Answer:
the degree of homogeneity is 20.
Step-by-step explanation:
In a polynomial P (x, y), homogeneous and complete in "x" and "y", the sum of the absolute degrees of all its terms is 420. What is its degree of homogeneity?
A homogeneous polynomial is one in which all monomials have the same degree.
This is an example of a homogeneous polynomial of degree 4 (the degree of all monomials is 4):
x ^ 4 + 3x ^ 3y + 2x ^ 2y ^ 2 + xy ^ 3 + 8y ^ 4.
As you can see, the sum of the exponents of the variables x, y in each monomial is 4.
And the number of terms is 5, that is, it is the degree of homogeneity plus 1.
In relation to the sum of the absolute degrees of all monomials or terms it will be: 4 + 4 + 4 + 4 + 4 = 4 * 5 = 20.
In general, you can say that the sum of the absolute degrees in a homogeneous polynomial will be the degree of each monomial by the number of terms = degree * (degree + 1)
Calling n, the degree of our polynomial, it must be fulfilled:
n (n + 1) = 420
=> n ^ 2 + n = 420
=> n ^ 2 + n - 420 = 0
Factoring:
(n + 21) (n - 20) = 0
=> n = -21 and n = 20.
Only the positive value makes sense, therefore n = 20.
In other words, the polynomial is of the form (excluding the coefficients):
x ^ 20 + x ^ 19 y + x ^ 18 y ^ 2 + x ^ 17 y ^ 3 + .... x ^ 3 y ^ 17 + x ^ 2y ^ 18 + xy ^ 19 + y ^ 20
That polynomial has 21 terms.
So the sum of the degrees will be 20 * 21 = 420, as required in the statement.
Therefore, the degree of homogeneity is 20.
Express the ratio as a fraction in simplest form:18 ounces to 3 cups. (Hint) 1 cup = 8 ounces
The ratio 18 ounces to 3 cups is equivalent to 18 ounces to 24 ounces. This is expressed as the fraction 18/24, which simplifies to 3/4 when you divide the numerator and denominator by their greatest common divisor (6).
Explanation:To express the ratio 18 ounces to 3 cups as a fraction in simplest form, we first need to convert the cups to ounces using the provided conversion factor (1 cup = 8 ounces). Therefore, 3 cups is 3 * 8 = 24 ounces.
So, the original ratio of 18 ounces to 3 cups is equivalent to a ratio of 18 ounces to 24 ounces. This can be written as the fraction 18/24. To simplify this fraction, we find the greatest common divisor (GCD) of 18 and 24, which is 6. We then divide both the numerator (18) and the denominator (24) by this GCD.
Doing so, we get 18/24 = 3/4. Therefore, the ratio 18 ounces to 3 cups expressed as a fraction in simplest form is 3/4.
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The ratio as a fraction in simplest form is 18/24 to get 3/4.
Convert cups to ounces:
3 cups = 3 * 8 ounces
= 24 ounces
The ratio is 18 ounces to 24 ounces, which can be written as the fraction
= 18/24.
GCD of 18 and 24= 6.
18 ÷ 6 = 3
24 ÷ 6 = 4
So, [tex]\frac{18}{24}[/tex] simplifies to [tex]\frac{3}{4}[/tex].
Thus, the ratio of 18 ounces to 3 cups in simplest form is 3/4.
Which side lengths form a right triangle?
Choose all answers that apply:
A 2,15, 17
B 1,8, √65
C 2,√80 , 9
Answer:
B. 1,8, root65
Step-by-step explanation:
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]1^{2}[/tex] = 1
[tex]8^2[/tex] = 64
[tex](\sqrt{65})^{2}[/tex] = 65
1 + 64 = 65
Final answer:
Only the set of side lengths B (1, 8, √65) forms a right triangle, according to the Pythagorean theorem, as 1^2 + 8^2 equals (√65)^2.
Explanation:
The question asks which set of side lengths form a right triangle. According to the Pythagorean theorem, in a right triangle, the sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse), which can be expressed as a^2 + b^2 = c^2.
To determine if each set of side lengths forms a right triangle, we can check each option using the Pythagorean theorem:
A: 2, 15, 17 - Check if 22 + 152 = 172.
B: 1, 8,
√65 - Check if 12 + 82 = (
√65)2.
C: 2,
√80, 9 - Check if 22 + (
√80)2 = 92.
After the calculations, we find that:
4 + 225 = 229, which is not equal to 289 (172).
1 + 64 = 65, which is equal to 65 ((
√65)2).
4 + 80 = 84, which is not equal to 81 (92).
Thus, only option B (1, 8,
√65) forms a right triangle.
A filing cabinet has a height of 4 feet and a length of 2 feet. The volume of the filing cabinet is 24 cubic feet. What is the width of the filing cabinet
Answer:
3 ft
Step-by-step explanation:
To find the width of the cabinet, we can use the formula:
length x width x height = volume
By plugging in the information that the problem gives, we can now solve this problem:
2 ft x 4 ft x width = 24 ft
8 ft x width = 24 ft
width = 24 ft / 8 ft
width = 3 ft
The width of the filing cabinet is found by dividing the volume (24 cubic feet) by the product of the length (2 feet) and height (4 feet), which results in a width of 3 feet.
A filing cabinet with a height of 4 feet and a length of 2 feet has a volume of 24 cubic feet. To find the width of the filing cabinet, we can use the formula for the volume of a rectangular solid: V = l x w x h. Given that V = 24, l = 2, and h = 4, substitute these values into the formula and solve for w:
Volume = length x width x height
24 = 2 x width x 4
width = 24 / (2 x 4) = 24 / 8 = 3.
Therefore, the width of the filing cabinet is 3 feet.
Suppose that triangle ABC is dilated to A'B'C' by a scale factor of 4 with a center of dilation at the origin. What is the distance from the center of dilation to the midpoint of B'C'?
The distance from the center of dilation to the midpoint of B'C' is 4 times the original distance from the center to the midpoint of BC, given the dilation scale factor is 4.
Explanation:To find the distance from the center of dilation to the midpoint of B'C', we use the properties of dilations in geometry. Since triangle ABC is dilated with a scale factor of 4, every length in triangle ABC is multiplied by 4 to get the corresponding length in triangle A'B'C'. If the original distance from the center of dilation (the origin) to the midpoint of BC was 'x', then after the dilation, the distance from the center (the origin) to the midpoint of B'C' is 4x. If the original distance x is known, we calculate the dilated distance by multiplying x by the scale factor of 4.
Find the value of m, when 4( m-2 ) =24.
Answer:
m = 8
Step-by-step explanation:
4( m-2 ) =24
Divide each side by 4
4/4( m-2 ) =24/4
m-2 = 6
Add 2 to each
m-2+2 = 6+2
m = 8
At the movie theater, tickets for children cost blank each and adult tickets cost $8.75 each. If ticket sales for a group of 35 people totaled $259, how many children were in this group?
11 children approx.
Let's denote the number of children's tickets as x and the number of adult tickets as y
Since each child ticket costs $4.50 and
each adult ticket costs $8.75,
we can set up the following equations based on the given information:
The total number of people= 35:
x + y= 35
The total revenue from ticket sales= $259:
4.50x + 8.75y = 259
Now we can solve this system of equations to find the values of x and y:
We can start by solving equation 1 for y :
y= 35 - x
Then substitute this expression for y into equation 2:
4.50x + 8.75(35 - x) = 259
Now, solve for x:
4.50x + 306.25 - 8.75x = 259
4.50x - 8.75x = 259 - 306.25
-4.25x = -47.25
Divide both sides by -4.25:
x = (-47.25) / (-4.25)
x = 11.12 approx.
Since the number of children must be a whole number, we can round to the nearest whole number.
So, approximately 11 children were in this group.
Which of the following is the graph of f(x)=cos(x-pi/4)?
Answer:
Step-by-step explanation:
vutdktsjtrsdkuygliydkyrsjyrsyik
What is the area of the circle?
Answer:
3.14
Step-by-step explanation:
HELP IMMEDIATELY
Simplify. Express the answers using positive exponents
1) -2a²b⁴÷4ab⁻⁸, a≠0, b≠0
A) -1/2ab¹²
B) -1/2ab⁻¹²
C) -a/2b⁴
D) -a/2b⁻⁴
2) -5w⁴y⁻²÷-15w⁻⁶y², w≠0, y≠0
A) 1/3w⁻²
B) 1/3y⁴w²
C) w¹⁰/3y⁴
D) w²/3y⁴
Answer:
A and C
Step-by-step explanation:
The expression -2a²b⁴÷4ab⁻⁸ is -1/2ab¹² and expression 5w⁴y⁻²÷-15w⁻⁶y² is w¹⁰/3y⁴
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is -2a²b⁴÷4ab⁻⁸, a≠0, b≠0
We have from properties of exponents that the denominator is multiplied with numerator by changing the sign.
1/aⁿ=a⁻ⁿ
-2a²b⁴/4ab⁻⁸
-1/2a²⁻¹b⁴⁺⁸
-1/2ab¹²
Now the expression is -5w⁴y⁻²÷-15w⁻⁶y²
-5w⁴y⁻²/-15w⁻⁶y²
5w⁴y⁻²/15w⁻⁶y²
1/3w⁴⁺⁶y⁻²⁻²
1/3w¹⁰y⁻⁴
w¹⁰/3y⁴
Hence, the expression -2a²b⁴÷4ab⁻⁸ is -1/2ab¹² and expression 5w⁴y⁻²÷-15w⁻⁶y² is w¹⁰/3y⁴
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Does anyone know this ??
Answer:
t = (log20)÷(0.3)
Step-by-step explanation:
The next model of a sports car will cost 11.2% less than the current model. The current model costs $36,000. How much will the price decrease in dollars? What will be the price of the next model?
Answer:
The decrease in the price will be $4032
The price of the next model is $31968
Step-by-step explanation:
The current model costs $36,000.
The next model of a sports car will cost 11.2% less than the current model
So, decrease in price =[tex]11.2\% \times 36000[/tex]
=[tex]\frac{11.2}{100} \times 36000[/tex]
=4032
So, the price of next model decrease by $4032
So, the price of the next model= 36000-4032 =31968
Hence the price of the next model is $31968
HELP ASAP!!!!
What is the axis of symmetry for f(x) = 2x2 − 8x + 8?
x = −2
x = −3
x = 3
x = 2
A total of 330 tickets were sold for the school play. They were adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?
Answer:
there were 110 adult tickets sold and 220 students tickets sold
Step-by-step explanation:
a+s=330
2a=s
a+2a=330
3a=330
330/3=a
110=a
330-110=s
s=220
Mr. Parsons wants to build a new banister for the stair case shown. If the
rise of the stairs of a building is 5 ft and the run is 12 ft. What will be the
length of the new banister? *
Answer:
I think the answer is 13 feet.
Connor randomly chooses a card from a deck of numbered cards. the cards are numbered 1 through 10, and each number appears only one time. What is the probability that the card Connor chooses has a number on it that is even or divisible by 5?
1) 7/10
2) 3/5
3) 1/2
4) 4/5
Answer:
i belive its 1/2
Step-by-step explanation:
what’s the answer for this question
Answer:
It's app. 50.24
Step-by-step explanation:
The area of a circle is A = pi * r ^2
So the area is
= pi * 16
in the question it says to use 3.14 for pi instead
so multiply 16 * 3.14 = 50.24
Answer:
50.24 square miles
Step-by-step explanation:
The formula for the area of a circle is A=[tex]\pi r^{2}[/tex]
Plug in 3.14 for pi and 4 for r
when you square the 4, you get 16
16 x 3.14 is 50.24
Yasmine has 4 containers of 4 different colors of flowers to plant. She had 1/3 of each color left over when she was done planting. Yasmine said she had planted more than 2 1/2 of the original 4 containers. Use what you know about fractions to determine the total amount of containers of flowers she planted.
Answer:
[tex]2\frac{2}{3}[/tex]
Step-by-step explanation:
Given the information
4 containers of 4 different colors1/3 of each color left overShe had planted more than 2 1/2 of the original 4 containers=> Total color were left = 1/3 x 4 = 4/3 of the original containers
=> Total color were planted = (1 - 1/3) x 4 = 2/3 x 4 = 8/3 of the original containers
However, 8/3 = [tex]2\frac{2}{3}[/tex] > 2[tex]\frac{1}{2}[/tex]
So she is true, hence, the fractions to determine the total amount of containers of flowers she planted is: [tex]2\frac{2}{3}[/tex]
Hope it will find you well
Question in picture
A
B
C
D
I believe the answer is B but im not sure
Answer:
the answer is A
Step-by-step explanation:
hope this helps
which figure has the greatest area
You roll a six-sided die twice. What is the probability of rolling a number divisible by 2 and then a number divisible by 3?
If I am rolling a single dice what is the probability of rolling a number that is divisible by 2 and 3? The only number divisible by 2 and 3 is 6. So, would the answer be 1 out 6 or 1/6
Answer:
1/6
Step-by-step explanation:
FIRST CORRECT ANSWER GETS BRAINLIEST, THANKS, AND FIVE STAR.
CDs R Us sells books on tape and on CD. Tapes sell for $10 and CDs sell for $15.Shayna purchased 16 items and spent a total of $220. What did Shayna purchase?
Answer:
22 tapes
Step-by-step explanation:
that answer could be wrong however, it wasn't specified if he bought a mixture of both items or just one .
also if you had the answer choices that could help a little
graph the circle (x-1)2+(y-8)2=4
Answer:
Use desmos graphing calculator
Step-by-step explanation:
Answer:
radius: (1,8)
distance: 2
Step-by-step explanation:
Please I need it please me
You have been assigned the job of doubling an investment by putting it in an account that earns 8% simple interest annually. About how many years will it take for this to happen?
A) 10
B) 12.5
C) 15
D) 17.5
Answer: b
Step-by-step explanation: 12.5
Tickets to a concert are $35 each. In addition to the cost for the tickets ordered, there is a $15 processing charge per order.
Write an expression that represents the total cost of an order of n number of tickets.
The total cost of an order of n concert tickets, with each ticket costing $35 and a fixed processing charge of $15, is represented by the expression 35n + 15.
To represent the total cost of an order of n number of tickets, we need to account for the cost of each ticket as well as the processing charge that applies to the entire order. The cost of one ticket is $35, and thus for n tickets, the total cost for the tickets alone would be 35n dollars. Since the processing charge is a fixed amount per order, not dependent on the number of tickets, we add the flat fee of $15 to the cost of the tickets. Therefore, the expression for the total cost of the order is 35n + 15.
NEED TO KNOW NOW!!!
inequality graph
Answer:
Graph of an inequality definition
Step-by-step explanation:
The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.
The flag of seychelles is shown below. The rectangular flag has a length of 3 feet and a width of 2 feet. The lines drawn from the bottom left corner to the top right sides of the flag divide those sides into 3 equal parts. What fraction of the falg is painted red?
Answer:
1/5
Sorry that there isn't really an explanation
How do I factorise out the negative?
The Question:
Factorise the following by factorising out the negative sign.
A) -8x -4
B) -4x -2
C) -10x -5y
Honest help will be greatly appreciated
• you have to find what * what = answer
or find the main factors
hope this helps :)
Kristyaks Lonnie to think of a number at 3 to it multiply The Sound by two and then subtract 6 letter n stand for Lonnie starting number which expression represents Lonnie's final number
Correct Question:
Kristyaks Lonnie thinks of a number, adds 3 to it and multiply the Sum by 2 and then subtract 6. Letter n stands for Lonnie's starting number, which expression represents Lonnie's final number
Answer:
The final number is represented by the expression, m = 2n
Step-by-step explanation:
Steps:
The starting number = nLonnie adds 3 to the starting number, i.e. n + 3He multiplies the sum by 2, i.e. 2* (n+3) = 2n + 6He then subtracts 6, i.e. 2n + 6 - 6 = 2nLet Lonnie's final number be mThe expression representing Lonnie's final number is, m = 2nA school district is conducting a survey regarding the effectiveness of its teachers. A random sample of 100 students from the district
are chosen to complete the survey.
Identify the population
A. The population is all teachers employed by the school district.
B. The population is all students enrolled in the school district.
C. The population is the administration
D. The population is all teachers employed by the school district and all students enrolled in the district.
E. The population is the 100 randomly selected students.
Answer:
Step-by-step explanation:
the population is all students enrolled in the school district
Answer:
the population is all students enrolled in the school district
Step-by-step explanation: