Which expression is the completely factored form of x6−64y3 ? (x2−4y)(x4−16y2) (x2−4y)3 (x2−4y)(x4+4x2y+16y2) (x2+4y)(x4−4x2y+16y2)
The expression which is obtained on factorising it completely is:
[tex]x^6-64y^3=(x^2-4y)(x^4+16y^2+4x^2y)[/tex]
Step-by-step explanation:We are asked to factorize the expression which is given by:
[tex]x^6-64y^3[/tex]
This expression could also be written as:
[tex]x^6-64y^3=(x^2)^3-(4y)^3[/tex]
Now, we know that:
[tex]a^3-b^3=(a-b)(a^2+b^2+ab)[/tex]
Here we have:
[tex]a=x^2\\\\and\\\\b=4y[/tex]
Hence,
[tex]x^6-64y^3=(x^2-4y)((x^2)^2+(4y)^2+x^2\times 4y)[/tex]
i.e.
[tex]x^6-64y^3=(x^2-4y)(x^4+16y^2+4x^2y)[/tex]
What is 1/6×2/3= to what
Can someone help me with this problem?
Iodine-125 has a half-life of about 60 days.
How many milligrams of a 500 mg sample will remain after 300 days?
the answer is 15.625mg
What is the algebraic expression that describes the monthly salary? Let x be the hours of training
The figure below shows a transversal t which intersects the parallel lines PQ and RS:
Write a paragraph to prove that the measure of angle 4 is equal to the measure of angle 8.
Answer:
For the proof, check the explanation part.
Step-by-step explanation:
In the given figure, the lines PQ and RS are parallel and line t is transversal.
It is required to prove that measure of angle 4 is equal to measure of angle 8.
Now, measure of angle 4 will be equal to measure of angle 6 because they are the alternate interior angles.
Now, the measure of angle 6 will be equal to measure of angle 8 because they are the vertically opposite angles.
So, form the above information, it can be concluded that,
[tex]\angle 4=\angle 6\\\angle 6=\angle 8\\\angle 4=\angle 8[/tex]
Hence proved.
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Which is f(5) for the function –2x2 + 2x – 3? –107 –63 –43 –37
(x x y)a = xa x ya illustrates which property of eponents
If I am choosing an outfit to wear, are the events "collared shirt" and "Long-sleeved shirt" Mutually exclusive or Inclusive? Mutually Exclusive Inclusive
Explain how knowing 1+7 helps you find the sum for 7+1
Approximately how many times greater is 8.5×10^8 than 3.4×10^5
seven more than the quotient of a number and 2 is 10
How many ounces are in 14 grams?
Twenty-five students go to lunch. Pizza costs $3 and sandwiches cost $2. Twelve students buy pizza. What is the total amount of money spent on sandwiches?
The total amount of money spent on sandwiches is $26.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Twenty-five students go to lunch. The pizza costs $3 and the sandwiches cost $2.
Twelve students buy pizza.
∴ 13 students bought sandwiches.
So, The total money they spent on Pizza and Sandwiches is (3×12) + (2×13) = 36 + 26 = $52.
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In a load of laundry, 60% of the socks are white. If there are 25 socks in the load, how many are white?
Answer:
15
Step-by-step explanation:
You have to multiply 0.60 by 25 in order to get 15! Easy, right?
The student store sells pencils that have a markup of 120 percent above their wholesale cost of $0.50 each. They also charge sales tax of 8 percent. What is the total cost of a pencil from the student store?
Answer:
The total cost of a pencil from the student store is $ 1.188
Step-by-step explanation:
Given,
The original cost or wholesale cost of each pencil = $ 0.50,
Markup percentage = 120 %,
So, the cost of the pencil after markup = 0.50 + 120% of 0.50
[tex]=0.50+\frac{120\times 0.50}{100}[/tex]
[tex]=0.50+\frac{60}{100}[/tex]
[tex]=0.50+0.6[/tex]
[tex]=1.1[/tex]
Now, sales tax = 8 %,
Hence, the final total cost of a pencil = 1.1 + 8 % of 1.1
[tex]=1.1 + \frac{8\times 1.1}{100}[/tex]
[tex]=1.1+\frac{8.8}{100}[/tex]
[tex]=1.1+0.088[/tex]
[tex]=\$1.188[/tex]
subtract the quoient of 8 divided by 7 from 9
Find slope of horizontal and vertical lines
The product of two ratio rational numbers is 48/5. If one of the rational number is 66/7, find the other rational number.
Final answer:
The other rational number is 384/7.
Explanation:
To find the other rational number, we can set up a proportion by setting the two ratios equal to each other. The given ratio is 66/7, and the product of the two ratios is 48/5.
Let the other rational number be represented by w. Writing the proportion, we have:
66/7 = w/(48/5)
Cross multiplying and solving for w:
w = (66/7) * (48/5)
w = 8*48/7
w = 384/7
Hence, the other rational number is 384/7.
A landscaper buys a tree that grows at a rate of 18 inches every 3 months.
How much does it grow in 1 year?
A. 30 in.
B. 36 in.
C. 54 in.
D. 72 in.
A plant grows 9 in. every 2 months.
How will it grow in a year?
A. 18 in.
B. 36 in.
C. 54 in.
D. 108 in.
1 it grows 18 inches every 3 months
there are 12 months in 1 year
12 dived by 3 = 4 so there are 4 times it will grow 18 inches
18 * 4 = 72 inches, amount it grows in 1 year
Answer is D
2. it grows 9 inches every 2 months
12/2 = 6 times a year it will grow
9 *6 = 54 inches total for 1 year
Answer is C
The distributive property loss of combined subtraction and multiplication for example 3 x (5-2) = (3X5) - (3x2) Explain how you could use the distributive property and mental math to find 5x198
Explain why you would make one of the addends a tens number when solving an addition problem.
Since we can add a number to a tens number easily, we make one of the addends a tens number when solving an addition problem.
Example 1:
Add 9 and 6.
9 + 6 = 9 + (1 + 5)
= (9 + 1) + 5
= 10 + 5 = 15
Note that adding 10 and 5 is much easier than adding 9 and 6.
Example 2:
Add 18 and 16.
18 + 16 = 18 + (2 + 14)
= (18 + 2) + 14
= 20 + 14 = 34
Note that adding 20 and 14 is much easier than adding 18 and 16.
A mean ogre stole 27 of your muffins. That was 3/5 of all of them! With how many did you start ?
Alex is making 12 pennants for the school fair.The pattern he is using to make the pennants is shown in the figure.The fabricfor the pennants costs $1.25 per square foot. How much will it cost Alex to make 12 pennants?
—
THIS IS URGENT!!!!
PLEASE ANSWER WITH WORK.
(04.02 LC)
The graph below shows the numbers of cups of grape juice that are mixed with cups of lemon-lime soda to make servings of grape soda:
A graph is shown. The values on the x-axis are 0, 1, 2, 3, 4, 5. The values on the y-axis are 0, 2, 4, 6, 8, 10. Points are shown on ordered pairs 0, 0 and 1, 2 and 2, 4 and 3, 6 and 4, 8. These points are connected by a line. The label on the x-axis is Lemon lime Soda in cups. The title on the y-axis is Grape Juice in cups.
What is the ratio of the number of cups of grape juice to the number of cups of lemon-lime soda?
using the points, the x is Soda and the Y is the grape juice
for (1,2) 1 soda to 2 juices
(2,4) 2 sodas to 4 juices
so the ratio is 2 juices to every 1 soda which is a 2/1 ratio
Answer:
C
Step-by-step explanation:
Movie rental at a video store, you have two options for renting movies. You can pay $4 per movie,or you can pay a one time membership fee of $20 and then pay only $1.50 per movie. After how many movie rentals will she cost of renting movies with the membership be less than the cost of renting movies without the membership?
After 8 movie rentals, will the cost of renting movies with the membership be less than the cost of renting movies without the membership.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the information given in the question,
There are two options for renting movies.
As per the first option,
Pay $4 per movie, so the equation will be,
y = 4x (i)
Where y is the total cost and x is the number of movies.
As per the second option,
Take a membership of $20, and they pay $1.50 per movie.
So, the equation will be,
y = 1.5x + $20 (ii)
Where y is the total cost and x is the number of movies.
Now, solve equations (i) and (ii)
4x = 1.5x + $20
4x - 1.5x = 20
2.5x = 20
x = 20/2.5
x = 8
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The quotient of 12 and opposite of 3 plus the product of the opposite of 14 and 4
Use the picture to answer. Which real number is not both a whole number and an integer? A. 423 B. 259 C. –156D. 0
What is 1,120 divided by 35
Kwan bought three rolls of regular wrapping paper with 6.7 square meters of paper each. He also bought a roll of fancy wrapping paper containing 4.18 square meters. How much paper did he have altogether?
Answer:
The answer is 24.28 square meters.
Step-by-step explanation:
Kwan bought three rolls of regular wrapping paper with 6.7 square meters of paper each.
The paper in three rolls become = [tex]3\times6.7=20.1[/tex] square meter
He also bought a roll of fancy wrapping paper containing 4.18 square meters.
So, total paper that Kwan had is = [tex]20.1+4.18=24.28[/tex] square meter.
Therefore, the answer is 24.28 square meters.
Answer: The answer is 20.1
Step-by-step explanation: To find out how much paper Kwan had altogether, we need to calculate each type's total square meters of wrapping paper and then add them together.
Kwan bought three rolls of regular wrapping paper, each with 6.7 square meters of paper. To find the total square meters for the traditional wrapping paper, we can multiply the number of rolls (3) by the square meters per roll (6.7):
3 rolls * 6.7 square meters/roll = 20.1 square meters
So, Kwan has 20.1 square meters of regular wrapping paper.
In addition, Kwan also bought a roll of fancy wrapping paper, which contains 4.18 square meters.
To find the total amount of wrapping paper Kwan has, we can add the square meters of regular wrapping paper to the square meters of fancy wrapping paper: