The graph of the linear inequality y < 7x + 4 represents a region in the two-dimensional Cartesian coordinate system. To understand this graph, we start by analyzing the corresponding linear equation, which is y = 7x + 4. 1. **Graphing the Boundary Line:**First, we plot the boundary line of the equation y = 7x ... Read more
To find the value of ‘a’ in the equation a² + 3a – 8 = 0, we can use the quadratic formula: a = rac{{-b ightarrow ext{±} ext{sqrt}{{b^2 – 4ac}}}}{2a} In our equation, we identify the coefficients: a = 1 (the coefficient of a²) b = 3 (the coefficient of a) c = -8 (the … Read more
The equation we need to analyze is: 3x + 6 = 1 + 3 + 4x First, let’s simplify the right side of the equation. Combining the constants gives us: 3x + 6 = 4 + 4x Next, we want to get all the terms involving x on one side of the equation. To do … Read more
The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both. To find the LCM of 7.56 and 5, we can follow these steps: Step 1: Convert to Whole Numbers First, it’s often easier to work with whole numbers. We can convert 7.56 to a whole number by … Read more
To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula can be expressed as: c² = a² + b². In this … Read more
If you invest $1000 today at an interest rate of 6% per annum, you can calculate the future value of that investment after one year using the formula: Future Value = Principal Amount x (1 + Interest Rate) In this case, the principal amount is $1000 and the interest rate is 0.06 (which is 6% … Read more
If the discriminant of a quadratic equation is negative, it indicates that the equation has no real solutions. In the context of a standard quadratic equation of the form ax2 + bx + c = 0, the discriminant is calculated using the formula D = b2 – 4ac. When the discriminant (D) is negative (D … Read more
To solve the compound inequality 6b < 24 or 4b < 12 + 4, we need to solve each part separately. Step 1: Solve the first inequality For the first part: 6b < 24. To isolate b, divide both sides by 6: 6b < 24 b < 4 This means b can be any number … Read more
Finding the Length of Line Segment AC in Triangle ABC To determine the length of line segment AC in triangle ABC, we want to consider the properties of triangles and the numerical values provided: 7, 9, 14, and 18. First, it’s important to visualize the triangle. Typically, the lengths of the sides must abide by … Read more
To find the value of side b in a scalene triangle with a given perimeter, we can use the definition of perimeter. The perimeter of a triangle is the sum of the lengths of all its sides. In this case, we know the perimeter is 546 cm, and we have the lengths of sides a … Read more