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All questions of Expressions for Grade 9 Exam
Write the additive inverse of 4/5.
- a)1
- b)-4/5
- c)4/5
- d)0
Correct answer is option 'B'. Can you explain this answer?
Write the additive inverse of 4/5.
a)
1
b)
-4/5
c)
4/5
d)
0
|
EduRev Class 8 answered |
additive inverse means adding what number will give you zero
so let that no be x
x + 4/5 = 0
x = -4/5
trick : just change the sign of number
so let that no be x
x + 4/5 = 0
x = -4/5
trick : just change the sign of number
Which of the following is an expression?- a)1/2
- b)3
- c)3x-2
- d)2
Correct answer is option 'C'. Can you explain this answer?
Which of the following is an expression?
a)
1/2
b)
3
c)
3x-2
d)
2
|
Mainak Sharma answered |
A) 1/2: This is a fraction and represents a rational number. It is not an expression because it is a single value.
B) 3: This is a whole number and represents an integer. It is not an expression because it is a single value.
C) 3x-2: This is an expression. It consists of variables, constants, and operators. In this expression, "x" represents a variable and "3" and "2" are constants. The "-" is the subtraction operator. The expression can be simplified or evaluated by substituting a value for the variable "x".
D) 2: This is a whole number and represents an integer. It is not an expression because it is a single value.
An expression is a mathematical phrase that represents a value or quantity. It can consist of variables, constants, and operators. In option C, the expression "3x-2" represents a value that can change based on the value of the variable "x". It can be used to calculate different values depending on the value of "x".
In contrast, options A, B, and D are not expressions because they do not have variables or operators. They represent single values that do not change. Option A is a fraction, option B is a whole number, and option D is a whole number. These values do not depend on any variables or operators.
Therefore, the correct answer is option C, "3x-2", because it is the only option that represents an expression.
B) 3: This is a whole number and represents an integer. It is not an expression because it is a single value.
C) 3x-2: This is an expression. It consists of variables, constants, and operators. In this expression, "x" represents a variable and "3" and "2" are constants. The "-" is the subtraction operator. The expression can be simplified or evaluated by substituting a value for the variable "x".
D) 2: This is a whole number and represents an integer. It is not an expression because it is a single value.
An expression is a mathematical phrase that represents a value or quantity. It can consist of variables, constants, and operators. In option C, the expression "3x-2" represents a value that can change based on the value of the variable "x". It can be used to calculate different values depending on the value of "x".
In contrast, options A, B, and D are not expressions because they do not have variables or operators. They represent single values that do not change. Option A is a fraction, option B is a whole number, and option D is a whole number. These values do not depend on any variables or operators.
Therefore, the correct answer is option C, "3x-2", because it is the only option that represents an expression.
_____ is the only rational number that is equal to its reciprocal. - a)2
- b)1
- c)1/2
- d)0
Correct answer is option 'B'. Can you explain this answer?
_____ is the only rational number that is equal to its reciprocal.
a)
2
b)
1
c)
1/2
d)
0
|
Pooja Shah answered |
1 because the reciprocal of 1 is 1/1 which is equal to 1.
Using identity (x − a) (x + a) = x2− a2 find 62− 52. - a)11
- b)12
- c)10
- d)none of these
Correct answer is 'A'. Can you explain this answer?
Using identity (x − a) (x + a) = x2− a2 find 62− 52.
a)
11
b)
12
c)
10
d)
none of these
|
Rahul Kumar answered |
To find: 62 - 52:
Putting x = 6 and a = 5 in identity x2 - a2 = (x - a)(x+a);
⇒ 62- 52 = (6 - 5)(6 + 5) = 11.
_______ are closed under addition.- a)Irrational numbers
- b)Negative numbers
- c)Rational numbers
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
_______ are closed under addition.
a)
Irrational numbers
b)
Negative numbers
c)
Rational numbers
d)
none of these
|
|
Ananya Das answered |
Rational Numbers: This set is closed under addition, subtraction, multiplication, and division (with the exception of division by 0).
Which of the following is an expression?- a)10
- b)3
- c)1/2
- d)4x + 7
Correct answer is option 'D'. Can you explain this answer?
Which of the following is an expression?
a)
10
b)
3
c)
1/2
d)
4x + 7
|
|
Amit Sharma answered |
An algebraic expression include constants, variables and coefficients, so answer is 4x+7
Find a rational number between 1/4 and 1/2.
- a)2
- b)1/2
- c)3/8
- d)0
Correct answer is option 'C'. Can you explain this answer?
Find a rational number between 1/4 and 1/2.
a)
2
b)
1/2
c)
3/8
d)
0
|
|
Amit Sharma answered |
A rational number between a and b is (a + b)/2
clearly it is there half so it will be between them
where a and b are numbers
a = 1/4, b = 1/2
Therefore, rational no. between 1/4 and 1/2 is
= (1/4 + 1/2)/2
= [(1 + 2)/4]/2
= 3/8
clearly it is there half so it will be between them
where a and b are numbers
a = 1/4, b = 1/2
Therefore, rational no. between 1/4 and 1/2 is
= (1/4 + 1/2)/2
= [(1 + 2)/4]/2
= 3/8
Expression that contains only one term is called a __________.- a)monomial
- b)binomial
- c)trinomial
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Expression that contains only one term is called a __________.
a)
monomial
b)
binomial
c)
trinomial
d)
None of these
|
Pranav Chauhan answered |
Monomial
A monomial is a mathematical expression that contains only one term. It is a type of polynomial that consists of a single term. The term can be a constant, a variable, or a product of constants and variables.
Examples of monomials:
- 5
- x
- 2xy
- -3a²
A monomial can be simplified by combining like terms. Like terms are terms that have the same variables raised to the same powers.
For example, the monomial 3x²y - 2xy² can be simplified as follows:
3x²y - 2xy² = xy(3x - 2y)
In this simplified form, the monomial is still a single term, but it is expressed as a product of a constant (xy) and a binomial (3x - 2y).
Binomial and Trinomial
Binomials and trinomials are also types of polynomials, but they contain two and three terms, respectively.
Examples of binomials:
- 2x + 5y
- 3a² - 4b
- 6xy + 2y²
Examples of trinomials:
- x² + 2x + 1
- 2a² - 5ab + 3b²
- 4xy² + 3x²y - 2y³
A monomial is a mathematical expression that contains only one term. It is a type of polynomial that consists of a single term. The term can be a constant, a variable, or a product of constants and variables.
Examples of monomials:
- 5
- x
- 2xy
- -3a²
A monomial can be simplified by combining like terms. Like terms are terms that have the same variables raised to the same powers.
For example, the monomial 3x²y - 2xy² can be simplified as follows:
3x²y - 2xy² = xy(3x - 2y)
In this simplified form, the monomial is still a single term, but it is expressed as a product of a constant (xy) and a binomial (3x - 2y).
Binomial and Trinomial
Binomials and trinomials are also types of polynomials, but they contain two and three terms, respectively.
Examples of binomials:
- 2x + 5y
- 3a² - 4b
- 6xy + 2y²
Examples of trinomials:
- x² + 2x + 1
- 2a² - 5ab + 3b²
- 4xy² + 3x²y - 2y³
When numbers/literals are added or subtracted, they are called _________.- a)identities
- b)expressions
- c)variables
- d)terms
Correct answer is option 'D'. Can you explain this answer?
When numbers/literals are added or subtracted, they are called _________.
a)
identities
b)
expressions
c)
variables
d)
terms
|
Lakshmi Basu answered |
Terms in Algebra
In algebra, expressions are made up of different parts called terms. Terms can be numbers, variables, or the product of both. When these terms are added or subtracted, they form what is known as algebraic expressions.
Definition of Terms
Terms are defined as individual parts of an expression that are separated by addition or subtraction signs. For example, in the expression 3x + 5y - 2, there are three terms: 3x, 5y, and -2. Each of these terms consists of a coefficient (3, 5, and -2) and a variable (x and y).
Types of Terms
There are two main types of terms: like terms and unlike terms.
Like terms have the same variables raised to the same powers. For example, 3x and 2x are like terms because they both have x raised to the first power. Similarly, 4y² and 5y² are like terms because they both have y raised to the second power.
Unlike terms have different variables or the same variables raised to different powers. For example, 3x and 2y are unlike terms because they have different variables. Similarly, 4y² and 5y³ are unlike terms because they have the same variable raised to different powers.
Importance of Terms
Understanding terms is essential in algebra because they form the building blocks of expressions. By identifying and grouping like terms, it becomes easier to simplify expressions and solve equations. For example, in the expression 3x + 5y - 2x - 4y, the like terms 3x and -2x can be combined to give x, and the like terms 5y and -4y can be combined to give y. This simplifies the expression to x + y.
Conclusion
Terms are an important concept in algebra, as they are the building blocks of expressions. When numbers/literals are added or subtracted, they are called terms. Understanding the different types of terms and how to identify and group them is essential in simplifying expressions and solving equations.
In algebra, expressions are made up of different parts called terms. Terms can be numbers, variables, or the product of both. When these terms are added or subtracted, they form what is known as algebraic expressions.
Definition of Terms
Terms are defined as individual parts of an expression that are separated by addition or subtraction signs. For example, in the expression 3x + 5y - 2, there are three terms: 3x, 5y, and -2. Each of these terms consists of a coefficient (3, 5, and -2) and a variable (x and y).
Types of Terms
There are two main types of terms: like terms and unlike terms.
Like terms have the same variables raised to the same powers. For example, 3x and 2x are like terms because they both have x raised to the first power. Similarly, 4y² and 5y² are like terms because they both have y raised to the second power.
Unlike terms have different variables or the same variables raised to different powers. For example, 3x and 2y are unlike terms because they have different variables. Similarly, 4y² and 5y³ are unlike terms because they have the same variable raised to different powers.
Importance of Terms
Understanding terms is essential in algebra because they form the building blocks of expressions. By identifying and grouping like terms, it becomes easier to simplify expressions and solve equations. For example, in the expression 3x + 5y - 2x - 4y, the like terms 3x and -2x can be combined to give x, and the like terms 5y and -4y can be combined to give y. This simplifies the expression to x + y.
Conclusion
Terms are an important concept in algebra, as they are the building blocks of expressions. When numbers/literals are added or subtracted, they are called terms. Understanding the different types of terms and how to identify and group them is essential in simplifying expressions and solving equations.
Zero has ________ reciprocal.
- a)1
- b)2
- c)no
- d)3
Correct answer is option 'C'. Can you explain this answer?
Zero has ________ reciprocal.
a)
1
b)
2
c)
no
d)
3
|
Akshay Mehra answered |
Zero has no reciprocal. Because 1/0 is not defined and also remember any number multiplied by zero gives 0. Therefore, if reciprocal was supposed to be there then that reciprocal when multiplied by 0 should give 1 which is not possible.
A number which can be written in the form, p/q where p and q are integers and _____ is called a rational number.
- a)q = 0
- b)q ≠ 0
- c)q = 1
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
A number which can be written in the form, p/q where p and q are integers and _____ is called a rational number.
a)
q = 0
b)
q ≠ 0
c)
q = 1
d)
none of these
|
|
Pooja Shah answered |
Given, A rational number is defined as a number that can be expressed in the form p/q , where p and q are integers
We have to find the condition that satisfies the definition.
A number that can be expressed in the form p/q , where p and q are integers and q ≠ 0, is called a rational number.
Therefore, the condition that satisfies the definition is q ≠ 0
Which of the following is like term as 7xy?- a)9
- b)9x
- c)9y
- d)9xy
Correct answer is 'D'. Can you explain this answer?
Which of the following is like term as 7xy?
a)
9
b)
9x
c)
9y
d)
9xy
|
Geetika Shah answered |
9xy is the like term of 7xy as ...9xy and 7xy contains the same variable (xy).. if we have to find like terms then.. we we should see that they both contains same variable ..numbers doesn't matter ..they can be sake itlr different.. therefore 9xy is the like term of 7xy and visa versa..
Using identity (x - a) (x + a) = x2 - a2 find 52− 42.- a)12
- b)14
- c)9
- d)none of these
Correct answer is 'C'. Can you explain this answer?
Using identity (x - a) (x + a) = x2 - a2 find 52− 42.
a)
12
b)
14
c)
9
d)
none of these
|
Gunjan Lakhani answered |
x2 - a2 = ( x + a) (x - a) using this equation.
52 - 42 = ( 5 + 4) ( 5 - 4 )= ( 9 ) (1 )= 9
Which of the following is a binomial?- a)4x + y +2
- b)2x + 7
- c)3x+4y-6
- d)3x
Correct answer is option 'B'. Can you explain this answer?
Which of the following is a binomial?
a)
4x + y +2
b)
2x + 7
c)
3x+4y-6
d)
3x
|
|
Geetika Shah answered |
An algebraic expression consisting of unlike terms is called a binomial.
so, 2x+7 is a binomial as it contains two unlike terms i.e 2x and 7.
Find the multiplicative inverse of 1/4.- a)4
- b)-1/4
- c)-4
- d)1/4
Correct answer is option 'A'. Can you explain this answer?
Find the multiplicative inverse of 1/4.
a)
4
b)
-1/4
c)
-4
d)
1/4
|
Urvashi Sharma answered |
In multiplicative inverse we reciprocal the numbers by which we get the answer =1 that's why 1/4×4/1 which we consider as 4 so 4 is the multiplicative inverse of 1/4
Multiplication of pq+qr+rp and ‘zero’ is- a)pq+qr
- b)pq+rp
- c)pq+qr+rp
- d)0
Correct answer is option 'D'. Can you explain this answer?
Multiplication of pq+qr+rp and ‘zero’ is
a)
pq+qr
b)
pq+rp
c)
pq+qr+rp
d)
0
|
|
Àrpita țřipathi answered |
Pq+qr+rp,0
=(pq+qr+rp)
=0
/(because 0×anything =is always zero)
n ( 4 + m) = 4n + ___ - a)4m
- b)4n
- c)4mn
- d)nm
Correct answer is option 'D'. Can you explain this answer?
n ( 4 + m) = 4n + ___
a)
4m
b)
4n
c)
4mn
d)
nm
|
Ishita Chauhan answered |
**Explanation:**
The given equation is n (4m) = 4n.
Let's break down the equation step by step to understand why the correct answer is option D.
**Step 1: Simplify the equation**
n (4m) = 4n
**Step 2: Apply the distributive property**
n * 4m = 4n
**Step 3: Simplify the left side of the equation**
4nm = 4n
**Step 4: Divide both sides of the equation by 4**
(4nm)/4 = (4n)/4
**Step 5: Simplify**
nm = n
**Step 6: Rearrange the equation**
n = nm
**Step 7: Divide both sides of the equation by m**
n/m = nm/m
**Step 8: Simplify**
n/m = n
From the given equation, we have proven that n = n/m. Therefore, the correct answer is option D, which states nm.
This equation shows that n is equal to n/m, meaning that the value of n is divisible by m. It does not matter what the value of m is, as long as it is a non-zero number.
The given equation is n (4m) = 4n.
Let's break down the equation step by step to understand why the correct answer is option D.
**Step 1: Simplify the equation**
n (4m) = 4n
**Step 2: Apply the distributive property**
n * 4m = 4n
**Step 3: Simplify the left side of the equation**
4nm = 4n
**Step 4: Divide both sides of the equation by 4**
(4nm)/4 = (4n)/4
**Step 5: Simplify**
nm = n
**Step 6: Rearrange the equation**
n = nm
**Step 7: Divide both sides of the equation by m**
n/m = nm/m
**Step 8: Simplify**
n/m = n
From the given equation, we have proven that n = n/m. Therefore, the correct answer is option D, which states nm.
This equation shows that n is equal to n/m, meaning that the value of n is divisible by m. It does not matter what the value of m is, as long as it is a non-zero number.
Terms are added to form ___________.- a)expressions
- b)terms
- c)identities
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Terms are added to form ___________.
a)
expressions
b)
terms
c)
identities
d)
none of these
|
Ritu Joshi answered |
A term can be a signed number, a variable, or a constant multiplied by a variable or variables. Each term in an
Which of the following is the reciprocal of the reciprocal of a rational number?- a) -1
- b) 1
- c) 0
- d)The number itself
Correct answer is option 'D'. Can you explain this answer?
Which of the following is the reciprocal of the reciprocal of a rational number?
a)
-1
b)
1
c)
0
d)
The number itself
|
|
Pooja Shah answered |
1 is the Multiplicative identity for rational numbers.
________ are closed under subtraction.
- a)Irrational numbers
- b)Negative numbers
- c)Rational number
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
________ are closed under subtraction.
a)
Irrational numbers
b)
Negative numbers
c)
Rational number
d)
none of these
|
|
Amit Sharma answered |
Rational numbers are closed under subtraction.Because if we subtract a rational number with another rational number we will get rational number. For example 45−35 = 10, which is also a rational number.
Correct option is C.
Correct option is C.
Which of the following is a binomial?
- a)7 – 3x + 4
- b)2x + 7
- c)4x + y + 2
- d)3x
Correct answer is option 'B'. Can you explain this answer?
Which of the following is a binomial?
a)
7 – 3x + 4
b)
2x + 7
c)
4x + y + 2
d)
3x
|
|
Geetika Shah answered |
2x + 7
A binomial is a mathematical expression consisting of two terms. In this case, 2x + 7 is a binomial because it has two terms: 2x and 7.
- 7 – 3x + 4 is not a binomial because it has three terms: 7, -3x, and 4
- 4x + y + 2 is not a binomial because it has three terms: 4x, y, and 2
- 3x is not a binomial because it has only one term: 3x
Expressions consists of _____________ and _______________.- a)variables , constants
- b)identities
- c)expressions
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Expressions consists of _____________ and _______________.
a)
variables , constants
b)
identities
c)
expressions
d)
none of these
|
Mikasi Ambade answered |
Variables and constants .This is because an expression is made up of these only.
Find the multiplicative inverse of 2/9 .- a)-9/2
- b)9/2
- c)-2/9
- d)2/9
Correct answer is option 'B'. Can you explain this answer?
Find the multiplicative inverse of 2/9 .
a)
-9/2
b)
9/2
c)
-2/9
d)
2/9
|
|
Rohit Sharma answered |
Multiplicative inverse is nothing but a reciprocal of a number 2/9 which is 9/2.
Using identity evaluate 297 × 303.- a)99999
- b)79991
- c)89991
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Using identity evaluate 297 × 303.
a)
99999
b)
79991
c)
89991
d)
None of these
|
|
Aditi Saxena answered |
(300-3) (300+3)
(300) whole square - (3) whole square
90000-9
89991
Using identity
(a+b) (a-b)= a square - b square
Which of the following is an expression?- a)7
- b)9
- c)9ab+7
- d)1/4
Correct answer is option 'C'. Can you explain this answer?
Which of the following is an expression?
a)
7
b)
9
c)
9ab+7
d)
1/4
|
Humaira Tabassum answered |
Option C is correct bcuz, an expression consists of at least one variable like :- x, y, z as well as a number.
An expression can also be like this :- 2xy, 3y², 5xy+8, 6z²-3, etc
1 is the __________ for rational numbers.- a)multiplicative identity
- b)Addition of zero
- c)additive identity
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
1 is the __________ for rational numbers.
a)
multiplicative identity
b)
Addition of zero
c)
additive identity
d)
none of these
|
|
Geetika Shah answered |
If you multiply any number with 1,the product will always be the same number which you multiply with 1. Therefore, 1 is the multiplicative identity.
Add: 7xy + 5yz – 3zx, 4yz + 9zx – 4y , –3xz + 5x – 2xy.- a)5xy + 3zx + 5x – 4y
- b)5xy + 9yz +2zx + 5x – 4y
- c)5xy + 9yz +3zx + 5x – 4y
- d)5xy + 9yz +3zx + 4y
Correct answer is option 'C'. Can you explain this answer?
Add: 7xy + 5yz – 3zx, 4yz + 9zx – 4y , –3xz + 5x – 2xy.
a)
5xy + 3zx + 5x – 4y
b)
5xy + 9yz +2zx + 5x – 4y
c)
5xy + 9yz +3zx + 5x – 4y
d)
5xy + 9yz +3zx + 4y
|
|
Sarita Verma answered |
Writing the three expressions in separate rows, with like terms one below the other, we have
7xy + 5yz – 3zx
+ 4yz + 9zx – 4y
+ –2xy – 3zx + 5x
-----------------------------------------
= 5xy + 9yz + 3zx + 5x – 4y
Thus, the sum of the expressions is 5xy + 9yz + 3zx + 5x – 4y. Note how the terms, – 4y
in the second expression and 5x in the third expression, are carried over as they are, since
they have no like terms in the other expressions.
Simplify: (x + y) (2x – 3y + z) – (2x – 3y)z - a)2x2− 3y2 − 4yz
- b)2x2− 3y2− xy + 3yz
- c)2x2− 3y2− xy − xz + 4yz
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Simplify: (x + y) (2x – 3y + z) – (2x – 3y)z
a)
2x2− 3y2 − 4yz
b)
2x2− 3y2− xy + 3yz
c)
2x2− 3y2− xy − xz + 4yz
d)
None of these
|
Sanjana Bose answered |
(x+y)(2x−3y+z)−(2x−3y)z
=> 2x^2−3xy+xz+2xy−3y^2+yz−2xz+3yz
=> 2x^2−xy−xz−3y^2+4yz
=>2x^2−3y^2−xy−xz+4yz
(x – a (x + a) =?- a)x2+ a2
- b)x −− a2
- c)x2−− a2
- d)x + a2
Correct answer is option 'C'. Can you explain this answer?
(x – a (x + a) =?
a)
x2+ a2
b)
x −− a2
c)
x2−− a2
d)
x + a2
|
Cav Lc answered |
(a-b)(a+b) = a^2 - b^2(x-a)(x+a) = x (x+a) -a (x+a) = x^2 + ax -ax -a^2 = x^2 - a ^2
If x + y = 12 and xy = 32, find the value of x2+ y2.- a)80
- b)70
- c)60
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
If x + y = 12 and xy = 32, find the value of x2+ y2.
a)
80
b)
70
c)
60
d)
None of these
|
|
Anshul Mukherjee answered |
Given: xy = 32 and x * y = 12
To find: x^2 * y^2
Solution:
Let's try to simplify the expression x^2 * y^2:
x^2 * y^2 = (x*y)^2
= 12^2 (from the given equation x*y = 12)
= 144
Now, we can substitute the value of x^2 * y^2 as 144 in the given expression.
Therefore, the answer is option A) 80.
Explanation:
The given equation is x * y = 12 and xy = 32
From the first equation, we can write y = 12/x
Substituting this value of y in the second equation, we get:
x * (12/x) = 32
Simplifying, we get:
x^2 = 32/3
y^2 = 144/x^2
Substituting the value of x^2 in the above equation, we get:
y^2 = 144/(32/3)
Simplifying, we get:
y^2 = 27
Substituting the values of x^2 and y^2 in the expression x^2 * y^2, we get:
x^2 * y^2 = (32/3) * 27
Simplifying, we get:
x^2 * y^2 = 288
Therefore, the correct answer is option A) 80.
To find: x^2 * y^2
Solution:
Let's try to simplify the expression x^2 * y^2:
x^2 * y^2 = (x*y)^2
= 12^2 (from the given equation x*y = 12)
= 144
Now, we can substitute the value of x^2 * y^2 as 144 in the given expression.
Therefore, the answer is option A) 80.
Explanation:
The given equation is x * y = 12 and xy = 32
From the first equation, we can write y = 12/x
Substituting this value of y in the second equation, we get:
x * (12/x) = 32
Simplifying, we get:
x^2 = 32/3
y^2 = 144/x^2
Substituting the value of x^2 in the above equation, we get:
y^2 = 144/(32/3)
Simplifying, we get:
y^2 = 27
Substituting the values of x^2 and y^2 in the expression x^2 * y^2, we get:
x^2 * y^2 = (32/3) * 27
Simplifying, we get:
x^2 * y^2 = 288
Therefore, the correct answer is option A) 80.
Which of the following is a trinomial?- a)4x + y
- b)3x
- c)7 – 3x + 4y
- d)2x + 7
Correct answer is option 'C'. Can you explain this answer?
Which of the following is a trinomial?
a)
4x + y
b)
3x
c)
7 – 3x + 4y
d)
2x + 7
|
Ritik Yadav answered |
Because monomial 1 term binomial, 2 terms and trinomial 3 terms therefor 7_3x+4y trinomial.
Multiplication of ‘ab’ and ‘a-b’ is- a)a2b-b
- b)a2b+b
- c)ba2b+ab2
- d)a2b - ab2
Correct answer is option 'D'. Can you explain this answer?
Multiplication of ‘ab’ and ‘a-b’ is
a)
a2b-b
b)
a2b+b
c)
ba2b+ab2
d)
a2b - ab2
|
Akhilesh Rajput answered |
Answer d is correct
(ab) ( a- b)
= a^2 b - ab^2 ok
(ab) ( a- b)
= a^2 b - ab^2 ok
The product of two rational numbers is always a _______.- a)irrational number
- b)negative number
- c)rational number
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
The product of two rational numbers is always a _______.
a)
irrational number
b)
negative number
c)
rational number
d)
None of these
|
|
Kavya Saxena answered |
Product of two rational numbers is always a rational number.
For example, 1/2 + 1/2 = 1
For example, 1/2 + 1/2 = 1
________ is not associative for rational numbers.- a)Subtraction or Division
- b)Addition or Multiplication
- c)Addition or Division
- d)Multiplication or Division
Correct answer is option 'A'. Can you explain this answer?
________ is not associative for rational numbers.
a)
Subtraction or Division
b)
Addition or Multiplication
c)
Addition or Division
d)
Multiplication or Division
|
|
Amit Sharma answered |
This is how associative property works. It states that you can add or multiply numbers regardless of how they are grouped. Addition and multiplication are associative for rational numbers. Subtraction and division are not associative for rational numbers.
Simplify: (xy + yz)2− (xy − yz)2- a)4xy2
- b)4xy2z
- c)4xz
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Simplify: (xy + yz)2− (xy − yz)2
a)
4xy2
b)
4xy2z
c)
4xz
d)
None of these
|
|
Shubham Sharma answered |
(xy+yz)²-(xy-yz)²
xy² +yz² +2.xy.yz -(xy²+yz²-2xy.yz)
(xy)² +(yz)² +2xy²z -[(xy)² +(yz)² -2xy²z
(xy)² +(yz)² +2xy²z -(xy²)-(yz)² + 2xy²z
Cancelled (xy)² +(yz)² and -(xy²)-(yz)².
2xy²z+ 2xy²z
=> 4xy²z
Hence, Value of (xy + yz)² – (xy – yz)² => 4xy²z
Note;-
(a+b)²-(a-b)² = 4ab
xy² +yz² +2.xy.yz -(xy²+yz²-2xy.yz)
(xy)² +(yz)² +2xy²z -[(xy)² +(yz)² -2xy²z
(xy)² +(yz)² +2xy²z -(xy²)-(yz)² + 2xy²z
Cancelled (xy)² +(yz)² and -(xy²)-(yz)².
2xy²z+ 2xy²z
=> 4xy²z
Hence, Value of (xy + yz)² – (xy – yz)² => 4xy²z
Note;-
(a+b)²-(a-b)² = 4ab
What is the value of 1/2 + 1/2 ÷ 1/2?
- a)7/4
- b)9/4
- c)5/4
- d)3/2
Correct answer is option 'D'. Can you explain this answer?
What is the value of 1/2 + 1/2 ÷ 1/2?
a)
7/4
b)
9/4
c)
5/4
d)
3/2
|
|
Rajani bajaj answered |
The expression 1/2 1/2 is not clear as to what operation is being performed between 1/2 and 1/2. However, if we assume that it is multiplication, then the value would be:
1/2 x 1/2 = 1/4
Therefore, the value of 1/2 1/2, if interpreted as multiplication, is 1/4.
1/2 x 1/2 = 1/4
Therefore, the value of 1/2 1/2, if interpreted as multiplication, is 1/4.
Simplify(xy + yz)2− 2x2y2z. Find the value when x = -1, y = 1 and z = 2.- a)4
- b)3
- c)-3
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Simplify(xy + yz)2− 2x2y2z. Find the value when x = -1, y = 1 and z = 2.
a)
4
b)
3
c)
-3
d)
none of these
|
|
Divya Das answered |
Step 1: Simplifying the Expression
To simplify the expression (xy + yz)² - 2x²y²z, we start by expanding (xy + yz)².
- Use the formula (a + b)² = a² + 2ab + b²:
- Here, a = xy and b = yz.
- Expanding gives:
- (xy)² + 2(xy)(yz) + (yz)²
- This results in x²y² + 2xy²z + y²z².
Now, we rewrite the full expression:
- x²y² + 2xy²z + y²z² - 2x²y²z.
Next, we combine like terms:
- Combine the x²y² and -2x²y²z terms:
Final simplified form:
- (x²y² + y²z² + 2xy²z - 2x²y²z).
Step 2: Substituting Values
Now, we substitute x = -1, y = 1, and z = 2 into the simplified expression.
- Substitute:
- x² = (-1)² = 1
- y² = (1)² = 1
- z² = (2)² = 4
Now, substitute into the expression:
- 1(1) + 4 + 2(-1)(1)(2) - 2(1)(-1)²(2)
Calculating each term:
- 1 + 4 + 2(-1)(2) - 2(1)(1)(2)
- = 1 + 4 - 4 - 4
- = 1 + 4 - 8
- = -3.
Final Result
The final value of the expression when x = -1, y = 1, and z = 2 is -3.
Thus, the correct option is C) -3.
To simplify the expression (xy + yz)² - 2x²y²z, we start by expanding (xy + yz)².
- Use the formula (a + b)² = a² + 2ab + b²:
- Here, a = xy and b = yz.
- Expanding gives:
- (xy)² + 2(xy)(yz) + (yz)²
- This results in x²y² + 2xy²z + y²z².
Now, we rewrite the full expression:
- x²y² + 2xy²z + y²z² - 2x²y²z.
Next, we combine like terms:
- Combine the x²y² and -2x²y²z terms:
Final simplified form:
- (x²y² + y²z² + 2xy²z - 2x²y²z).
Step 2: Substituting Values
Now, we substitute x = -1, y = 1, and z = 2 into the simplified expression.
- Substitute:
- x² = (-1)² = 1
- y² = (1)² = 1
- z² = (2)² = 4
Now, substitute into the expression:
- 1(1) + 4 + 2(-1)(1)(2) - 2(1)(-1)²(2)
Calculating each term:
- 1 + 4 + 2(-1)(2) - 2(1)(1)(2)
- = 1 + 4 - 4 - 4
- = 1 + 4 - 8
- = -3.
Final Result
The final value of the expression when x = -1, y = 1, and z = 2 is -3.
Thus, the correct option is C) -3.
Simplify the expression x²(x – 3y²) – xy(y² – 2xy) – x(y³ – 5x²).- a)6x³ – x²y² – 2xy³
- b)5x³ – x²y² – 2xy³
- c)6x³ – 2x²y² – 2xy³
- d)6x³ – x²y² – 2xy²
Correct answer is option 'A'. Can you explain this answer?
a)
6x³ – x²y² – 2xy³
b)
5x³ – x²y² – 2xy³
c)
6x³ – 2x²y² – 2xy³
d)
6x³ – x²y² – 2xy²
|
|
EduRev Class 8 answered |
The simplified form of the expression is 6x³ – x²y² – 2xy³.
The product of 3xy2z and 4x is:- a)12xyz
- b)12xy2
- c)12x2y2z
- d)12x2yz
Correct answer is option 'C'. Can you explain this answer?
The product of 3xy2z and 4x is:
a)
12xyz
b)
12xy2
c)
12x2y2z
d)
12x2yz
|
Trisha Vashisht answered |
The product of 3xy2z and 4x is:
⇒ (3xy2z) (4x)
⇒ 3.x.y2.z.4.x
⇒ 12x2y2z
⇒ (3xy2z) (4x)
⇒ 3.x.y2.z.4.x
⇒ 12x2y2z
Find 5/12 + 3/8.- a)16/24
- b)17/24
- c)13/24
- d)19/24
Correct answer is option 'D'. Can you explain this answer?
Find 5/12 + 3/8.
a)
16/24
b)
17/24
c)
13/24
d)
19/24
|
|
Yashvi Chaudhary answered |
Adding Fractions:
Adding fractions involves finding a common denominator and then adding the numerators. Here, we are adding 5/12 and 3/8.
Find a Common Denominator:
To add 5/12 and 3/8, we need to find a common denominator. The least common multiple of 12 and 8 is 24.
Convert Fractions:
- To make the denominator of 5/12 as 24, we multiply both the numerator and denominator by 2. This gives us 10/24.
- To make the denominator of 3/8 as 24, we multiply both the numerator and denominator by 3. This gives us 9/24.
Add the Fractions:
Now that both fractions have a common denominator of 24, we can add the numerators:
10/24 + 9/24 = 19/24
Therefore, 5/12 + 3/8 = 19/24.
So, the correct answer is option D. 19/24.
Adding fractions involves finding a common denominator and then adding the numerators. Here, we are adding 5/12 and 3/8.
Find a Common Denominator:
To add 5/12 and 3/8, we need to find a common denominator. The least common multiple of 12 and 8 is 24.
Convert Fractions:
- To make the denominator of 5/12 as 24, we multiply both the numerator and denominator by 2. This gives us 10/24.
- To make the denominator of 3/8 as 24, we multiply both the numerator and denominator by 3. This gives us 9/24.
Add the Fractions:
Now that both fractions have a common denominator of 24, we can add the numerators:
10/24 + 9/24 = 19/24
Therefore, 5/12 + 3/8 = 19/24.
So, the correct answer is option D. 19/24.
The product of two rational numbers is 15/11. If one rational number is 5/9 then find the other.- a)13/11
- b)21/11
- c)17/11
- d)27/11
Correct answer is option 'D'. Can you explain this answer?
The product of two rational numbers is 15/11. If one rational number is 5/9 then find the other.
a)
13/11
b)
21/11
c)
17/11
d)
27/11
|
|
Varsha khanna answered |
Solution:
Given, the product of two rational numbers is 15/11 and one rational number is 5/9.
Let the other rational number be x.
Then, we have 5/9 * x = 15/11.
Solving for x, we get:
x = (15/11) / (5/9) = (15/11) * (9/5) = 27/11.
Therefore, the other rational number is 27/11.
Hence, the correct answer is option 'D', 27/11.
Given, the product of two rational numbers is 15/11 and one rational number is 5/9.
Let the other rational number be x.
Then, we have 5/9 * x = 15/11.
Solving for x, we get:
x = (15/11) / (5/9) = (15/11) * (9/5) = 27/11.
Therefore, the other rational number is 27/11.
Hence, the correct answer is option 'D', 27/11.
What is the sum of 3/7 + (-6/11) + (-8/21) + 5/22 ?- a)-125/462
- b)-125/446
- c)-100/462
- d)125/462
Correct answer is option 'A'. Can you explain this answer?
What is the sum of
3/7 + (-6/11) + (-8/21) + 5/22 ?
a)
-125/462
b)
-125/446
c)
-100/462
d)
125/462
|
|
Trisha Vashisht answered |
3/7 + (-6/11) + (-8/21) + 5/22
= [3/7 + (-8/21)] + [(-6/11) + 5/22]
(by using commutativity and associativity)
(by using commutativity and associativity)
= [9/21 + (-8/21)] + [-12/22 + 5/22]
LCM of 7 and 21 is 21; LCM of 11 and 22 is 22
= 1/21 + (-7/22)
= 22/462 + (-147/462)
= -125/462
= 22/462 + (-147/462)
= -125/462
If we add, 7xy + 5yz – 3zx, 4yz + 9zx – 4y and –3xz + 5x – 2xy, then the answer is:- a)5xy + 9yz +3zx + 5x – 4y
- b)5xy – 9yz +3zx – 5x – 4y
- c)5xy + 10yz +3zx + 15x – 4y
- d)5xy + 10yz +3zx + 5x – 6y
Correct answer is option 'A'. Can you explain this answer?
If we add, 7xy + 5yz – 3zx, 4yz + 9zx – 4y and –3xz + 5x – 2xy, then the answer is:
a)
5xy + 9yz +3zx + 5x – 4y
b)
5xy – 9yz +3zx – 5x – 4y
c)
5xy + 10yz +3zx + 15x – 4y
d)
5xy + 10yz +3zx + 5x – 6y
|
Shivam Chavan answered |
Understanding the Problem
To solve the problem of adding the given expressions, we need to combine like terms systematically. The expressions to be added are:
1. 7xy + 5yz - 3zx
2. 4yz + 9zx - 4y
3. -3xz + 5x - 2xy
Step-by-Step Addition
Let's break down the addition step-by-step.
1. Combine like terms:
- xy Terms:
7xy - 2xy = 5xy
- yz Terms:
5yz + 4yz = 9yz
- zx Terms:
-3zx + 9zx - 3zx = 3zx
- x Terms:
5x
- y Terms:
-4y (no other y terms to combine)
2. Write the final expression:
Now, we can compile all the results from the like terms we've calculated:
- 5xy (from xy terms)
- 9yz (from yz terms)
- 3zx (from zx terms)
- 5x (from x terms)
- -4y (from y terms)
This results in:
Final Expression:
5xy + 9yz + 3zx + 5x - 4y
Conclusion
The final answer matches option 'A':
5xy + 9yz + 3zx + 5x - 4y
Thus, the correct answer is indeed option 'A'.
To solve the problem of adding the given expressions, we need to combine like terms systematically. The expressions to be added are:
1. 7xy + 5yz - 3zx
2. 4yz + 9zx - 4y
3. -3xz + 5x - 2xy
Step-by-Step Addition
Let's break down the addition step-by-step.
1. Combine like terms:
- xy Terms:
7xy - 2xy = 5xy
- yz Terms:
5yz + 4yz = 9yz
- zx Terms:
-3zx + 9zx - 3zx = 3zx
- x Terms:
5x
- y Terms:
-4y (no other y terms to combine)
2. Write the final expression:
Now, we can compile all the results from the like terms we've calculated:
- 5xy (from xy terms)
- 9yz (from yz terms)
- 3zx (from zx terms)
- 5x (from x terms)
- -4y (from y terms)
This results in:
Final Expression:
5xy + 9yz + 3zx + 5x - 4y
Conclusion
The final answer matches option 'A':
5xy + 9yz + 3zx + 5x - 4y
Thus, the correct answer is indeed option 'A'.
What is the additive inverse of -4/9?- a)1/9
- b)7/9
- c)4/9
- d)2/9
Correct answer is option 'C'. Can you explain this answer?
What is the additive inverse of -4/9?
a)
1/9
b)
7/9
c)
4/9
d)
2/9
|
|
Bhaskar Patel answered |
Explanation:
Additive inverse of a number is the number that when added to the given number gives zero. In other words, the sum of a number and its additive inverse is always zero.
Let x be the additive inverse of -4/9. Then, we have:
x + (-4/9) = 0
Adding 4/9 to both sides, we get:
x = 4/9
Therefore, the additive inverse of -4/9 is 4/9.
Answer: C. 4/9
Additive inverse of a number is the number that when added to the given number gives zero. In other words, the sum of a number and its additive inverse is always zero.
Let x be the additive inverse of -4/9. Then, we have:
x + (-4/9) = 0
Adding 4/9 to both sides, we get:
x = 4/9
Therefore, the additive inverse of -4/9 is 4/9.
Answer: C. 4/9
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Mathematics: Algebra 1
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