A polynomial function of least degree with a leading coefficient of 1 and zeroes at -2, 3, 6 is given by: "f(x) = (x + 2)(x - 3)(x - 6) = x^3 - x^2 - 9x - 12)".
According to the Factor Theorem, k is a zero of a given polynomial function f (x), if and only if (x - k) is a factor of the given polynomial function f(x).
Since -2,3 and 6 are zeros to be given of f (x), so
you need to put -2,3 and 6 in (x - k)
such as
f (x) = { (x - k) (x - k) (x - k) }
= { (x - (-2) (x - 3) (x - 6) }
= {(x+2) (x-3)(x-6) }
= {( x^3 - x^2 - 9x - 12) }
'f(x) = { (x^3 - x^2 - 9x - 12) }' is the required polynomial function.
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Elena is 59 inches. Some people are taller than Elena
Answer:
that even a complete problem?
spara
2:
Back to task
Calculate the coordinates of the midpoint of point P and point Q, which are
shown below.
12
11
10
9
8
7
65
Calculator
Bookwork code: J44 not allowed
6
5-
43
3
2-
1
P
Q
#I
0 1 2 3 4 5 6 7 8 9 please can u help me this is due soon and I’m stuck on it
Answer:
(3, 8 )
Step-by-step explanation:
given 2 points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = P (1, 6 ) and (x₂, y₂ ) = Q (5, 10 ) , then
midpoint = ( [tex]\frac{1+5}{2}[/tex], [tex]\frac{6+10}{2}[/tex] ) = ( [tex]\frac{6}{2}[/tex] , [tex]\frac{16}{2}[/tex] ) = (3, 8 )
What is The quotient of anumber and nine is less than the number. In algebraic expressions
Answer: [tex]x-\frac{x}{9}[/tex]
Step-by-step explanation:
1) quotient is the answer of a division problem
with that in mind and letting "a number" = x . . .
"The quotient of a number and nine..." would be [tex]\frac{x}{9}\\[/tex]
2) "is less than" always means you but the previous statement BEHIND . . .
[tex]x-\frac{x}{9}[/tex]
What are the 3 types of multiplication?.
Answer: Commutative, associative, distributive
Step-by-step explanation: I hope this helped!
please answer fast its due tomorrow
Solve for u.
–11u = 759
Answer:
u = -69
Step-by-step explanation:
Now we have to,
→ find the required value of u.
The equation is,
→ -11u = 759
Then the value of u will be,
→ -11u = 759
→ u = 759/-11
→ u = -(759/11)
→ [ u = -69 ]
Hence, the value of u is -69.
Mr. Berry had $120,000 in a retirement account. The account paid 4.25% simple interest. How much money was in the account at the end of 10 years?
What is the slope of this line y =- 3x 3?.
The slope of y = -3x + 3 is -3, it's the coefficient of the x variable.
What is slope ?
Slope, also known as gradient, is a measure of the steepness of a line. It is the ratio of the change in the y-coordinate to the change in the x-coordinate between any two distinct points on the line. It is represented by the letter "m" in the slope-intercept form equation of a line y = mx + b, where m is the slope, x is the independent variable, y is the dependent variable and b is the y-intercept, the point where the line crosses the y-axis.
The slope of a line is a measure of its steepness or incline. It is the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. The slope is represented by the letter "m" and it is the coefficient of the x variable in the equation of the line y = mx + b, where b is the y-intercept.
In this case, the equation of the line is y = -3x + 3,
The slope of y = -3x + 3 is -3, it's the coefficient of the x variable.
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Point A represents a positive number. Which point represents the opposite of that number?
A number line. Point E is 5 units to the left of zero. Point D is 3 units to the left of zero. Point C is 2 units to the right of zero. Point A is 2 units to the right. Point B is 4 units to the right.
The point opposite to point A is not labeled in the number line.
What is a number line?A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.
Given a number line,
for any number line points left of zero are negative numbers and points right to the zero are positive numbers,
Given points, Point A is 2 units to the right = +2
Point B is 4 units to the right = +4
Point C is 2 units to the right of zero = +2
Point D is 3 units to the left of zero = -3
Point E is 5 units to the left of zero = -5
so the point opposite to +2 is -2 which is 2 units left of zero,
but it is not given on the labeled points.
Therefore, the opposite point of A is not labeled.
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What is the difference between greatest 6 digit number and smallest 6 digit number?.
The difference between the greatest 6-digit and smallest 6-digit numbers is 899999.
The aim is to find the smallest and largest 6-digit numbers, and then we need to find how many numbers are between these two values.
Let's start by finding the smallest 6-digit number.
We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit; that is, 1 and 1 can be used in the highest place value.
Thus, we can create the required 6-digit smallest number with 0 and 1.
Hence, the smallest 6-digit number is 100000.
Now, we will discover the largest 6-digit number.
As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 6-digit number with the digit 9.
Thus, the largest 6-digit number is 999999.
Next, we need to find the difference between these two values.
So, we can determine the difference between the smallest 6-digit number and the largest 6-digit number by subtracting the smallest from the largest.
Thus, we get,
⇒999999−100000
⇒899999
Hence, 899999 is the difference between the smallest 6-digit and the largest 6-digit numbers.
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What is the value of X? 3 ,4,5,6,8
Answer:
but it is not possible to determine the value of X with the information provided. The numbers 3, 4, 5, 6, and 8 are all different values, and without any additional context or information, it is impossible to determine which one is X.
It would be helpful if you could provide more information such as an equation or some context, to help determine the value of X.
Simplify the mathematical expression (a) 7 x 6 – 5 x 4 + 1 x 3
The order of operations is a collection of rules that gives the correct sequence of steps for doing a calculation. BIDMAS is an acronym used to tell you the correct order to complete a calculation when there are different operations . It stands for Brackets, Indices , Division, Multiplication, Addition and Subtraction.
Thus solving the expression;
we first solve all the multiplication parts:
7 x 6 - 5 x 4 + 1 x 3
Now addition:
= 42 - 20 + 3
Lastly subtraction:
= 42 - 23
= 19
Is co-prime a number 9?.
Yes, the numbers 2 and 9 are co-prime numbers, i.e., HCF(2,9) = 1.
Two numbers a and b are relatively prime if their only common divisor is 1. If the only highest common factor of two numbers a and b is 1, then a and b are co-prime numbers. In this case,(a, b) is said to be a co-prime pair. Properties of relatively prime numbers:
The greatest common divisor (HCF) of two relatively prime numbers is always 1.The least common multiple (LCM) of two relatively prime numbers is always their product.Two even numbers must not be relatively prime.Every pair of two consecutive numbers is primeWe have, two numbers say 2 and 9 and we have to check they are co-prime or not. The factors of 2 are 1 and 2. Factors of 9 are 1, 3 and 9. So, highest common factor between 2 and 9 is 1. As 9 and 2 have no common factor other than 1, they are co-prime.
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Complete question:
Is 2 co-prime number with 9?.
What are the solutions of the quadratic equation 3x² 14x 5 0?.
On simplifying the given quadratic equation , we get that the solution of the quadratic equation 3x² -14x -5 = 0 are x = -1/3 and x = 5 .
The Quadratic Equation are given as : 3x² -14x -5 = 0 ;
to find the solutions of this equation , we use the split the middle term method ;
⇒ 3x² -14x -5 = 0 ;
we split "-14" as the sum of -15 and 1 .
⇒ 3x² -15x + x -5 = 0 ;
⇒ 3x(x - 5) +1(x - 5) = 0;
⇒ (3x + 1)(x - 5) = 0 ;
Solving the factors separately ,
we have ;
⇒ 3x + 1 = 0 and x - 5 = 0 ;
⇒ x = -1/3 and x = 5 ;
Therefore , the solutions of given quadratic are x = -1/3 and x = 5 .
The given question is incomplete , the complete question is
What are the solutions of the quadratic equation 3x² -14x -5=0 ?
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What is the factor of 9x2 24xy 16y2?.
The factor of 9x² 24xy 16y² is (3x−4y)²
A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, usually smaller or simpler things of the same kind.
Factorization in mathematics is the method of dividing a large number into tiny ones that, when multiplied together, give you the original number. Factorization is the split of a number into its factors or divisors.
9x²−24xy+16y²
=(3x)²−24xy+(4y)²
=(3x)²−2(3x)(4y)+(4y)²
Using (a−b)²=a²−2ab+b², we get
=(3x−4y)²
Factorization, also known as factoring, is the process of dividing or decomposing a thing into factors that, when multiplied together, form the original number, matrix, etc.
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PLEASE HELP ASAP!!
Select the correct answer.
Simplify the following expression.
5-^3
Answer: A
Step-by-step explanation:
when you have a number to a negative power, putting it as a fraction under 1 will turn the negative power positive
URGENT!
find the value of x in each supplementary angle pair
[tex] \frac{x}{3° } + 49° = 180° \\ [/tex]
Cross multiply
[tex]x + 147° = 180°[/tex]
simplify
x = 180° - 147°
answer : x = 33°
Rectangle A B C D is transformed by a combination of two transformations so that all points on AB are invariant and there are no other invariant points.
The first transformation is
a reflection in the line with equation y = k, where ‘k’
is an integer and k ≠1
Describe fully the second transformation.
(2 marks)
It is a translation by vector
(?)
The second transformation that is applied to rectangle A B C D is a translation.
Explain about fully the second transformation:A translation is a transformation that moves an object a certain distance in a certain direction without changing its size or orientation. In this case, the translation is represented by a vector, which is a mathematical object that has both magnitude and direction. The vector for this translation would have the form (x, y), where x and y are the horizontal and vertical distances that the object is moved.In the case of rectangle A B C D, since all points on AB are invariant, it means that the translation vector has the same magnitude in the horizontal direction as it does in the vertical direction. This is why the vector for the translation is represented by (?), as the values of x and y are not given. The only thing that is specified in the problem is that the translation vector moves the rectangle in a direction that is different from the reflection line y = k, as there are no other invariant points.To learn more about second transformation refer to;
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What is the factored form of x² +8x +16?.
To find the factored form of the quadratic equation x^2 + 8x + 16, we can use the technique of factoring by grouping.
First, we write the equation in the form of (x^2 + ax + b) + (x + c) = 0
x^2 + 8x + 16 = 0
Next, we find two numbers that multiply to b and add to a, in this case, b = 16 and a = 8
We can factor out a common factor of x from the first two terms and x + 4 from the last two terms: x^2 + 8x + 16 = (x^2 + 8x) + (16)
Finally, we can factor out a common factor of x + 4 from both terms:
x^2 + 8x + 16 = x(x + 8) + 4(4)
So the factored form of x^2 + 8x + 16 is (x+4)^2.
You can also find the factored form of the quadratic equation x^2 + 8x + 16 by using the difference of squares method:
x^2 + 8x + 16 = (x+4)^2
It's worth noting that this is a perfect square trinomial, which means that it can be factored into the square of a binomial.
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If all of the following are non-terminating decimals, which would be classified as a rational number?
A. 1.25468902
B. 12.4587984
C. 3.12541254
D. 2.15435321
Answer:c
Step-by-step explanation:
What are the 3 types of multiplication?.
The three types of multiplication properties are given by :
1. Commutative property : a × b = b × a , a, b ∈R
2. Identity property : a × 1 = a , a ∈ R
3. Distributive property : a × ( b + c ) = a × b + a × c , a, b, c ∈R.
As given in the question,
Three types of multiplication property is given by :
Let us consider variable a, b, c belongs to real number R.
1. Commutative property :
Order of the multiplication having no affect on the final outcome.
a × b = b × a
Example : 5 × 4 = 20
4 × 5 = 20
2. identity property :
Multiplying one to any real number always gives the same number.
a × 1 = a
Example : 3 × 1 = 3
3. Distributive property :
Adding first two numbers and then multiplying or first multiplying each pair and then adding result remain same.
a × ( b + c ) = a × b + a × c
Example:
5 × ( 2 + 1 ) = 5 × 2 + 5 × 1
Therefore, the three types of multiplication property are given by :
1. Commutative property
2. Identity property
3. Distributive property
The above question is incomplete , the complete question is :
What are the 3 types of multiplication properties ?.
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From the top of a tower, John ee hi friend Julie on the ground at an angle of depreion of 49. If the tower i 83 ft. In height, how far i Julie from the bae of the tower? Round your anwer to the nearet tenth
Julie is approximately 40.6 ft away from the base of the tower.
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. One of the main uses of trigonometry is to calculate distances in a triangle when the lengths of two sides and the measure of the angle between them are known.
We can calculate this by using the formula:
Distance = (tower height) / (tan(angle of depression))
Distance = (83 ft) / (tan(49))
Distance = 40.6 ft (rounded to the nearest tenth)
Therefore, Julie is approximately 40.6 ft away from the base of the tower.
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Pine Grove High School has a total of one thousand and twenty
students. Ten percent of the students are out sick, and twenty-five
percent of the students are on a field trip. How many students are
currently in the school?
10 pointss!! Huryyyy nowww
663.
i found out what 35% of 1020 is and then subtracted that by 1020.
What is the additive inverse of the polynomial –9xy2 + 6x2y – 5x3?
Answer:
9xy² -6x²y +5x³
Step-by-step explanation:
You want the additive inverse of –9xy² + 6x²y – 5x³.
Additive inverseThe additive inverse is the value that gives zero when added to the original. It can be formed by changing the signs of the terms in the sum:
9xy² -6x²y +5x³
DIG DEEPER There is a total of 4,752 passengers on 3 subway
trains. Each subway train has 8 cars. The number of
passengers in each car is the same. How many
passengers are in each car?
There are 198 passengers in each car.
What is division?
The division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. It is the inverse operation of multiplication.
To determine the number of passengers in each car, we need to divide the total number of passengers by the total number of cars.
We know that:
There are 4,752 passengers in total
There are 8 cars per train and 3 trains
So, the total number of cars is 8 cars/train x 3 trains = 24 cars
To find the number of passengers per car, we divide the total number of passengers by the total number of cars:
4,752 passengers / 24 cars = 198 passengers per car.
Hence, there are 198 passengers in each car.
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(a) this is part of thr fibonacci sequence;21,34,55
what is the next term of the sequence
a 68
b 76
c 88
d 89
Answer:
89
Step-by-step explanation:
fibonacci sequence is a famous sequence where each number is the sum of the last two.
Therefore :
34+55 will give us the next number which is 89
which neurotransmitter is released from the parasympathetic ganglion
The amount of neurotransmitter released from the parasympathetic ganglion is acetylcholine.
The parasympathetic nervous system is part of the autonomic nervous system which helps to regulate involuntary bodily functions such as heart rate, digestion and other processes.
The parasympathetic nervous system is responsible for calming the body and restoring it to its resting state. Parasympathetic ganglia are clusters of neurons that receive and transmit nerve signals from the brain to the organs and muscles.
The amount of neurotransmitter released from these ganglia is acetylcholine, which helps to slow the heart rate and promote relaxation.
The parasympathetic nervous system is part of the autonomic nervous system which helps to regulate involuntary bodily functions such as heart rate, digestion and other processes.
The parasympathetic nervous system is responsible for calming the body and restoring it to its resting state. Parasympathetic ganglia are clusters of neurons that receive and transmit signals from the brain to the organs and muscles.
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What relation exists between x and y so that
the two solids have the same volume? Please help!
The volume of solid₁ and solid₂ is related with y = x + 1 where x = 1 × 2 units.
What is volume?The amount of actual space a 3D object takes up is measured by its volume. It represents the area in three dimensions of a two-dimensional shape. It is measured in cubic units like cm3, for example. This can be determined by multiplying the object's length, height, and width.
Based on a fundamental equation, which is one of the first equations that students encounter in school, this method of measuring volume was developed. Because it lays the foundation for further equation study, math volume is very important.
We cane see that
y = x + 1
1/2 of 2 = x/2 = 1
x = 2
Lets find the value of the variables
y = (2)+ 1
y = 3
Volume of solid₁ = x × y × 2 = 2 × 3 × 2 = 12 cube unit
Volume of solid₂ = x × y × 2 = 2 × 3 × 2 = 12 cube unit
Thus, the volume of solid₁ and solid₂ is related with y = x + 1 where x = 1 × 2 units.
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What are the two 2 methods used in solving a system of linear equations?.
Two different methods used to solve the system of linear equation is given by :
a. Elimination method.
b. Substitution method
As given in the question,
Let us consider system of linear equation be :
2x + 5y = 3 __(1)
3x + 4y = 1 __(2)
a. Elimination method :
Multiply (1) by 3 and ( 2) by -2 and add them we get,
6x + 15y = 9
-6x -8y = -2
7y = 7
⇒ y = 1
b. Substitution method :
Substitute the value of y = 1 in any one equation we get,
2x + 5(1) = 3
⇒ 2x = 3 - 5
⇒ x = -1
While solving two equation substitute the value of one variable from one equation into the other.
Therefore, the two methods used to solve the system of linear equation is equal to :
a. Elimination method.
b. Substitution method
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I need some help please
Answer:
x = 39
m ∠1 = 63°
m ∠2 = 117°
Step-by-step explanation:
m∠1 + m∠2 = 180° since they are adjacent linear angles lying on the same straight line
Therefore x + 24 + 3x = 180
4x + 24 = 180
4x = 180-24 = 156
x = 156/4 = 39
Therefore x = 39 (a)
FOr (b) substitute this value of x = 39 into each equation
m∠1 = x + 24 = 39 + 24 = 63°
m∠2 = 3x = 3(39) = 117°
