devyy To determine the length of side QR in triangle PQR, we first need to establish some basic rules about triangles. Given that in any triangle, the sum of the lengths of any two sides must always be greater than the length of the third side, we can utilize this principle to analyze the options available. … Read more
To solve the quadratic equation x2 + 10x + 24 = 0 by completing the square, follow these steps: Move the constant to the other side: Start by subtracting 24 from both sides of the equation: x2 + 10x = -24 Complete the square: To do this, take the coefficient of x (which is 10), … Read more
To solve the equation 8 + 2x + 8x = 14, we will follow a series of steps to isolate the variable x. Combine like terms: In the equation, we have 2x and 8x, which can be combined. 2x + 8x = 10x Now, rewrite the equation with the combined terms: 8 + 10x = … Read more
To convert the speed of a bird from miles per minute to miles per hour, we need to understand the relationship between minutes and hours right away. There are 60 minutes in an hour. If a bird flies 23 miles in one minute, to find out how far it flies in one hour, we can … Read more
One cubic centimeter (cm³ or cc) is a unit of volume that is defined as the volume of a cube with edges that are each one centimeter long. This means that if you were to visualize a small cube where every side measures exactly 1 cm, the space it occupies inside that cube represents one … Read more
To find the value of sin 75°, we can use the angle addition formula for sine. The angle 75° can be expressed as the sum of two angles that are easier to work with: 45° and 30°. Thus, we can write: sin 75° = sin(45° + 30°) Using the angle addition formula, which states that: … Read more
To transform the quadratic expression x² + 2x into a perfect square trinomial, we need to complete the square. A perfect square trinomial is of the form (a + b)², which expands to a² + 2ab + b². Looking at x² + 2x, we can identify: a = x (since it is the coefficient of … Read more
To find out what percentage of the cinema seats are filled when there are 98 people present, you can use the following formula: Percentage filled = (Number of people in the cinema / Total number of seats) × 100 In this case, the total number of seats in the cinema is 280, and the number … Read more
Solving the Equation To solve the equation x³ + 2x² + 0 = 0, we start by substituting u = x². This simplifies the equation significantly. Step 1: Rewrite in Terms of u Substituting u into the equation, we get: u² + 2u + 0 = 0 Step 2: Factor the Equation Next, we need … Read more
A function expressed in the form f(x) = mx + b is known as a linear function. In this equation: f(x) represents the output of the function, x is the input variable, m is the slope of the line, which indicates how steep the line is, and b is the y-intercept, which is the point … Read more