ensure that the shape of the binomial distribution is similar to that of a normal distribution, which allows for the approximation of the binomial distribution by the normal distribution. When performing a hypothesis test of a single population proportion, it is imperative that the sample data meet these conditions to ensure a valid test. Therefore, the correct answer to the question is d. np and nq must be > 5.
If you have 5 distinct positive integers and the median is 17 and the mean is 12, what are the 5 numbers? How do you know for sure? Can you find 5 distinct positive integers with a median of 17 and a mean of 10? What whole-number means will work for 5 distinct positive integers with a median of 17? What medians will work for 5 distinct positive integers with a mean of 12?
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If the median is 17, that means that one number is 17, two numbers are greater than 17 and two numbers are less than 17.
Remember that the five numbers are distint positive integers.
If the mean is 12, that means that the sum of the five numbers is 12 * 5 = 60
The minimum values could be 1 and 2, with which the partil sum of the three first terms would be 1 + 2 + 17 = 20.
So, the partial sum of the two greater terms is 60 - 20 = 40.
That leads to these possibilities:
1, 2, 17, 18, 22
1, 2, 17, 19, 21
If the two smaller terms are 1 and 3, the possibilities are:
1, 3, 17, 18, 21
1, 3, 17, 19, 20.
If the two smaller terms are 2 and 3, the only possibility is:
2, 3, 17, 18, 20
If the smaller terms are 1 and 4, the only possibility is
1, 4, 17, 18, 20
Other options are:
1, 5, 17, 18, 19
2, 4, 17, 18, 19
You can realize that you cannot use other set of numbers.
2) Part 2: five distinctive numbers with median 17 and mean 10.
sum of the five numbers = 5 * 10 = 50
Given that 17 + 18 + 19 = 54, it is not possible to find those five distinctive numbers.
3) Part 3: What whole-number means will work for 5 distinctive integers with a median of 17.
=>the minimum whole-number means that will work is the whole number equal or greater than [1+2+17+18+19] / 5 = 11.4 => 12.
So, the whole-number means that will work are 12 or more.
4) Part 4. What medians will work for 5 distinctive positive integers with a mean of 12:
total sum = 5*12 = 60.
The smallest median would be 3, because the smaller values would be 1 and 2. The highest median would be.
Also, 1 + 2 = 3 => the median + the two greatest values = 60 - 3 = 57.
=> 18, 19, 20
=> 1, 2,18, 19, 20
So the median has to be between 3 and 18, inclusive.
Ivanna deposits $600 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in the first 2 years?
Answers
Principle [P] = $600
Rate [R] = 3
Time [T] = 2
We know,
[tex]Simple Interest = \frac{Principle * Rate * Time}{100} [/tex]
[tex]= \frac{600*3*2}{100} = 36[/tex]