What is the sum of the polynomials 7x³ and 2x³ and 4x² and 4x²?
To find the sum of the polynomials 7x³, 2x³, 4x², and 4x², we need to combine like terms. First, let’s identify the like terms in the given polynomials: 7x³ and 2x³ are like terms because they both contain the variable x raised to the same power (³). 4x² and 4x² are also like terms as […]
What is the formula for finding exterior and interior angles of a polygon?
The formula for finding the sum of the interior angles of a polygon is given by the equation: Sum of Interior Angles = (n – 2) × 180° Here, n represents the number of sides of the polygon. For example, in a triangle (which has 3 sides), the sum of the interior angles would be […]
How to Turn an Improper Fraction into a Proper Fraction
An improper fraction has a numerator that is greater than or equal to its denominator. To convert it into a proper fraction, which has a numerator less than its denominator, you can follow these steps: Divide the numerator by the denominator. This will give you a whole number. The remainder from this division will become […]
What is 175 as a mixed number?
To express 175 as a mixed number, we first need to understand what a mixed number is. A mixed number consists of a whole number and a proper fraction. In this case, the number 175 is an integer without any fractional part. Since 175 is a whole number, it can simply be written as a […]
How do you factorise the quadratic expression x² + 2x + 8?
To factorise the quadratic expression x² + 2x + 8, we first look for two numbers that multiply to the constant term (8) and add up to the coefficient of the linear term (2). Unfortunately, there are no two real numbers that satisfy these conditions. When we try to find two numbers that multiply to […]
What If There Is No Mode in a Set of Numbers?
The mode is the number that appears most frequently in a set. When a set of numbers does not have a mode, it means either all the numbers occur with the same frequency, or each number occurs only once. This situation can arise in various datasets. For instance, consider the set of numbers {1, 2, […]
What constant can be added to x² + 6x to form a perfect square trinomial?
To form a perfect square trinomial from the expression x² + 6x, we need to determine the constant that completes the square. First, let’s recall the formula for a perfect square trinomial, which is (a + b)² = a² + 2ab + b². In our case, ‘a’ corresponds to x and ‘2b’ is equivalent to […]
What are the zeroes of f(x) = x^2 – 2x + 3?
To find the zeroes of the function f(x) = x^2 – 2x + 3, we need to solve the equation f(x) = 0. This means we set the equation equal to zero: x^2 – 2x + 3 = 0 Next, we can use the quadratic formula to find the roots of this quadratic equation, which […]
What is 30% of 10?
To find 30% of 10, we use the formula for calculating percentages. First, we convert the percentage to a decimal by dividing it by 100. So, 30% becomes 0.30. Next, we multiply this decimal by the number we want to find the percentage of, which is 10 in this case. The calculation looks like this: […]
How to Multiply Square Roots
Multiplying square roots involves a straightforward process that simplifies the operation significantly. To multiply square roots, you can use the property of square roots that states: √a × √b = √(a × b). This means that you can first multiply the values inside the square roots and then take the square root of the result. […]