How to Properly Insert Commas and Name Numbers in the Indian Numbering System?
To insert commas suitably in the numbers provided, we need to follow the Indian system of numeration, which uses lakh (100,000) and crore (10,000,000) as its basic units. Here’s how the numbers should be formatted: a) 87595762: This number is written as 8,75,95,762, which translates to 8 crores, 75 lakhs, 95 thousand, and 762. b) […]
Using the Completing the Square Method to Rewrite f(x) = x² – 6x + 2 in Vertex Form
To rewrite the quadratic function f(x) = x² – 6x + 2 in vertex form, we will use the completing the square method. First, we’ll focus on the x² and -6x part of the equation: x² – 6x Next, we need to complete the square. To do this, take half of the coefficient of x […]
What is the value of 3 + 3i + 2 + 3i?
To find the value of the expression 3 + 3i + 2 + 3i, we need to combine like terms. First, group the real parts and the imaginary parts separately: Real part: 3 + 2 Imaginary part: 3i + 3i Now, calculate each part: Real part: 3 + 2 = 5 Imaginary part: 3i + […]
If x² – 6x + 8 = 0, then x = 4 or x = 2: True or False?
This statement is True. To verify, we can factor the quadratic equation x² – 6x + 8. We are looking for two numbers that multiply to 8 (the constant term) and add up to -6 (the coefficient of x). The numbers -2 and -4 work because: -2 * -4 = 8 -2 + -4 = […]
What Are the X-Intercepts of y = 2x² + 3x – 20?
To find the x-intercepts of the quadratic equation y = 2x² + 3x – 20, we need to set y to 0 and solve for x. This means we are looking for the points where the graph of the equation crosses the x-axis. So, we start with the equation: 0 = 2x² + 3x – […]
What are the x and y intercepts of the graph of y = x² + 7x + 12?
To find the x and y intercepts of the graph of the equation y = x² + 7x + 12, we need to follow a few steps. Finding the x-intercepts The x-intercepts occur where the graph crosses the x-axis, which means at these points, y = 0. So, we set the equation to zero: 0 […]
What percent of 224 is 28?
To find out what percentage 28 is of 224, we can use the formula: Percentage = (Part / Whole) x 100 In this case, the ‘Part’ is 28 and the ‘Whole’ is 224. Plugging these values into the formula: Percentage = (28 / 224) x 100 Now, we perform the division: 28 / 224 = […]
What is the exact real value of arcsin(√3/2)?
The exact real value of arcsin(√3/2) is π/3 radians or 60°. To understand why this is the case, let’s recall that the arcsin function, also known as the inverse sine function, is defined as the angle whose sine is a given number. In this scenario, we are looking for an angle whose sine value equals […]
What is the degree of the polynomial 4xy + 11y + 3?
The degree of a polynomial is determined by the highest sum of the exponents of the variables in each term of the polynomial. In the case of our polynomial 4xy + 11y + 3, we can break down each term: For the term 4xy, the exponents are: For x: 1 For y: 1 The sum […]
If A is B and B is C, then what can we say about A and C?
In logical terms, this question is exploring the concept of transitive relations. If we state that ‘A is B’ and ‘B is C’, we can infer that ‘A must also be C’ under certain conditions. This reasoning follows the basic principles of deductive logic. To put it simply, if A is identical to B, and […]