devyy 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
To calculate the probability of rolling two fair six-sided dice and getting the same number on both, we start by identifying the total possible outcomes and the favorable outcomes. When rolling two dice, each die can land on one of 6 faces (numbered from 1 to 6). Therefore, the total number of possible outcomes when … Read more
To solve the equation 2×2 + 7x + 9 = 0, I would choose the quadratic formula method. The quadratic formula states that for any quadratic equation of the form ax2 + bx + c = 0, the solutions for x can be found using: x = (-b ± √(b2 – 4ac)) / 2a In … Read more
To express the fractions 34/716 and 5/8 with a common denominator, we first need to determine the least common denominator (LCD) of the two fractions. Step 1: Simplifying 34/716 First, we need to simplify 34/716. We can find the greatest common divisor (GCD) of 34 and 716. 34 can be factored into 2 and 17, … Read more
The metric system, a decimal-based system of measurement, uses prefixes to convey various magnitudes of a unit. These prefixes enhance clarity and precision, making it easier to express both very large and very small quantities. For instance, consider the meter, the base unit for length. When we talk about distances, we might use prefixed units … Read more