Simplify: 3x(x – 1) – 7x2 :
To simplify the given algebraic expression, we need to first expand the product term by distributing the monomial over the binomial, and then combine like terms.
The original expression is: \(3x(x - 1) - 7x^2\)
After expansion, it becomes: \(3x^2 - 3x - 7x^2\)
The like terms are \(3x^2\) and \(-7x^2\).
\[ 3x^2 - 7x^2 = (3 - 7)x^2 = -4x^2 \]The remaining term is \(-3x\).
So, the simplified expression is: \(-4x^2 - 3x\)
D) \(-4x^2 - 3x\) is the correct simplified form of the given expression.
Answer the questions based on the information given below.
If '+' is '×', '-' is '+', '×' is '÷' and '÷' is '-' 28 ÷ 16 × 2 + 3 - 1 = ?
This problem requires us to substitute the given new meanings for the arithmetic operators into the expression and then evaluate the resulting expression following the order of operations (BODMAS/PEMDAS).
Original expression: \(28 \div 16 \times 2 + 3 - 1\)
Applying the substitutions:
So, the new expression is: \(28 - 16 \div 2 \times 3 + 1\)
BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Division and Multiplication have the same precedence and are performed from left to right. Similarly, Addition and Subtraction have the same precedence and are performed from left to right.
The expression is: \(28 - 16 \div 2 \times 3 + 1\)
First, perform Division:
\[ 28 - (16 \div 2) \times 3 + 1 \]\[ 28 - 8 \times 3 + 1 \]Next, perform Multiplication:
\[ 28 - (8 \times 3) + 1 \]\[ 28 - 24 + 1 \]Now, perform Addition and Subtraction from left to right:
\[ (28 - 24) + 1 \]\[ 4 + 1 \]\[ 5 \]A) The final calculated value of the expression after substituting the operators and following the order of operations is 5.
The question asks about the fundamental principle governing voting rights in a cooperative society. Understanding the core values of cooperation is key to answering this.
Therefore, the principle of "one man one vote" is central to the democratic functioning of cooperative societies.
Correct Option: B) One man one vote
This question asks about the state of Liquefied Petroleum Gas (LPG) when stored in a domestic cylinder. Understanding the properties of LPG and how it's stored is key to answering this question.
C) Liquid State. LPG is stored as a liquid under pressure in domestic gas cylinders to maximize the amount of fuel that can be stored in a given volume.
Answer the questions based on the information given below.
If '+' is '×', '-' is '+', '×' is '÷' and '÷' is '-' 15 × 5 ÷ 3 + 1 - 1 = ?
This problem involves substituting given symbol transformations into a mathematical expression and then evaluating the new expression following the order of operations (BODMAS/PEMDAS).
\[ 15 \times 5 \div 3 + 1 - 1 \]
\[ 15 \div 5 - 3 \times 1 + 1 \]
\[ 3 - 3 \times 1 + 1 \]
\[ 3 - 3 + 1 \]
\[ 0 + 1 \]
\[ 1 \]
The final value of the expression is 1.
Correct Option: D) 1
Answer the questions based on the information given below.
If '+' is '×', '-' is '+', '×' is '÷' and '÷' is '-' 9 - 3 + 2 ÷ 16 × 2 = ?
This problem involves applying a set of given symbol substitutions to a mathematical expression and then evaluating the modified expression using the order of operations (BODMAS/PEMDAS).
A) 7 is the correct answer. After correctly substituting the operators and applying the BODMAS rule, the final value of the expression is 7.
What is the normal shape of the orbits of planets?
This question asks about the typical shape of planetary orbits. This is a fundamental concept in astronomy and physics, specifically related to Kepler's Laws of Planetary Motion.
C) Elliptical — Kepler's First Law of Planetary Motion explicitly states that planets orbit the Sun in elliptical paths, with the Sun located at one of the two foci of the ellipse. While some orbits are very close to circular, they are technically ellipses.
The question asks to identify the pair of words that is different from the rest, based on a common relationship shared by three of the four pairs. We need to analyze the relationship between the words in each pair.
The pair Stallion : Colt represents an adult male horse and its young male offspring. The other three pairs (Horse : Mare, Dog : Bitch, Drake : Duck) represent the adult male and adult female of the respective species. Therefore, Stallion : Colt is different from the rest.
On which river is Hirakud Dam built?
The question asks to identify the river on which the Hirakud Dam is constructed. This is a factual question related to Indian geography and major river valley projects.
Correct Option: C) Mahanadi
Which of the following is not one of Kepler's rules for planetary bodies?
A planet's orbit is an ellipse with the Sun at one of the two foci.
A line segment connecting a planet and the sun sweeps out equal areas during equal intervals of time.
The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
The orbital period depends on the mass of the planet
The question asks to identify which statement is NOT one of Kepler's laws of planetary motion. We need to recall each of Kepler's three laws and compare them with the given options.
Correct Option: D) The orbital period depends on the mass of the planet