If two polynomials have different degrees, the degree of the sum is the maximum of the degrees of each polynomial.
A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).
In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.
Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.
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Divide the following: Please show your work. (Lots of points.)
Answer:
-27
10x +8.
Step-by-step explanation:
x² - 9 ÷ x² - 4x - 5
=x²+5x+4 x² - 2x - 15
x² - 9 × x² - 2x - 15
=x² +5x +4 x² - 4x - 5
-9 × 3
=5x. 4. 2
-27.
=10x + 8 .
The mass of a cube, M (kg), is proportional to the cube of the length of its edge,
L (m).
The mass of the cube is 40 kg when the length of its edge is 35 cm.
Work out M (to 2 DP) when L = 0.6 m
Thank you
Answer:
We are given that the mass of a cube, M, is proportional to the cube of the length of its edge, L. This means that we can write the relationship between M and L as:
M = kL^3
where k is the proportionality constant.
We are also given that when the length of the cube's edge is 35 cm, the mass of the cube is 40 kg. So we can use this information to find the value of the proportionality constant k.
35 cm = 0.35 m (converting cm to m)
Now we can substitute the given values into the equation and find k:
40 = k(0.35)^3
k = 40 / (0.35)^3
Now that we have the value of k, we can use it to find the mass of the cube when the length of its edge is 0.6 m.
M = kL^3
M = 40 / (0.35)^3 * (0.6)^3
M = 40 / (0.35)^3 * (0.216)
M = 40 / (0.003375) * (0.216)
M = 40 / 0.00726 * 0.216
M = 40 / 0.015856
M = 2511.53 kg (to 2 decimal places)
So the mass of the cube when the length of its edge is 0.6m is 2511.53kg
The answer would be M = 204.6 kg
The mass of the cube, M, is given by the equation M = kL^3, where k is the proportionality constant.
Given that M = 40 kg when L = 0.35 m, we can find k by substituting these values into the equation:
40 = k(0.35)^3
k = 40 / (0.35)^3
= 40 / 0.0421875
= 947.125
To find M when L = 0.6 m, we can substitute this value of L into the equation:
M = 947.125 * (0.6)^3
= 947.125 * 0.216
= 204.6
The given information is that M is proportional to the cube of L. This means that the mass of the cube is directly proportional to the cube of the length of its edge. The proportionality constant k is found by using the given values of M and L, and then using that constant value we can find the mass when we know the length of the edge.
We have found the mass of the cube when the length of its edge is 0.6m is 204.6 kg by using the proportionality constant and equation we have derived from the given information.
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Pat has a fever. His temperature is 99.3 degrees F.
If the conversion to Celsius is C=5/9 (F-32), what is the most accurate measurement of Pat's temperature in degrees Celsius?
Answer: the most accurate measurement of Pat's temperature in degrees Celsius is 37.3 degrees.
Step-by-step explanation:
The conversion from Fahrenheit to Celsius is C = 5/9 (F-32).
First, we substitute Pat's temperature of 99.3 degrees Fahrenheit into the equation:
C = 5/9 (99.3-32)
C = 5/9 * 67.3
C = 37.3 degrees Celsius
So the most accurate measurement of Pat's temperature in degrees Celsius is 37.3 degrees.
Answer:
37.4 degrees
Step-by-step explanation:
C = 5/9 (F-32)
F = 99.3 so plug F into the equation
C = 5/9 (99.3 - 32)
C = 5/9 (67.3)
5/9 in a calculator = .555 repeating
.555 x 67.3 = 37.35
Rounded = 37.4 degrees
What is an example of Avogadro's number?.
According to the definition of Avogadro's number , the correct statement is (d) Avogadro’s number is 6.02×10²³ , which equals the number of items in one mole.
The Avogadro number or Avogadro constant is the number of units present in one mole of any substance is .
The Avogadro number is equal to 6.022140857 × 10²³ .
The Avogadro number creates a bridge between the macroscopic world and microscopic world by relating the amount of substance to number of particles.
Therefore , the correct statement is (d) .
The given question is incomplete , the complete question is
What is the correct statement about Avogadro's number ?
(a) Avogadro’s number is 8.31, which equals the number of items in one mole.
(b) Avogadro’s number is 1.60×10¹⁹ , which equals the number of items in one mole.
(c) Avogadro’s number is 1.38×10²³, which equals the number of items in one mole.
(d) Avogadro’s number is 6.02×10²³ , which equals the number of items in one mole.
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Solve the following inequality, show your work.
q+19>49
Answer:
[tex]\boxed{\bf q=30}[/tex]
Step-by-step explanation:
[tex]\bf q+19 > 49[/tex]
Subtract 19 from both sides:-
[tex]\bf q+19-19 > 49-19[/tex]
[tex]\bf q=30[/tex]
________________
Hope this helps!
Have a great day!
Answer:
q>30
Step-by-step explanation:
SolutionThis question tests on Inequality.
Given Information from the question, we have to make sure the left side of the inequality has only q, which is the variable, then we will simplify it.
[tex]q + 19 > 49 \\ q + 19 - 19 > 49 - 19 \\ q > 30[/tex]
Therefore the inequality is q>30.
how do you solve for the midsegment of a trapezoid with only the coordinates given?
The midsegment of a trapezoid with only the coordinates given can be determine by following steps 1,2 and 3 below
How to solve for the midsegment of a trapezoid with only the coordinates given?The midsegment of a trapezoid is a line segment that connects the midpoints of the two parallel sides of the trapezoid.
To solve for the midsegment of a trapezoid with only the coordinates given, you can use the following steps:
1. Find the coordinates of the midpoints of the two parallel sides of the trapezoid. To do this, you need the coordinates of the four vertices of the trapezoid. For example, if the trapezoid has vertices A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4), the midpoints of the two parallel sides are:
Midpoint of AB: ((x1 + x2)/2, (y1 + y2)/2)
Midpoint of CD: ((x3 + x4)/2, (y3 + y4)/2)
2. Use the coordinates of the two midpoints found in step 1 to find the equation of the line that contains the midsegment. The slope of the midsegment is the average of the slopes of the two parallel sides of the trapezoid.
The equation of the line can be written in slope-intercept form (y = mx + b) or point-slope form (y - y1 = m(x - x1))
3. Once you have the equation of the line you can use it to find the y-intercept b and the slope m.
For example:
Trapezoid with coordinates A(2,3), B(4,4) , C(7,5) and D(5,6)
Midpoint of AB: (3,3.5)
Midpoint of CD: (6,5.5)
Slope of AB = (y2-y1)/(x2-x1) = (4-3)/(4-2) = 1/2
Slope of CD = (y4-y3)/(x4-x3) = (6-5)/(5-7) = -1/2
Midsegment slope = (1/2 + (-1/2))/2 = 0
The equation of the midsegment line is y = 0x+b
by using the point (3,3.5)
we can find the value of b = 3.5
Thus, the equation of midsegment is y = 0x + 3.5
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What type of a straight line will be represented by the system of equation 2x 3y 5 and 4x+ 6y 7?.
A straight line with a positive and constant slope can be represented by the system of equation 2x + 3y = 5 and 4x + 6y = 7.
The line is a linear equation, which is a line of constant slope. The slope of the line is determined by the coefficients of the variables in the equation.
It can be calculated by dividing the coefficient of the x-term by the coefficient of the y-term. In this example, the slope of the line is calculated by dividing 2/3, which is equal to 0.67.
This indicates that the line has a positive slope. The line is a line of best fit, meaning that it will pass through all the points defined by the two equations. The line will also pass through the point of intersection of the two equations, which is the point (2,1).
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what is the intermediate step in the form of (x+a)=b for x^2+5x+11=13x
To find the intermediate step in the form of (x+a)=b for the equation x^2+5x+11=13x, we need to first move all the terms to one side of the equation.
x^2+5x+11 = 13x
x^2 - 8x + 11 = 0
To solve this equation, we can factor it.
x^2 - 8x + 11 = 0
(x-11)(x-1) = 0
So, we have two solutions for x: x = 11 and x = 1
To find the intermediate step in the form of (x+a)=b, we can write each solution as (x+a)=b
x = 11, so (x+(-11)) = 11
x = 1, so (x+(-1)) = 1
So, the intermediate step in the form of (x+a)=b for the equation x^2+5x+11=13x is:
(x-11) = 11 and (x-1) = 1
How many different 5-digit PIN codes are there that only include the digits 6, 2, 5, 4, 8 and 7?
Answer:
First, there are NO 5-digit pin codes that include the digits 7, 2, 4, 6, 9, and 3. But, there are 720 pin codes that include 5 out of the 6 digits.
Step-by-step explanation:
What is the product of 6x4?.
The product of 6x4 is 24.
A product is the outcome of multiplication in mathematics, or an expression that specifies the factors (numbers or variables) to be multiplied. For instance, the sum of 6 and 5 is 30. (the result of multiplication).
Integers, natural numbers, fractions, real numbers, complex numbers, and quaternions are examples of typical special instances where it is possible to define the product of two numbers or the multiplication of two numbers.
In linear algebra, there are numerous different types of products. Some of them have names that sound confusingly close but have very distinct meanings (outside product, external product), while others have names that sound completely different but basically imply the same thing (outer product, tensor product, Kronecker product). These are briefly discussed in the sections that follow.
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Roman and Sienna are comparing the number of pages they’ve each read over the Winter Break. Roman said he read 40% of his book, which has a total of 200 pages. Sienna’s book has a total of 400 pages, and she read 1/5 of it. Who do you predict has read more pages of their book? Explain your reasoning.
Roman and Sienna read equal number of the pages of the book.
What is comparison?Comparison or comparing is the act of evaluating two or more things by determining the relevant, comparable characteristics of each thing, and then determining which characteristics of each are similar to the other, which are different, and to what degree.
Given that, Roman and Sienna are comparing the number of pages they’ve each read over the Winter Break. Roman said he read 40% of his book, which has a total of 200 pages. Sienna’s book has a total of 400 pages, and she read 1/5 of it.
Book read by Roman = 40% of 200
= 40 / 100 x 200
= 80 pages
Book read by Sienna = 1/5 of 400
= 400 x 1/5
= 400/5
= 80 pages
Since, both of them read equal number of pages.
Hence, Roman and Sienna read equal number of the pages of the book.
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Which diagram represents the net of a square pyramid? Choose all that apply.
Option (1) and (3) indicate a net of a pyramid with a square base.
What is meant by square pyramid?Having a square base and four lateral sides, a square pyramid is a type of pyramid in geometry. Having three or more triangle faces that meet above the base and a base, a pyramid is a type of polyhedron (the apex). It is called a pentahedron because a square pyramid is a three-dimensional object with a total of five faces.
We must determine which of the provided diagrams best depicts the net of a square-based pyramid.
Think about the overall net that depicts the pyramid with a square base (as shown in figure 1)
Triangle 3 and triangle 2 are flipped to the left to create the diagram (3).
Diagram (1) is produced by flipping triangles 1 and 3 to their opposite sides.
As a result, Option (1) and (3) indicate a net of a pyramid with a square base.
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HELP MEEEEEE PLEASEEEEE
what 5 1/3 minus 3 2/3 and 8 4/7 minus 7 5/7 is? And if possible try simplifying the answers. But at least show a step by step explanation.
The answers to each part is -
(5 1/3) - (3 2/3) = 5/3(8 4/7) - (7 5/7) = 6/7What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is to find -
(5 1/3) - (3 2/3) (8 4/7) - (7 5/7) ( 1 ) -We can write the expression as -
{x} = [tex]5\frac{1}{3} - 3\frac{2}{3}[/tex]
{x} = 16/3 - 11/3
{x} = 5/3
( 2 ) -We can write the expression as -
{x} = [tex]8\frac{4}{7} - 7\frac{5}{7}[/tex]
{x} = 60/7 - 54/7
{x} = 6/7
Therefore, the answers to each part is -
(5 1/3) - (3 2/3) = 5/3(8 4/7) - (7 5/7) = 6/7To solve more questions on algebraic expressions, visit the link below -
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What is set Give 2 example?.
A Set is a collection of well-defined entities or elements.
A capital alphabetic symbol represents a set, and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}. For example, set A is a collection of all the natural numbers, such as A = {1, 2, 3, 4, 5, 6, 7, 8,…..∞}.
Sets can be represented in three forms:
Roster Form: Set of even numbers less than 8 = {2, 4, 6}
Statement Form: A = {Set of Odd numbers less than 9}
Set Builder Form: A = {x: x = 2n, n ∈ N and 1 ≤ n ≤ 4}
Examples of sets are,
(a) Set of first 8 multiples of 7
Suppose the set of first 8 multiples of 7 is A
Set A = {7, 14, 21, 28, 35, 42, 49, 56}.
As there are 8 elements in the set, cardinal number n(A) = 8
(b) Set B = {a, e, i, o, u, j, k}
Set B = {a, e, i, o, u, j, k}. This set contains 7 elements,
Thus, the cardinal number of set B, n(B) = 7.
(c) Set C = {x | x are even numbers between 10 and 20}
Set C = {12, 14, 16, 18}. These numbers create the elements of set C.
Thus, the cardinal number of set C, n(C) = 4.
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16% of what number is 2? Pls reply quick I. Need help
Answer:
12.5
Step-by-step explanation:
A contractor can spend at most $250 a day on operating costs and payroll. It costs $45 each day to operate the forklift and $60 a day for each crew member. Write an inequality to represent the contractor's budget for the day.
60x + 45 ≥ 250
60x + 45 ≤ 250
60 − 45x ≥ 250
60 − 45x ≤ 250
PLEASEE HELP ME ILL GIVE U BRAINLIST
A triangle has vertices located at coordinates (-2, 4), (-2,-4), and (1, 0)
What are the coordinates of the centroid of this triangle?
The centroid is the object's focal point. The centroid of a triangle is the location where the three medians of the triangle intersect.
What is centroid of triangle?The centroid is the object's focal point. The centroid of a triangle is the location where the three medians of the triangle intersect. The junction of all three medians is another definition for it. The median is a line that connects the middle of a side to the triangle's opposite vertex. The centroid of the triangle can then be determined by averaging the x and y coordinates of each of the three vertices. Thus, G(x, Y) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3 is a mathematical expression for the centroid formula.The triangle's centroid is the point at where its three medians cross. These characteristics apply to it: Always in the center of the triangle is where the centroid. The segment that connects the vertex to the opposite side's midpoint has the centroid at a distance from the vertex of two thirds of that segment.To learn more about centroid of triangle refer to:
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How do you find the value of x in a logarithmic function?.
To find the value of x in a logarithmic function, you need to use the definition of logarithms, which states that log_b x is the power to which b must be raised to produce x.
In other words, if f(x) = log_b x, then b^(f(x)) = x. To find x, you simply need to raise b to the power of f(x), using the inverse of the logarithmic function, which is the exponential function. This can be done using a calculator or by using logarithmic rules and properties to simplify the expression and solve for x. It's important to remember that logarithmic functions are only defined for positive values of x and that the base b must be positive and not equal to 1.
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When solving a system of equations with substitution What do we do after solving for one of the variables?.
The same line of equations can be written in two different ways in a dependent equation. The lines that appear when we graph dependent equations are the same.
The solutions to these kinds of equations are infinite rather than fixed.
When the same line is written in two different ways, a dependent system of equations has infinite possible solutions. When attempting to solve for a system of equations, these two scenarios arise. When working through a system of equations, you'll need to keep track of a few words from your vocabulary.
What are examples of dependent equations?A system of equations is formed by the two equations y=2x+5 and y=4x+3. The system's solution is the ordered pair that results from resolving both equations. One solution, an infinite number of solutions, or nothing at all can be found for a system of two linear equations.
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Every math class is made up of 18 twelve graders and 4 eleventh graders. The twelve grades averaged a 83, on the midterm exam, and the eleventh graders averaged a 79 on the midterm exam. What was the average grade on the midterm exam for the entire class? Round to the nearest whole number.
The average midterm exam grade for the entire class is 82.
What is average?The middle value in a set of numbers is the average, which is calculated by dividing the total of all the values by the number of values.
Here given that,
Math class contains 18 twelve graders.
Also contains 4 eleventh graders
Total number of students = 18 + 4 = 22
Total marks of students in the twelve grade = 18 x 83 = 1494
Total marks of students in the eleventh grade = 4 x 79 = 316
Total marks = 1494 + 316 = 1810
Therefore to find the average grade of midterm exam is :
1810 / 22 = 82.2
Therefore the average grade on the midterm exam for the entire class is 82.
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What is the difference of (- 2x + 9) and (3x - 4)
Answer:
[tex]-5x+13[/tex]
Step-by-step explanation:
[tex](-2x+9)-(3x-4)\\=-2x+9-3x+4\\=-5x+13[/tex]
The following table how how many pie 4 baking team made at a pie-baking competition. For example, Team Cruty baked 28 pie in 8 hour Which team made pie at a rate of 4. 5 point, 5 per
The team Pie Peace made pies at a rate of 4.5 per hour
The complete data is,
Team Pies Hours
Crusty 28 8
Pie Peace 27 6
Fab bakers 20 4
Yum 26 5
We have from the table provided,
In 8 hours, Team Crusty produced 28 pies.
In 6 hours, Team Pie Peace produced 27 pies.
In 4 hours, Team Crusty produced 20 pies.
In 5 hours, Team Crusty produced 26 pies.
We must divide the number of pies produced by the total time required in order to determine the rate of pies produced.
As a result,
28 pies divided by 8 hours equals 3.5 pies per hour for Team Crusty.
4.5 pies per hour or Team Pie Peace = 27 pies in 6 hours.
20 pies divided by 4 hours yields 5 pies each hour for Team Crusty.
26 pies divided by 5 hours yields 5.2 pies per hour for Team Crusty.
Therefore, team Pie Peace made pies at a rate of 4.5 per hour
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How do you graph the inverse of a linear graph?.
The inverse of a linear graph can be graphed by x and y coordinates.
When a function is stated in the form which is y = mx + b, where m and b are real integers and m is not equal to 0, the function is said to be linear. The variables in this equation are x and y, while the coefficients are m and b. A linear graph is the graph of a linear function, where a linear function has a straight line as its graph; its slope is m and its y-intercept is (0,b). The inverse of a linear graph can be thus created as -
Firstly, all the points on the original graph should have their x and y coordinates switched.Second, there should be reflecting the new points on the y = x line.Thus, the inverse function's graph will be a line that crosses the line y = x and reflects it on the original graph.Read more about the linear graphs on:
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A giraffe is 18 feet tall and casts a shadow of 12 feet. Corry casts a shadow of 4 feet. How tall is Corry? Use similar triangles to find the missing information.
Find the 10th term for 5-,20,-80,320
The 10th term of the sequence is -131072.
What is a geometric sequence?
A geometric sequence is a sequence of numbers such that the quotient between any two consecutive terms is a constant called the common ratio.
This sequence appears to be a geometric sequence with a common ratio of -4.
To find the nth term of a geometric sequence, we can use the formula:
[tex]a_n = a_1 * r^{n-1}[/tex]
where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the position of the term in the sequence.
So, in this case:
[tex]a_10 = 5 * (-4)^(10-1) = 5 * (-4)^9 = 5 * -262144 = -131072[/tex]
Therefore, the 10th term of the sequence is -131072.
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Last week, Nico bought 11 shirts and hats for total of $194. Today, Nico bought shirts and hats for total of $120. Assuming neither item has changed price, what is the cost of a shirt dollars?
Answer:
2 dollers
Step-by-step explanation:
120$ +194$ divided by C square is e square so in conclution the sum will eventually be 4$ and 4$÷2= 2$
The notation "f(x)" (f of x) is another way of representing y-values in a function question 1 options: true false
The given statement " the notation "f(x)" is another way of representing y-values in a function" is true because f (x) and y are the same things.
The notation f(x), read as "f of x", indicates a function named f. It reflects that 'y is a function of x'. The letter 'x' refers to the input value or independent variable. While the letter 'y' is replaced by f(x) and it refers to the output value or dependent variable.
The notation 'f (x)' is exactly the same as that of 'y'. Even on graphs, y-axis can be labelled with 'f (x)'.
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How do you convert a mixed fraction to an improper fraction Class 4?.
To transform a mixed fraction into an improper fraction, first, we multiply the denominator of the proper fraction by the whole number attached to it, and then we add the numerator.
An improper fraction is a kind of fraction in which the numerator will be greater than or equal to the denominator.
Let's take an example to understand the process completely.
For example, 3(1/2) is a mixed fraction. Convert it into an improper fraction.
Step 1: Multiply the denominator with the whole number of the fraction, i.e. Multiply 2 with 3 in the given example, 3(1/2).
2 × 3 = 6
Step 2: Add the numerator of the Fraction to the answer from step 1. i.e., Add 1 + 6
= 7.
Step 3: Keep the Denominator the same, i.e. 2.
Step 4: The Improper fraction obtained is: 7/2.
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if[ tex]x-\frac{1}{x} =1[/tex] then what is [tex]\frac{x}{x^{2}+3x-1 } =\frac{1}{4}[/tex]
The value of the equation is x² - x - 1 = 0
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
x - ( 1/x ) = 1 be equation (1)
On simplifying the equation , we get
( x² - 1 ) / x = 1
Multiply by x on both sides of the equation , we get
x² - 1 = x
Subtracting x on both sides of the equation , we get
x² - x - 1 = 0
Now , given that ( x / ( x² + 3x - 1 ) ) = 1/4
On simplifying the equation , we get
Cross multiplying the equation , we get
4x = ( x² + 3x - 1 )
Subtracting 4x on both sides of the equation , we get
x² - x - 1 = 0
Hence , the equation is x² - x - 1 = 0
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