Calculating the Percentage Change To find the percentage change when a value is increased from 40 to 56, you can follow these steps: First, determine the difference between the new value and the original value. In this case, you subtract the original value (40) from the new value (56): Difference = New Value – Original … Read more
To solve the quadratic equation x² + 14x + 24 = 0 by completing the square, we will follow these steps: Move the constant term to the other side: Start by rewriting the equation: x² + 14x = -24 Complete the square: To complete the square, we need to take the coefficient of x (which … Read more
To understand how many millions make up a billion, we first need to define the numbers clearly: A million is represented as 1,000,000 (one thousand thousand), while a billion is 1,000,000,000 (one thousand million). Now, if we break it down: 1 billion = 1,000 million Therefore, it takes a total of 1,000 millions to equal … Read more
The perimeter of a parallelogram can be calculated using the formula: Perimeter = 2 × (Length + Width) In the case of parallelogram WXYZ, to determine the perimeter, we need to identify the lengths of its sides. Let’s represent the length of side WX as ‘a’ and the length of side XY as ‘b’. Assuming … Read more
To find the angle between a diagonal of a cube and one of its edges, we can use some basic geometry principles. Let’s start by visualizing a cube. The diagonal we are referring to runs from one corner of the cube to the opposite corner, while one of the cube’s edges connects two adjacent corners. … Read more
To determine which binomial is a factor of the polynomial x³ – 4x² + x – 6, we can use the factor theorem or perform polynomial division. The polynomial can be factored by checking potential roots. Possible rational roots can be derived from the factors of the constant term (-6) divided by the leading coefficient … Read more
The equation of the line given is 3x + 9y = 4. To find the slope of this line, we need to rearrange the equation into the slope-intercept form, which is y = mx + b, where m represents the slope and b the y-intercept. Let’s isolate y in the equation: Start with the original … Read more
The proof that the square root of 2 is an irrational number is typically presented using a method known as proof by contradiction. This method highlights the absurdity of assuming that the square root of 2 can be expressed as a fraction of two integers. Let’s assume, for the sake of contradiction, that √2 is … Read more
To find the value of 13 raised to the power of 5, we can express it mathematically as 135. This means we multiply 13 by itself a total of 5 times: 13 x 13 = 169 169 x 13 = 2,197 2,197 x 13 = 28,561 28,561 x 13 = 371,293 Thus, 135 = 371,293. … Read more
To find the roots of the quadratic equation x² + 7x + 10 = 0, we can use the quadratic formula, factorization, or completing the square. Here, we’ll explore both factorization and the quadratic formula methods. Method 1: Factorization Step 1: Rewrite the equation in standard form: x² + 7x + 10 = 0 Step … Read more