Identification if a polynomial is a sum or difference of two cubes can be done by factorizing the provided polynomial.
What is a polynomial?A polynomial is a mathematical expression that is a sum of one or more terms. Each term is a constant or a variable raised to a non-negative integer power and multiplied by a coefficient. The degree of a polynomial is the highest degree of the terms in the expression. A polynomial with one variable is called a univariate polynomial, and a polynomial with more than one variable is called a multivariate polynomial. Polynomials are used in various areas of mathematics, physics, engineering, computer science, and other fields. They can be used to model a wide range of phenomena and to solve problems that involve polynomial equations or inequalities.
What do you mean by factorization?Factorization, also known as factoring, is the process of breaking down a mathematical expression into a product of simpler factors. The goal is to express a given expression as a product of simpler expressions, which can be useful in solving equations and understanding the structure of the expression.
Factor the polynomial completely into its irreducible factors.
Look for terms that are of the form (x - a)^3 or (x + a)^3, where a is a constant. These are the cubes that you are looking for.
If there are two such terms, check if they can be combined into a single term by adding or subtracting them. If they can, then the polynomial is a sum or difference of two cubes.
If there are more than two such terms, check if any two of them can be combined in the same way. If they can, then the polynomial is a sum or difference of two cubes.
To learn more about polynomials visit:
https://brainly.com/question/11536910
#SPJ4
At Florida A&M University, the ratio of students from Florida to students not from Florida is about `3\ :\ 1`.
How many of its `12000` students are from Florida?
Based on the information given, the number of students from Florida will be; 9000 students.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that At Florida A&M University, the ratio of students from Florida to students not from Florida is about 3 : 1
The Total number of students = 12000
Fraction from Florida = 3/4
Fraction of students not from Florida = 1/4
Therefore, the students from Florida will be:
= 3/4 × 12000
= 9000
Hence, the number of students from Florida is 9000.
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ2
Please help me with my HW
Answer:
24d^5
Step-by-step explanation:
fraction bigger than 2 out of 5 and smaller than 2 out of 3. When i divided numerator by denominator , it will be 0.533.
The fraction that is bigger than 2/5 and smaller than 2/3 is 8/15.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Let the fraction be a/b.
2/5 < a/b < 2/3
Now,
a/b
= (2/3 + 2/5) / 2
= (10 + 6) / 30
= 16/30
= 8/15
= 0.533
Thus,
The fraction is 8/15.
Learn more about fractions here:
https://brainly.com/question/24370499
#SPJ1
1. Length and breadth of a rectangular table-top are 36 cm and 24 cm respectively. Find its perimeter.
Answer:
120 cm.
Step-by-step explanation:
The perimeter of a rectangle is found by adding up the length of all four sides. In this case, the length is 36 cm and the breadth is 24 cm. Therefore, the perimeter of the rectangular table-top is
2 (length + breadth) = 2 (36 + 24) = 2 × 60 = 120 cm.
A tank contains 60 kg of salt and 1000 L of water. A solution of a concentration 0. 03 kg of salt per liter enters a tank at the rate 9 L/min. The solution is mixed and drains from the tank at the same rate. A. ) What is the concentration of our solution in the tank initially?concentration = (kg/L)b. ) Find the amount of salt in the tank after 2. 5 hours. Amount = (kg)c. ) Find the concentration of salt in the solution in the tank as time approaches infinity. Concentration = (kg/L)
(a) The concentration of our solution in the tank initially is 0.060 kg/L. (b) the amount of salt in the tank after 2. 5 hours is 44.45 kg. (c) The concentration of salt in the solution in the tank as time approaches infinity is 0.030 kg/L.
How do you find the concentration of a salt solution?Divide the solute's gram weight by the total weight of the solution, then multiply the result by 100 to get the mass/mass percent of the solution. The amount of solute (measured in grams) per milliliter of solution is known as the mass/volume percent.
(A) Tank contains 60 kg of salt and 1000 L of water. So the concentration of solution in the tank initially = 60/1000 kg/l
The concentration of solution in the tank initially = 0.060 kg/L
(B) Let y(t) denote the amount of salt in the tank at any time t.
Rate In
A solution of concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min.
[tex]R_{i}[/tex] =(concentration of salt in inflow)(input rate of solution)
= (0.03kg/L)*(9L/min)
= 0.27kg/min
Rate Out
The solution is mixed and drains from the tank at the same rate.
Concentration, C(t) = Amount/Volume = y(t)/1000
[tex]R_{out}[/tex] =(concentration of salt in outflow)(output rate of solution)
= {y(t)/1000}kg/L*9L/min
= 0.009y(t) kg/min
Therefore, the differential equation for the amount of Salt in the Tank at any time t:
dy/dt = 0.27 - 0.009y(t)
So the amount of salt in the tank after 2. 5 hours (2.5*60 min = 150 min) is 44.45 kg.
(c) The concentration of salt in the solution in the tank as time approaches infinity
As t -> -∞, e^-∞ = 0
so, the concentration of salt in the solution in the tank as time approaches infinity is 0.030 kg/L.
To learn more about concentration of a salt solution visit:
brainly.com/question/11740694
#SPJ4
Mr. Reginer's class has been struck with hiccups. Three of the students track their number of hiccups over time
Answer:
Step-by-step explanation:
I dont understand the question.
2. Noah said the equation 1. 20(d+5)=42 also represents the situation. Do you agree with Noah? Explain your reasoning ✓ Share with Class
No, I'm not agree with Noah. Because the equation 1. 20(d+5)=42 is a mathematical equation and can be false depending on the value of the variable d.
THE EQUATION REPRESENT SITUATION BY VARIABLEThe equation 1. 20(d+5)=42 is a mathematical equation that contains a variable d. The equation states that when you multiply 20 with (d+5) the result should be 42.
The equation is true if there is a value of d that makes the equation true. For example, if d=1, then 20(1+5)=20(6)=120 which is not equal to 42, so this value of d does not make the equation true.
On the other hand, if d=-7, then 20(-7+5)=20(-2)= -40 which is equal to 42, so this value of d makes the equation true.
Therefore, the equation can be true or false depending on the value of the variable d. In general, without knowing the specific context or situation in which the equation is being used, it is impossible to determine if the equation accurately represents a situation or not.
Learn more about equation here:
https://brainly.com/question/29657983
#SPJ4
Absolute value equations and inequalities.
An absolute value equation is an equation that contains an absolute value expression. An inequality is a mathematical statement that compares algebraic expressions using greater than (>), less than (<), and other inequality symbols.
What are absolute value equations and inequalities?The absolute number of a number a is written as |a|
And represents the distance between a and 0 on a number line.
An absolute value equation is an equation that contains an absolute value expression. The equation IxI = a
Has two solutions x = a and x = -a because both numbers are at the distance a from 0.
To solve an absolute value equation as
x+7|=14
You begin by making it into two separate equations and then solving them separately.
x+7=14
x+7−7=14−7
x=7
or
x+7=−14
x+7−7=−14−7
x=−21
An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.
The inequality |x|<2 represents the distance between x and 0 that is less than 2 Whereas the inequality |x|>2 represents the distance between x and 0 that is greater than 2.
You can write an absolute value inequality as a compound inequality.
$$\left | x \right |<2\: or
−2<x<2
This holds true for all absolute value inequalities.
|ax+ b| < c, where c>0
=−c < ax+ b < c
|ax+ b|> c, where c>0
=ax+ b <−corax+ b>c
You can replace > above with ≥ and < with ≤.
When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.
To know more about absolute value equations and inequalities, check out:
https://brainly.com/question/1779337
#SPJ1
An absolute value equation is an equation that contains an absolute value expression. An inequality is a mathematical statement that compares algebraic expressions using greater than (>), less than (<), and other inequality symbols.
What are absolute value equations and inequalities?The absolute number of a number a is written as |a|
And represents the distance between a and 0 on a number line.
An absolute value equation is an equation that contains an absolute value expression. The equation IxI = a
Has two solutions x = a and x = -a because both numbers are at the distance a from 0.
To solve an absolute value equation as
x+7|=14
You begin by making it into two separate equations and then solving them separately.
x+7=14
x+7−7=14−7
x=7
or
x+7=−14
x+7−7=−14−7
x=−21
An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.
The inequality |x|<2 represents the distance between x and 0 that is less than 2 Whereas the inequality |x|>2 represents the distance between x and 0 that is greater than 2.
You can write an absolute value inequality as a compound inequality.
[tex]$$\left | x \right | < 2\[/tex]: or
−2<x<2
This holds true for all absolute value inequalities.
[tex]|ax+ b| < c, where c > 0\\=−c < ax+ b < c\\|ax+ b| > c, where c > 0\\=ax+ b < −corax+ b > c[/tex]
You can replace > above with ≥ and < with ≤.
When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.
To know more about absolute value equations and inequalities, check out:
brainly.com/question/1779337
#SPJ1
30 students went on a field trip to the science museum. 60% of the students tried the new Gravity Buster ride at the museum.
p = -log(2.1x10^12)
what is p?
The value of p is 12.322
what is the logarithmic function?In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as: For x > 0 , a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.
Given here p=-log(2.1×10¹²)
p= - ( log(2.1) +12 log10)
p= -(0.322+12)
p=12.322
Hence, the value of p is 12.322
Learn more about logarithmic function here:
https://brainly.com/question/30085872
#SPJ1
What are the factors of 2x^2 7x 3?
The factors of 2[tex]x^{2}[/tex] + 7x + 3 are ( x + 3) and (2x + 1)
Now, According to the question:
The given function is :
f(x) = [tex]2x^2+7x+3[/tex]
To find the factors of [tex]2x^2+7x+3[/tex] we need to split the middle term, that is, 7x.
7x = 6x + x
Therefore, 2[tex]x^{2}[/tex] + 7x+ 3 can be written as 2[tex]x^{2}[/tex] + 6x + x + 3 .
On taking '2x' common from first two terms and +1 from next two terms we get
2x (x + 3) +1 (x + 3)
(x + 3) (2x + 1)
Thus, the factors of 2x2 + 7x + 3 are (x+3) and (2x+1)
Learn more about Factorization at:
https://brainly.com/question/2760395
#SPJ4
The complete question is this:
What are the factors of 2x^2+7x +3?
This year, there was 40% more snow than last year. The amount of snow this year is 140% of the amount of snow last year.
1. This year, there were 25% fewer sunny days than last year. The number of sunny days this year is (BLANK)% of the number of sunny days last year.
2. Compared to last month, there was a 50% increase in the number of houses sold this month. The number of houses sold this month is (BLANK)% of the number of houses sold last month.
3. The runner’s time to complete the marathon was 10% less than the time to complete the last marathon. The runner's time to complete the marathon was (BLANK)% of the time to complete the last marathon.
PLEASE FILL IN THE BLANKS. This is in fact the full question
Answer:
75%150%90%Step-by-step explanation:
You want the percentage multiplier associated with the following changes:
25% decrease50% increase10% decreaseMultiplierTo find the multiplier, add 1 to the change. When you want the multiplier in percent, then add 100% to the change expressed as a percent. (1 = 100%)
1. 25% fewer100% -25% = 75% . . . . of last year
2. 50% increase100% +50% = 150% . . . . of sales last month
3. 10% less100% -10% = 90% . . . . of last marathon's time
at a local restaurant the amount of time that customers have to wait for their food is normally distributed with a mean of 32 minutes what is the probability that a randomly selected customer
The probability that a randomly selected customer will have to wait between 32 minutes and 37 minutes is 59.81%
What is meant by probability?How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability. Look up all the related responses.
The likelihood that an event will happen is quantified by probability. An event's likelihood is determined by how frequently it will occur over the long run. Probabilities are all digits that fall between 0 and 1, inclusive—that is, all digits that fall between 0 and 1.
Let the equation of Z score be:
z = (raw score - mean) / standard deviation
Given mean of 36 minutes and a standard deviation of 3 minutes.
If x = 32:
z = (32 - 36)/3 = -1.33
and x = 37:
z = (37 - 36)/3 = 0.33
P(-1.33 < z < 0.33) = P(z < 0.33) - P(z < -1.33)
= 0.6179 - 0.0198
= 0.5981
A consumer selected at random has a 59.81% chance of having to wait between 32 and 37 minutes.
The complete question is:
At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 36 minutes and a standard deviation of 3 minutes. What is the probability that a randomly selected customer will have to wait between 32 minutes and 37 minutes, to the nearest thousandth?
To learn more about probability refer to:
https://brainly.com/question/13604758
#SPJ4
h(a) = a^2 + 4 when a = -3
Answer:
[tex] \sf \: h(-3) = 13[/tex]
Step-by-step explanation:
Given information,
→ h(a) = a² + 4
The value of h(a) when a is -3,
→ h(a) = a² + 4
→ h(-3) = (-3)² + 4
→ h(-3) = 9 + 4
→ [ h(-3) = 13 ]
Hence, required answer is 13.
22. The table shows the number of students
going on a field trip. One chaperone is
needed for every 12 students.
Fifth grade students 310
Sixth grade students 305
Seventh grade students 225
Write two equations with variables that you can use to find a number of chaperones needed
How many chaperones are needed?
Answer:
Step-by-step explanation: i'd say jus divide
Graph the line that passes through the points (9, -1) and (6, 1) and determine the equation of the line.
The equation of the line will be y = -2/3x + 5.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the line passes through points (9, -1) and (6, 1).
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 1 - (-1) / ( 6 - 9 )
Sloe = - 2 / 3
The y-intercept will be calculated as,
y = mx + c
-1 = (-2/3) x 9 + c
c = 5
The equation of the line,
y = mx + c
y = -2/3x + 5
To know more about an equation of the line follow
https://brainly.com/question/18831322
#SPJ1
What do 7th graders learn in math?
In 7th grade math, students learn basic algebra, ratios and proportions, geometry, graphing, probability, equation and statistics.
In 7th grade math, students typically learn basic algebraic principles, including linear equations, variables, and functions. They also learn about ratios, proportions, and percents. Geometry is typically introduced, with topics such as angles, lines, triangles, and circles. Additionally, students may be taught more advanced topics such as graphing, probability, and statistics.In 7th grade math, students learn basic algebra, ratios and proportions, geometry, graphing, probability, and statistics.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
How to simplify an equation?
The process of simplify the equation is explained below.
The term equation is known as a mathematical statement that defines the equality between two expressions.
Here we have to define the process of simplifying the equation.
The first and foremost step is to remove parentheses and brackets by multiplying factors.
And then we have to use the exponent rule to remove grouping if the terms contain exponents.
Then we have to combine like terms by adding or subtracting coefficients.
Finally, we have to Combine the constants.
To know more about equation here.
https://brainly.com/question/10413253
#SPJ4
without computing, decide whether the vaule of each expresstion is much smaller than 1, close to 1, or much greater than 1
Answer: uhm...
Step-by-step explanation:
2...?
Elijah has some candy bars he wants to give away. He will give each person 8 of a candy bar. If he has 3 2- 4 candy bars to give away, how many people will get candy? Show your thinking.
Answer:
He got 32 candy, he give each person , 3,50. or give only tree each person. and he live 8 candy.
raph g(x)=(x+2)(x - 1) - x^{2}g(x)=(x+2)(x−1)−x 2 by making a table and plotting the corresponding points. Then, determine if the function is linear, quadratic, or neither.
The graph from the function is a linear graph
How to determine the graph from the functionFrom the question, we have the following parameters that can be used in our computation:
g(x)=(x+2)(x−1)−x 2
Express properly
So, we have the following representation
g(x) = (x + 2)(x − 1) − x²
Next, we set x = 0, 1, 2 and 3 to determine the table of values
g(0) = (0 + 2)(0 − 1) − (0)² = -2
g(1) = (1 + 2)(1 − 1) − (1)² = -1
g(2) = (2 + 2)(2 − 1) − (2)² = 0
g(3) = (3 + 2)(3 − 1) − (3)² = 1
So, the table is
x 0 1 2 3
g(x) -2 -1 0 1
From the table above, we can see that as x increases by 1, y constantly increase by 1
This means that the function is a linear function
See attachment for the graph
Read more about linear functions at
https://brainly.com/question/15602982
#SPJ1
Big orange trucking is designing an information system for use in "in-cab" communications. It must summarize data from eight sites throughout a region to describe typical conditions. Compute an appropriate measure of central location for the variables wind direction, temperature, and pavement
Wind direction [Mode] is South west
The [Mean] temperature is
The [Bimodal] pavement is Dry Wet
From the question the first question is to determine the wind direction
Generally from the wind direction would be the data with the highest frequency on the wind column i.e the mode of the data, this because this variable(wind direction ) is a nominal level type of level of measurement where the value assigned to the variable are for classification of the data (i.e telling what the data is all about )
So
The mode is Southwest
This means that the wind direction is Southwest
From the question second question is to determine the temperature
Generally given that their are are no outlier that will skew the data we can obtain the temperature by calculating the mean for the temperature column
This is mathematically represented as
T = 89+86+....+93+93/8
T = 91
From the question, the first question is to determine the pavement
Generally from the pavement would be the data with the highest frequency on the pavement i.e the mode of the data, this because this variable(pavement ) is a nominal level type of level of measurement where the value assigned to the variable are for classification of the data (i.e telling what the data is all about )
From the table we see that the pavement that the pavement column is bimodal
So the mode is Dry Wet
This mean that the pavement is Dry Wet
To learn more about Appropriate measure, Visit
https://brainly.com/question/17433567
#SPJ4
Evaluate the expression (-243)1/5
[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ (-243)^{\frac{1}{5}}\implies \sqrt[5]{(-243)^1}\implies \sqrt[5]{(-3)(-3)(-3)(-3)(-3)} \\\\\\ \sqrt[5]{(-3)^5}\implies -3[/tex]
A mountain on a tropical island experiences changes in its height due to volcanic activity. Its current height is 2,827 meters, which is 10% taller than it was when the mountain was last measured. How tall was it then?
Answer:
2,570 meters
Step-by-step explanation:
110% of what number is 2827
1.1x = 2827 Divide both sides by 1.1
[tex]\frac{1.1x}{1.1}[/tex] = [tex]\frac{2827}{1.1}[/tex]
x = 2570
Solve the formula V = πr²h for r.
Answer:
v=πr²h
divide both sides by πh
v/πh=r²
r²=v/πh
square root both sides
r=√v/√πh
I hope this helps
What is an equivalent expression example?
A given set of expressions are known as equivalent expression if and only if the result after evaluating those expression is the same number.
Example,
3 + 2 = 5
4 + 1 = 5
5 + 0 = 5
These three are equivalent as because the sum of all of them is same , i.e., 5.
An equivalent expression is an expression which consists of variables, coefficients, constants, and mathematical functions such as addition, subtraction, multiplication, and division.
In general, if two objects are identical, they are then called as identical.
These expressions are also known as duplicates of each other though they look different but they are same.
To learn more about equivalent expression
brainly.com/question/28170201
#SPJ4
What is the answer to 2/3x=-36
the answer to your question is 36
what is the next operation that should be done when evaluating this expression?
9-12+-2+3(-3)
a) 3(-3)=-9
b)-2+3=1
and if you dont mind showing how you did it so i can learn it thanks!
The next operation that should be done when evaluating this expression 9-12+-2+3(-3) is A. 3(-3)=-9
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
In this case, it should be noted that the expression given is written as 9-12+-2+3(-3). In PEDMAS, the first operation is parentheses. Therefore, the number on parentheses will be solved first.
In this case, the number in parentheses will be 3(-3). Therefore, the correct option is A.
Learn more about expressions on:
https://brainly.com/question/723406
#SPJ1
The diameter of the cylinder barrel was 20 in. When the barrel was lifted away it left an imprint of a circle on the ground. What is the area of the circle?
The area of the circle is 1256.64 square inches.
What is a Circle ?All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
A closed 2D form that isn't a polygon is a circle. It has one face that curves.If two circles have the same radius, they are said to be congruent.Equal chords are always located equally from the circle's center.The center of the circle is the perpendicular bisector of a chord.The line joining the points of two overlapping circles will be perpendicular to the line joining the points of the circles' centers.The tangents drawn at the diameter's endpoints are perpendicular to one another.One of the most fundamental curvilinear geometric forms, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its basis in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.
The diameter of the cylindrical barrel is 20 in
So the diameter of the circular base is 20 in = 10 inches in radius.
Area of the circle = [tex]\pi\ r^{2}[/tex] = π*20*20 = 1256.64 square inches.
To learn more about Volume and area refer to :
https://brainly.com/question/16110853
#SPJ4
What is:
(7*8) + (42-8) / 4
Answer:
5.5
Step-by-step explanation:
7*8=56
42-8=34
56-34=22
22/4=5.5