Which of the following numbers is an example of an integer?
An integer is a whole number that can be positive, negative, or zero. Examples of integers include -3, 0, and 7. In contrast, numbers like 1.5, -2.3, and 3/4 are not integers because they are either fractions or decimals. To identify an integer, remember that it must not have any fractional or decimal parts. Therefore, […]
What are the sine, cosine, and tangent of 2π/3 radians?
To find the sine, cosine, and tangent of 2π/3 radians, we can start by identifying the angle in terms of the unit circle. The angle 2π/3 radians is equivalent to 120 degrees. This angle is located in the second quadrant of the unit circle. In the second quadrant: The sine value is positive. The cosine […]
Find a formula for the general term of the sequence 2, 6, 12, 20, 30
The given sequence is 2, 6, 12, 20, 30. To find a formula for the general term, let’s first look for a pattern in the sequence. If we examine the terms: 1st term: 2 2nd term: 6 3rd term: 12 4th term: 20 5th term: 30 Next, let’s look at the differences between consecutive terms: […]
What is 20 of 50?
To find 20 of 50, you need to determine what 20% of the number 50 is. To calculate this, you can use the formula: Percentage = (Part / Whole) × 100 In this case, we want to find out what 20% means in relation to 50. So we can rearrange the formula to find the […]
Solve x² + 14x + 24 by Completing the Square. What is the Solution Set of the Equation?
To solve the equation x² + 14x + 24 by completing the square, follow these steps: Start with the equation: x² + 14x + 24 = 0. Move the constant term to the other side: x² + 14x = -24. Next, to complete the square, take half of the coefficient of x (which is 14), […]
What is the completely factored form of xy³ x³y xyy xy x xyy xy x?
To factor the expression xy³ x³y xyy xy x xyy xy x, we can first rewrite it as: xy³ x³y xyy xy x xyy xy x Now, let’s combine all the terms: xy³ x³y = x² imes x imes y xyy = x imes y^2 xy = x imes y x xyy = x imes […]
What is the discriminant of the quadratic equation x² + 4x + 2 = 0?
The discriminant of a quadratic equation is a value that helps determine the nature of the roots of the equation. For the standard form of a quadratic equation, which is given by ax² + bx + c = 0, the discriminant (D) is calculated using the formula: D = b² – 4ac In the equation […]
If a is a rational number and b is an irrational number then the sum a + b is?
The sum of a rational number a and an irrational number b is always an irrational number. This can be understood through the properties of rational and irrational numbers. A rational number is defined as a number that can be expressed as the quotient of two integers, where the denominator is not zero. Examples include […]
What is the lowest common multiple of 12 and 9?
The lowest common multiple (LCM) of 12 and 9 is 36. To find the LCM, we can start by listing the multiples of each number: Multiples of 12: 12, 24, 36, 48, 60, … Multiples of 9: 9, 18, 27, 36, 45, … Now, we look for the smallest multiple that appears in both lists. […]
Is tan 2x sec 2x = 1 an identity?
To determine if the equation tan(2x) sec(2x) = 1 is an identity, we need to analyze both sides of the equation. First, let’s recall the definitions of the tangent and secant functions: tan(θ) = sin(θ) / cos(θ) sec(θ) = 1 / cos(θ) Applying these definitions to our equation: tan(2x) = sin(2x) / cos(2x> and sec(2x) […]