Answer:
The factored form is [tex]8x^9-27y^{15}=(2x^3-3y^5)(4x^6+6x^3y^5+9y^{10}[/tex]
Step-by-step explanation:
Given : Expression [tex]8x^9-27y^{15}[/tex]
To find : Factor the expression ?
Solution :
Re-write expression as
[tex]8x^9-27y^{15}=(2x^3)^3-(3y^5)^3[/tex]
Applying identity, [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
Here, [tex]a=2x^3[/tex] and [tex]b=3y^5[/tex]
[tex]8x^9-27y^{15}=(2x^3-3y^5)((2x^3)^2)+(2x^3)(3y^5)+(3y^5)^2[/tex]
[tex]8x^9-27y^{15}=(2x^3-3y^5)(4x^6+6x^3y^5+9y^{10}[/tex]
Therefore, The factored form is [tex]8x^9-27y^{15}=(2x^3-3y^5)(4x^6+6x^3y^5+9y^{10}[/tex]
At Chelsea's workplace, 30 people drink 2 cups of coffee a day on average. A pot of coffee has 10 cups of coffee. How many pots of coffee are needed each day?
6 pots
6 pots
6 pots
6 pots
5.Thomas walked 1 1/4 miles from his home to his school. Jackson walks 1 2/3 miles from his home to work. How much farther does Jackson walk to school than Thomas?
Jackson walks 5/12 miles farther than Thomas to work. So, Jackson walks approximately [tex]\( \frac{5}{12} \)[/tex] miles farther than Thomas.
To find out how much farther Jackson walks to work than Thomas, we need to subtract the distance Thomas walks from the distance Jackson walks.
Thomas walks 1 1/4 miles, which is equivalent to 5/4 miles. Jackson walks 1 2/3 miles, which is equivalent to 5/3 miles.
To subtract fractions, we need a common denominator, which in this case is 12. So, 5/3 is equivalent to 20/12, and 5/4 is equivalent to 15/12.
Now, subtracting, we get 20/12 - 15/12 = 5/12 miles.
Therefore, Jackson walks 5/12 miles farther than Thomas.
PLEASE HELP QUICK I'M OFFERING 12PTS AND BRAINLIEST ANSWER
what is the solution set for the open sentence with the given replacement set w^2 + 9 = 6w, (0,3,6,9)
write an expression for the quotient of a number and 5 decreased by 4
How would I solve -x^2 = -36?
Billy picked 18 oranges. Taylor picked 3 times as many oranges as Billy did. They want to put them in bags with 9 oranges in each bag.
How many bags will they need for all the oranges?
[11 (y- 10)] = (4y- 5) what is y
After 2 months on a diet, John’s weight dropped from 168 pounds to 147 pounds. By what percent did John’s weight drop?
Final answer:
John's weight dropped by 12.5%.
Explanation:
To calculate the percent by which John's weight dropped, we need to find the difference between his initial weight and final weight, and then divide that difference by his initial weight. We can then multiply the result by 100 to express it as a percentage.
Initial weight = 168 pounds
Final weight = 147 pounds
Difference = 168 - 147 = 21 pounds
Percent drop = (Difference / Initial weight) x 100
Percent drop = (21 / 168) x 100 = 12.5%
Therefore, John's weight dropped by 12.5%.
Final answer:
To calculate the percent by which John's weight dropped, subtract his final weight from his initial weight, and divide the difference by his initial weight, then multiply by 100. John's weight dropped by 12.5%.
Explanation:
To calculate the percent by which John's weight dropped, you need to find the difference between his initial weight and his final weight, then divide that difference by his initial weight and multiply by 100.
Difference in weight = Final weight - Initial weight = 147 - 168 = -21 Percent weight drop = (Difference in weight / Initial weight) * 100 = (-21 / 168) * 100 = -12.5%So, John's weight dropped by 12.5%.
5,550 divide 10 to the power of 3
This would be 5.55
5550÷10^3=5.55
Hope this helps
The solution involves dividing 5,550 by 1,000, which gives 5.55. The expression 10³ represents 1,000, simplifying the division. Therefore, 5,550 divided by 10 to the power of 3 equals 5.55.
To solve the problem 5,550 divided by 10 to the power of 3, follow these steps:
First, understand that 10 to the power of 3 is equivalent to 10³.Calculate 10³: 10 × 10 × 10 = 1,000. Now, divide 5,550 by 1,000: 5,550 ÷ 1,000 = 5.55.Therefore, 5,550 ÷ 10³ = 5.55.
What is the value of x?
Please help!! Rewrite the expression as the product of two binomials. What are the two binomials for the expression? x(x-8)-9(x-8)
At 1 P.M., there were 16 seagulls on the beach. At 3p.m., there were 40 seagulls. What is the constant rate?
If a sports car is traveling at 95 miles per hour, how long would it take the sports car to overtake a family car traveling at 35 miles per hour that left the same starting point 4.5 hours earlier?
does this equation describe a linear function
Y=2/x-28
If f(x)=-2(5)^x what is f(2)
WHO IS GOOD AT MATH!!!!! Solve this problem.
326-9²+32= ?
is 3.774447444744474447444 a rational number
Martene got a small aquarium for her birthday. The aquarium is a right rectangular prism 18.5cm long by 15cm wide. Martene put 3885 cm3 of water in the aquarium. How deep is the water in the aquarium -
Define a new random variable by y = 2px. show that, as p l 0, the mgf of y converges to that of a chi squared random variable with 2r degrees of freedom by showing that
To show that the moment generating function (mgf) of a random variable y = 2px converges to that of a chi-squared random variable with 2r degrees of freedom as p approaches 0, we need to find the mgf of y using the definition of the mgf and substitute the new random variable. Then, by applying the limit as p approaches 0, we can demonstrate the convergence.
In this question, we are asked to define a new random variable, y = 2px, and show that as p approaches 0, the moment generating function (mgf) of y converges to that of a chi-squared random variable with 2r degrees of freedom.
To show this, we need to find the mgf of y by using the definition of the mgf and substituting the new random variable.
Then, as p approaches 0, we need to simplify the mgf and show that it converges to the mgf of a chi-squared random variable with 2r degrees of freedom.
By applying the limit as p approaches 0, we can demonstrate that the mgf of y converges to the mgf of a chi-squared random variable with 2r degrees of freedom.
what is w reduced by 22? f(w)=
Which of the following is more than 0.35 but less than 0.41
A.
8/25
B.
3/10
C.
2/5
D.
9/26
Answer:
C. [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Let x be the number which is more than 0.35 but less than 0.41,
⇒ 0.35 < x < 0.41
[tex]\implies \frac{35}{100}< x < \frac{41}{100}[/tex]
[tex]\implies \frac{7}{20} < x < \frac{41}{100}[/tex]
∵ Only [tex]\frac{2}{5}[/tex] is between [tex]\frac{7}{20}[/tex] and [tex]\frac{41}{100}[/tex],
Hence, option C is correct.
At tennis practice, Tim practices his backhand and his serve at least 2 hours each day. He works less on his backhand than his serve and practices his serve more than 1/2 hour daily.
Which system of inequalities represents Tim’s daily tennis practice if x represents the number of hours spent practicing his backhand and y represents the number of hours practicing his serve?
The images below are the possible answers,
Answer:
[tex]\left\{\begin{matrix}x+y\geq 2\\ x< y\\ y> \frac{1}{2}\end{matrix}\right.[/tex]
Step-by-step explanation:
Let x represents the number of hours spent practicing his backhand
Let y represents the number of hours practicing his serve.
Since we are given that Tim practices his backhand and his serve at least 2 hours each day i.e. he practices his backhand and serves for two hours or more than two hours
⇒ x+y≥2 --(a)
We are also given that He works less on his backhand than his serve
⇒x < y --(b)
And we are also given that he practices his serve more than 1/2 hour daily.
⇒ y > 1/2 --(c)
Thus the inequalities are :
[tex]\left\{\begin{matrix}x+y\geq 2\\ x< y\\ y> \frac{1}{2}\end{matrix}\right.[/tex]
Thus the Option C is correct .
Seth is reading a long novel. if he reads 45 pages per hour, how many hours will it take him to read 585 pages?
The top of a manhole cover is shaped like a circle. The area of the manhole cover is 380 square inches. What is the circumference of the manhole cover, to the nearest inch?
need to find the radius first
area = pi*r^2
380 = PI *r^2
380/PI = r^2
r^2 = 121
r = sqrt(121) = 11 inches
radius is 11 inches
now calculate circumference:
c = 2*PI*r
C = 2 * 3.14 * 11
circumference = 69.08 = 69 inches
How do you construct a line segment perpendicular to the segment given through the point given?
Find the missing measures for the rectangle.
l = _?_
w = 2 cm
A = _?_
P = 25 cm
A) 12.5 cm; 25 cm2
B) 10.5 cm; 21 cm2
C) 12.5 cm; 21 cm2
D) 10.5 cm; 25 cm2
Show why the function f(x) = 3rad x is not differentiable at x=0
Which of the following characteristics of a parallelogram leads to the conclusion that every square can always be classified as a parallelogram? Select all that apply.
four equal sides
two pair of opposite equal angles
bisecting diagonals
two pair of opposite parallel sides
Answer:
two pair of opposite equal angles
bisecting diagonals
two pair of opposite parallel sides
How do you solve this equation
Answer:
-4
Step-by-step explanation:
Use your knowledge of multiplication facts.
[tex]\sqrt[3]{-64}=\sqrt[3]{(-4)^3}=-4[/tex]
__
Your calculator may be able to do this for you.
The parent function of a graph is f(x) = x2. The graph shifts a units to the left and down b units. Which function models the transformed function?
A) y = x2 - a + b
B) y = (x - a)2 - b
C) y = (x + a)2 - b
D) y = (x - b)2 - a
B was incorrect, whats answer?