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
Understanding Angles and Linear Pairs In geometry, a linear pair refers to a pair of adjacent angles whose sum is exactly 180 degrees. This occurs when two angles are next to each other and share a common arm (line). When Considering Three Angles Now, when we introduce three angles that sum up to 180 degrees, … Read more
In an isosceles triangle, two sides are of equal length, and the angles opposite those sides (the base angles) are also equal. The vertex angle is the angle formed by the two equal sides. To find the measure of the base angles when the vertex angle is given, we can use the properties of triangles. … Read more
Understanding the Probability of Rolling Two Dice to Get a Sum of 7 When rolling two six-sided dice, there are a total of 36 possible outcomes. This is because each die has 6 faces, and the outcomes can be combined. To calculate the probability of obtaining a specific sum, such as 7, we need to … Read more
Determining the X and Y Intercepts To find the x and y intercepts of the equation x = 4y + 8, we need to follow these steps: Finding the Y-Intercept The y-intercept occurs when x = 0. We substitute x = 0 into the equation: 0 = 4y + 8 Now, rearranging the equation gives … Read more
To find the sum of the numbers 1, 9, 2, 3, and 5, 18, we first need to clarify the format of the numbers for accurate addition. Assuming you meant to add the digits from two groups: (1 + 9 + 2 + 3) and (5 + 18). Let’s break it down step by step: … Read more