What is the HCF and LCM of 18 and 45?
The highest common factor (HCF) of 18 and 45 is 9, while the least common multiple (LCM) is 90. Explanation: To find the HCF, we can list the factors of both numbers: Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 45: 1, 3, 5, 9, 15, 45 The common factors of 18 […]
What is the circumference of the circle below in terms of pi p?
The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle. If the radius of the circle is given as p, then we can substitute r with p in the formula: C = 2πp This means that the circumference of […]
The graph represents y = x + 1; what is f(275)?
To find f(275), we need to substitute 275 for x in the equation y = x + 1. This means we are calculating the value of y when x is 275. So, we plug in the value: f(275) = 275 + 1 = 276. Therefore, the value of f(275) is 276.
Find the Area of the Shaded Region Given in Fig
To find the area of the shaded region, we first need to identify the shapes involved in the figure. Let’s assume the shaded region is formed by a combination of shapes such as rectangles, circles, or triangles. Here’s a step-by-step approach to calculate the area: Identify the Total Area: Calculate the area of the entire […]
What is the volume of a block of ice measuring 3 meters long, 1.5 meters wide, and 2 meters high?
The volume of a block of ice can be calculated using the formula for the volume of a rectangular prism, which is: Volume = Length × Width × Height In this case, the dimensions of the ice block are: Length = 3 meters Width = 1.5 meters Height = 2 meters Now, substituting the values […]
What is the solution to the expression 4x² + 9x + 4?
To solve the quadratic expression 4x² + 9x + 4, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a In this expression, the coefficients are: a = 4 b = 9 c = 4 Now, let’s calculate the discriminant (b² – 4ac): b² = 9² […]
Which set represents the domain of the function shown 3 6 0 2 4 7 11 15?
The domain of a function consists of all the possible input values (often represented as ‘x’) that can be used in the function without causing any issues like division by zero or taking the square root of a negative number. In this case, the values provided are: 3, 6, 0, 2, 4, 7, 11, and […]
How do you factorise 2x² + 2x – 364?
To factorise the quadratic expression 2x² + 2x – 364, we start by simplifying it. The first step is to factor out the common factor, which is 2: 2(x² + x – 182) Next, we need to factor the trinomial x² + x – 182. To do this, we look for two numbers that multiply […]
Find an explicit solution of the given initial value problem: x² dy/dx + y = xy + 1/4
To solve the initial value problem given by the equation x² dy/dx + y = xy + 1/4, we start by rearranging it into a more manageable form. First, we can rewrite the differential equation as follows: x² dy/dx = xy + 1/4 – y This simplifies to: dy/dx = (xy + 1/4 – y)/x² […]
In a college of 300 students, every student reads 5 newspapers, and 60 students read every newspaper. What is the number of newspapers?
To find the number of newspapers in this scenario, we can use some logical deductions based on the information given. We know that: There are 300 students in total. Each student reads 5 newspapers. 60 students read every newspaper. Let’s denote the total number of newspapers as N. Since 60 students read every newspaper, we […]