a) The first five members of the sequence is
a1 = a0 + 2
a2 = a1 + 2 = a0 + 4
a3 = a2 + 2 = a0 + 6
a4 = a3 + 2 = a0 + 8
a5 = a4 + 2 = a0 + 10
b) The explicit formula for this sequence is:
an = 2n + a0, for n ≥ 0
A recursive sequence is a sequence where each term is defined in terms of the previous term(s). In this case, we have a sequence that is defined recursively.
Let's assume that the first term of the sequence is a0 and that the recursive formula for the sequence is given by:
an+1 = an + 2, for n ≥ 0
To find the first few terms of the sequence, we can apply the recursive formula repeatedly. Starting with a0, we get:
a1 = a0 + 2
a2 = a1 + 2 = a0 + 4
a3 = a2 + 2 = a0 + 6
a4 = a3 + 2 = a0 + 8
a5 = a4 + 2 = a0 + 10
From this, we can see that the sequence is simply the sequence of even numbers, starting with a0. So, the explicit formula for this sequence is:
an = 2n + a0, for n ≥ 0
To verify this formula using mathematical induction, we need to show that it holds for the base case (n = 0) and for the induction step (n+1).
For the base case, we have:
a0 = 2(0) + a0
a0 = a0
For the induction step, we assume that the formula holds for n and show that it also holds for n+1.
Assume that:
an = 2n + a0
Then, we have:
an+1 = an + 2 (by the recursive formula)
an+1 = 2n + a0 + 2 (substituting in the formula for an)
an+1 = 2(n+1) + a0 (simplifying)
Therefore, the formula holds for all n ≥ 0.
In conclusion, we have found the first 5 members of the sequence by applying the recursive formula, and we have found the explicit formula for the sequence by identifying a pattern in the first few terms. We have also used mathematical induction to verify the correctness of the formula.
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solve for x (x-1)(x-12)=0
Answer:
x = 1, 12
Step-by-step explanation:
Given the equation:
[tex]\displaystyle{(x-1)(x-12)=0}[/tex]
This can be set as:
[tex]\displaystyle{x-1 = 0 \ \, \text{or} \ \, x - 12 = 0}[/tex]
Solve equations like linear, add both sides by 1 for x - 1 and add both sides by 12 for x - 12:
[tex]\displaystyle{x-1 +1= 0+1\ \, \text{or} \ \, x - 12+12 = 0+12}\\\\\displaystyle{x= 1\ \, \text{or} \ \, x = 12}[/tex]
Instead of using "or" for conjunction, we can simply write the solution as x = 1, 12 (or you can also write x = 12, 1)
Additional Info
If you see the equation in form of [tex]\displaystyle{(ax+b)(cx+d)=0}[/tex] then you can just simply solve like linear separately and combine solutions together as one.
What is the base in a power of 2?
A power of two is a number of the form 2ⁿ where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent.
Exponential FunctionThe exponential function is a type of mathematical function which are helpful in finding the growth or decay of population, money, price, etc that are growing or decay exponentially.
Example: Jonathan was reading a news article on the latest research made on bacterial growth. He read that an experiment was conducted with one bacterium. After the first hour, the bacterium doubled itself and was two in number. After the second hour, the number was four. At every hour the number of bacteria was increasing. He was thinking what would be the number of bacteria after 100 hours if this pattern continues. When he asked his teacher about the same the answer he got was the concept of an exponential function.
What is Exponential FunctionExponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.
Exponential Function DefinitionIn mathematics, an exponential function is a function of form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
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What are the 3 main types of 3D objects?
The three main types of 3D objects are polygonal meshes, NURBS, and implicit surfaces.
There are several types of 3D objects, but the three main categories are:
Polygonal meshes: These objects are made up of a large number of small polygons, such as triangles or quadrilaterals, that are connected to form the surface of the object. These are the most common type of 3D objects used in computer graphics and 3D modeling.NURBS (Non-Uniform Rational B-Splines): These objects are defined by mathematical equations and are used in CAD (computer-aided design) and other applications that require precise, smooth surfaces.Implicit surfaces: These objects are defined by an implicit equation, such as F(x,y,z) = constant, rather than a set of discrete points. They are used in scientific visualization and other applications that require smooth, continuous surfaces.To learn more about 3D objects at
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The function F gives the number of copies a book has sold W weeks after that it was published the equation FW equals 500×2 to the W power defines this function 
Select all domains for which the average rate of change could be a good measure for the number of books sold
Good models are expected to reflect the number of books sold between zero and w numbers of weeks where w is defined.
What is a domain?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Here, we have
Given: The function f gives the number of copies a book has sold w weeks after it was published. The equation f(w) = 500 * 2^w defines this function.
The following are all domains for which the average rate of change could be a good measure of the number of books sold:
0 ≤ w ≤ 2
0 ≤ w ≤ 7
0 ≤ w ≤ 10
Hence, good models are expected to reflect the number of books sold between zero and w numbers of weeks where w is defined.
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a polynomial function has zeros at "-4(multiplicity" 3), "-1(multiplicity" 1). which graph could represent this function?
Therefore the solution to the given question is option d)128.78 for this particular equation.
What is Equation?Many different definitions exist for a mathematical equation. In algebra, a statement that mathematically establishes the equality of two mathematical expressions is known as an equation.. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." Mathematical variables are used in even the most fundamental and straightforward algebraic equations.
Here,
=> v/9.4 = 13.7
Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal." Even the simplest and most easy algebraic equations need mathematical variables.
=> v = 13.7*9.4
=> v= 128.78
Therefore the solution to the given question is option d)128.78 for this particular equation
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Parker could pay for 45% of hi college tuition with hi cholarhip. The remaining $10,500 he paid for with a tudent loan. What wa the cot of Parker' tuition? Show your work
The cost of parkers tuition is $19090.9.
The percentage is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.
Given that,
The percent he pays with college tuition = 45%
The fee in percent which is not paid by scholarship = 100 - 45 = 55%
Let x be the total amount of parker's tuition, then the value of x:
55/100x = 10,500
55x = 10,50000
x= 19090.9
x = $19090.9
Thus, the cost of parkers tuition is $19090.9 if Parker was able to pay for 45 percent of his college tuition with his scholarship. The remaining $10,500 he paid for with a student loan.
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Solve 2(4x+2)= 4x -12(x-1) the solution is x
The Value of x is -1/2 in this Linear equation
As we have the equation 2(4x+2)= 4x -12(x-1)
2(4x+2)= 4x -12(x-1) 8x + 4 = 4x - 12x + 12................. On opening the brackets8x + 4 = -8x + 1216 x + 4 = 12 ----------------- on subtraction 8x from both the sides( As we can perform any operation in both the sides of equation)16x = 8 -------- On subtracting 4 from both the sidesx= 1/2So we can conclude that the Value of x is 1/2
we can verify the answer by putting back the value of x in the equation and both sides will have the same value.
2(4x+2)= 4x -12(x-1)
2(4*1/2+2)= 4*1/2 -12(1/2-1)
2(2+2) = 2-6+12
8=8
Hence Proved that x=1/2 is the correct answer
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ashely bought 6 yds of ribbon for 5.28 . what ratio is proportional to this?
A) $1.36/2 yards C)$2.64/3 yards
B) $1.92/3yards D)$3.25/4 yards
PLEASE HELP AND SHOW WORK!
477➗9 using distributive property
Answer:
53
Step-by-step explanation:
[tex]\frac{477}{9}[/tex]
53
9[477]
-45
27
-27
0
Is 256 an exponential form?
Yes, 256 can be written in exponential form as 2^8 where 2 is the base and 8 is the exponent.
Which of the following expressions are polynomials ? (i) x^3−5x+2(ii) y^2+√2y–√5(iii) 2√x+7(iv) −6(v) 4t^2+1/6t+2√3(vi) z^2+5/z^2+1(vii) 1/3x(viii) 1−√5x(ix) 1/14x^−2+3x+5(x) 6√x+x^3/2/√x
In the given expression, expression [tex]x^3[/tex]−5x+2 is a polynomial expression. So the option (i) is correct.
In the given question we have to find which of the following expression are polynomials.
As we know that,
The Greek words "polynomial" and "nominal" are the origins of the word polynomial, which is translated as "many phrases" when combined. There is no limit to the number of terms that a polynomial can have.
Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents. The expression is categorized as monomial, binomial, or trinomial depending on how many terms are present in it.
So if we see on the given expression then we can see that the option (i) [tex]x^3[/tex]−5x+2 have the degree 3 so [tex]x^3[/tex]−5x+2 is a polynomial expression.
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20 pts!!!! Danielle pays a monthly charge of $69 for her cable bill. She also pays a fee every time she watches a movie on demand.
Answer: y=69x+b
Step-by-step explanation:
x=# of months of her cable bill
b=# movie fees
y=total bill
The expression [tex](x^{-8} )(x^2)[/tex] is equivalent to [tex]x^{n}[/tex] what is the value of n?
n = -6 is the value of n in the expression .
What does a mathematical expression mean?
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. This mathematical operation may be addition, subtraction, multiplication, or division.
Any combination of a number, a variable, and operation symbols is considered an expression. Two expressions are combined to form an equation, which is joined by the equal sign.
(Xⁿ) = (X⁻⁸)(X²)
(Xⁿ) = X⁻⁸⁺²
(Xⁿ) = X⁻⁶
n = -6
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What 3 lengths make a triangle?
The Triangle Inequality Theorem, which asserts that the sum of a triangle's two side lengths is always greater than the third side, will suffice. You will have a triangle if this holds true for each of the three possibilities of increased side lengths.
Let's use the triangle inequality theorem to examine the characteristics of a triangle's sides.
The two requirements for a triangle's sides are:
(1) The two sides added together are always larger than the third side.
a+b>c
a+c>b
b+c>a
(2) Less exists between the two sides than there does between the third side.
|a-b|<c
|a-c|<b
|b-c|<a
Therefore, if and only if the total of two sides is always larger than the third side and the difference of the two sides is less than the third side, 3 lengths could be the measures of the edges of a triangle.
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Write the relation as a set of ordered pairs.
a.
ordered pairs: {(4, –2), (0, 0), (2, 4)}
b.
ordered pairs: {(–2, 4), (0, 0), (4, 2)}
c.
ordered pairs: {(-2, 4), (0, 0), (2, 4)}
d.
ordered pairs: {(4, -2), (0, 0), (4, 2)}
The correct option is C. The ordered pairs: {(–2, 4), (0, 0), (2, 4)}
What is an ordered pair?An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples or 2-length sequences.
It's important to remember that, the first the showed in the image represents a domain, and the second set represents a range. That means the values -2, 0, 2, must appear as the first value in the coordinate, and the values 4 and 0, must appear second.
Now, if we associate the given diagram with coordinates, it would be like
Therefore, the right answer is choice c.
Additionally, this relation models a quadratic function actually, because -2 and 2 have the same image 4.
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600=5+60 what was the annual interrest rate
On solving the provided question, annual rate is 2% while doing calculations through simple interest.
What is simple interest?Borrowers must pay simple interest to lenders as a fee for a loan. Compound interest is not taken into account while calculating it; just the principal is used. Simple interest is applicable to all loans. It is also the form of interest that banks give their customers on their savings accounts. Simple interest can be calculated using a simple formula. Simply multiply the loan's principal by the interest rate and the period to get the total. Although some mortgages employ this calculation approach, this type of interest typically relates to auto loans or short-term loans.
Let the annual rate be x%
Principal Amount (p)= $600
Annual Rate (r) = x % (Assumed)
Time (t) = 5 years
Simple Interest (I) = $60
Use the simple interest formula given below:
SI = p×r×t/100
r = 60 ×100/600× 5
r = 2%
Thus, the annual rate of interest is 2 %.
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Question:
April took out a $600 loan from the bank. At the end of 5 years, she pays back the principal, plus $60 simple interest. What was the interest rate? Enter your answer in the box.
How do you solve a table of values in a function?
The link between data pieces is displayed in tables of values. In science lesson, you might utilize a values table.
what is functions ?Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. based on one-to-one functions, many-to-one functions, on functions, within functions, and one-to-one functions.
given
The link between data pieces is displayed in tables of values. In science lesson, you might utilize a values table.
Data is recorded in tables of values by scientists and researchers, who then examine the data to look for patterns. As a result, they can use this pattern to anticipate future events.
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please help me with this
Answer:
answer is 23&11
Step-by-step explanation:
no explanation
Joseph has a bag filled with 2 red, 4 green, 10 yellow, and 9 purple marbles. Determine P(not green) when choosing one marble from the bag.
The probability that the selected marble will not be green is 21/25.
What is probability?Probability is a measure of how likely something is to occur.
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
So, we know that:
The bag contains: 2 red, 4 green, 10 yellow, and 9 purple
Probability formula: P(E) = favourable events/total events
Now, calculate as follows:
P(not green) = 21/25
Therefore, the probability that the selected marble will not be green is 21/25.
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Answer:
60%
Step-by-step explanation:
Answer: The answer to your question is 60%
Step-by-step explanation: The total number of marbles in Joseph's bag is:
2 (red) + 4 (green) + 10 (yellow) + 9 (purple) = 25
The probability of choosing one marble that is not yellow can be found by dividing the total number of marbles that are not yellow by the total number of marbles in the bag:
P(not yellow) = (2 red + 4 green + 9 purple) / 25
P(not yellow) = 15/25
P(not yellow) = 3/5
P(not yellow) = 0.6 or 60%
Therefore, the answer is 60%.
How do you label the sides of a 30-60-90 triangle?
We label sides as: the shorter leg is 30-degree angle, the longer leg is 60-degree angle and the hypotenuse is 90 degrees.
Any triangle with a 90-degree angle is considered a right triangle. A unique variety of right triangle with a 30-degree angle and a 60-degree angle in addition to the right angle is known as a 30-60-90 triangle.
Triangle Properties 30-60-90
A triangle with sides of 30-60-90 can be recognized by how they relate to the angles.
The shorter leg is the one that faces the 30-degree angle.
The longer leg is the one that faces the 60-degree angle.
The hypotenuse is the side that faces the right angle of 90 degrees.
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Can a triangle be formed with 7 cm 10 cm and 5 cm as its sides?
The sum of 2 sides is greater than the largest side so the triangle can be formed.
How to create triangle ?Triangle Properties
A triangle's (of all varieties) total sum of angles is 180°.The length of a triangle's two longest sides added together is longer than the third side.Similar to this, the length of the third side of a triangle's third side is shorter than the difference between its two sides.Any two triangle sides can add up to a length that is longer than the third side. The greatest side of a triangle is the side that faces the largest angle. The sum of the triangle's internal opposing angles is equal to any of its outer angles.
According to the sides of a triangle rule, the lengths of any two sides of a triangle must add up to more than the length of the third side.
Sum of 2 sides each are :
7 + 10 = 17 cm
7 + 5 = 12 cm
5 + 10 = 15 cm
So the sum of 2 sides is greater than the largest side so the triangle can be formed.
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Sam is proving the product property of logarithms. Step justification given substitution which expression and justification completes the third step of her proof? ; power rule of exponents subtraction property of exponents multiplication rule of exponents division property of exponents.
Sam's rationale for the third step based on logarithm properties would be logb(b^x+y), power rule of exponents. Thus, the correct answer is C.
The first step of Sam's proof is to show that logb(MN) is equal to logb(b^x.b^y), which is a substitution of MN for b^x.b^y. This is based on the product property of logarithms, which states that logb(MN) = logb(M) + logb(N) for any positive numbers M and N and any base b, as long as b doesn't equal 1.
The third step of her proof is to simplify logb(b^x.b^y) further by applying the power rule of exponents, which states that:
b^(x+y) = b^x.b^ySo, by substituting b^(x+y) for b^x.b^y, we get:
logb(b^(x+y)) = logb(b^x+y)So, in short, the justification of the third step is based on the power rule of exponents, and it shows that logb(b^x.b^y) can be simplified further to logb(b^x+y).
The answer choice A, logb(b^xy), power rule of exponents, is incorrect because it implies that the third step is to multiply x and y instead of adding them.
This question should be provided with answer choices, which are:
A. logb(b^xy), power rule of exponents.B. logb(b^x-y), subtraction property of exponents.C. logb(b^x+y), power rule of exponents.D. logb(b^x/y), division property of exponents.The correct answer is C.
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Answer: its c
Step-by-step explanation:
cop a hoodie at moneymotivated.us thanks
How is 13 a prime number?
13 is considered as a prime number as there are only two factors of 13 which are equals to 1 and 13 itself.
As given in the question,
Given number is equal to 13,
Prime numbers are those numbers which has only two factors : one and the number itself.
Here is not divisible by any other number.
Factors of 13 are equals to :
1 and 13 itself.
There are only two factors of thirteen which are equals to one and number 13 itself.
Therefore, 13 is considered as a prime number because there are only two factors of 13.
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What is the rule of substitution?
In this rule, we have to find the value of any of the variables either first or second and substitute its value in the other equation.
It is best to use the substitution method when equations are either given in form or can be gain into the form of x = ay + b and y = mx + n.
A procedure to answer a system of linear equations in more than two variables algebraically is the substitution method. In this process, we find the value of any one of the variables by alienating it on one side and taking every other term on the other side of the equation.
Then we substitute that first value in the second equation.
The substitution method is one of the algebraic processes to answer simultaneous linear equations. It implies substituting the value of any one of the variables from one equation into the other equation.
And at last, we can put the value of y in any of the given equations to find x.
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How does the rational root theorem and factor theorem helps you in solving polynomial equation?
The rational root theorem and factor theorem helps you in solving polynomial equation as they help in solving the question and finding the roots of it.
what are polynomials?A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.
here,
The rational root theorem and factor theorem helps you in solving polynomial equation as they help in solving the question and finding the roots of it.
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The Hawaiian resort has large palm trees. In a photo the tree measures 6 inches tall. The scale is 1.5 inches = 2.5 feet. How tall is the actual palm tree?
(Please i need help )
By the way I'm not in high school I don't know why it says that.
Answer:
10 ft
Step-by-step explanation:
You have a photo of a palm tree in which the tree is 6 inches tall. The scale of the photo is 1.5 in : 2.5 ft, and you want the know the height of the actual tree.
ProportionThe heights of things in the photo are presumed to be related to their actual height by the given scale factor.
actual height / photo height = 2.5 ft / (1.5 in)
actual height / 6 in = (2.5 ft)/(1.5 in)
Multiplying by 6 in gives ...
actual height = (2.5 ft)(6/1.5) = 10 ft
The actual palm tree is 10 feet tall.
__
Additional comment
It says "high school" because that is the level you have on your Brainly profile. You can change this under Edit Profile > Preferences.
Jason's paycheck was $324.60. He put 12 of his paycheck into a savings acount and used 13 of what was left to pay for a new bike tire. How much money does he have remaining from his paycheck?
Answer:
456 money left and 3 left
Answer:
$246.70
Step-by-step explanation:
Assuming this is a percentages question
12% of $324.60 is $38.95
$324.60-$38.95=$285.65
13% of what was left ($285.65) is $37.13
$285.65-$37.13=$246.70
Which of the following are Pythagorean triplets 4 cm 6 cm 8 cm 24 cm 10 cm 26 cm 13 cm 27 cm 30 cm 2 cm 17 cm 9 cm?
Pythagorean triplets 4cm,6cm,8cm,24cm,10cm,26cm,13cm,27cm,30cm 2 cm 17 cm 9 cm are 4 , 6 , 8cm and 24 , 10 , 26cm.
What is Pythagorean triplets ?
Pythagorean triplets are a set of three positive integers (a, b, c) such that [tex]a^{2}+b^{2} = c^{2}[/tex]. This relationship is known as the Pythagorean theorem, named after the ancient Greek mathematician Pythagoras. These triplets are often used in geometry, particularly in the study of right triangles.
To find pythagorean triplets ,
The question is asking to identify which sets of 3 positive integers from the given list satisfy the equation [tex]a^{2}+b^{2} = c^{2}[/tex]. The sets of numbers that satisfy this equation are 4 cm, 6 cm, 8 cm and 24 cm, 10 cm, 26 cm, these are pythagorean triplets. The other sets of numbers do not satisfy the equation and hence are not Pythagorean triplets.
Pythagorean triplets 4cm,6cm,8cm,24cm,10cm,26cm,13cm,27cm,30cm 2 cm 17 cm 9 cm are 4 , 6 , 8cm and 24 , 10 , 26cm.
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What is a different common denominator you could use in promblem 2 describe how would you add fractions using this different common denominator is the result equivalent to the sun found In promblem 2 Promblem 2 is: 1/2+3/8
16 is the different common denominator, we can use to solve 1/2+3/8.
The result using 16 as common denominator is equivalent to the sum 1/2+3/8.
What is common denominator?A common denominator is a denominator that you can reach by both denominators.
We can obtain common denominators by multiplying both numerator (top) and denominator (bottom) by the same amount.
Given expression
1/2 + 3/8
multiplying and dividing 4 with 1/2
4/8 + 3/8
Lowest common denominator = 8
= (4 + 3)/8
= 7/8
Sum = 0.875
Taking expression:
1/2 + 3/8
Multiplying and dividing 8 with 1/2 and 2 with 3/8.
8/16 + 6/16
Different common denominator = 2 × 8 = 16
Now,
= (8 + 6)/16
= 14/16
Result = 0.875
Hence, the result using different common denominator = 16 for solving
1/2 + 3/8 is equivalent to the sum of 1/2 + 3/8.
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Please please help meeeee
We get the Polynomials quotient and remainder as 2x+7 and 5 respectively.
What are Polynomials ?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.
Polynomial long division is an extended variant of the well-known mathematical operation known as long division. It is an algorithm for dividing a polynomial by another polynomial of the same or lower degree. Due to the fact that it breaks down a more difficult division issue into simpler ones, it may be completed quickly by hand.
The polynomials are
2X^2 - X +16
and
x - 3
Dividing by 2X^2 - X +16 BY x-3 = 2x + 7
We get the quotiant and remainder as 2x+7 and 5 respectively.
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