devyy

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

To completely factor the expression 3x² + 21 + 3x² + 7 + 3x + 7x + 7 + 3x + 7x + 3, we first combine like terms and reorganize the expression. 1. **Combine Like Terms:** First, let’s combine all the x² terms: We have 3x² + 3x² = 6x². Next, we combine the … Read more

To find the three numbers in arithmetic progression (AP) whose sum is 18, we start by denoting the three numbers as: Let the three numbers be a – d, a, and a + d, where a is the middle term, and d is the common difference. The sum of these three numbers can be expressed … Read more

To solve the equation x + 72 = 36, we need to isolate the variable x. We can do this by performing some basic arithmetic operations. First, we will subtract 72 from both sides of the equation: x + 72 – 72 = 36 – 72 This simplifies to: x = 36 – 72 Now, … Read more

Finding the value of n To solve the equation 2x9yn + 4x2y10 = 8x11y20, we need to simplify and compare the coefficients of both sides of the equation. Step 1: Simplify the equation Firstly, notice that both terms on the left can be factored. Let’s factor out the common term from the left side: 2x9yn … Read more