What Should Judy Do to Tackle a Multiple Choice Test Without Studying?
Judy finds herself in a tough spot, facing a multiple choice test with 12 questions, each offering 5 possible answers, but only one correct answer. Since she forgot to study, she’ll need to rely on some strategies to maximize her chances of selecting the right answers. Firstly, Judy should read each question carefully. Sometimes, questions […]
What is the first step in solving the quadratic equation 5x² + 8 = 133?
To solve the quadratic equation 5x² + 8 = 133, the first step is to isolate the term with x. This is done by subtracting 8 from both sides of the equation. When we subtract 8 from each side, we are moving the constant term to the other side, making it easier to work with […]
A triangle has side lengths of 20 cm, 99 cm, and 108 cm. Classify it as acute, obtuse, or right.
To classify the triangle based on its side lengths, we can use the triangle inequality theorem and properties of triangles. In this case, the sides are 20 cm, 99 cm, and 108 cm. First, let’s check if these sides can form a triangle using the triangle inequality theorem, which states that the sum of the […]
At noon ship A is 100 km west of ship B. Ship A is sailing east at 35 km/hr and ship B is sailing north at 25 km/hr. Where will the ships be after 2 hours?
To find the positions of the ships after 2 hours, we will calculate their individual movements based on their speeds and directions. Position of Ship A: Ship A is initially 100 km west of Ship B. Since Ship A is sailing east at 35 km/hr, in 2 hours it will cover: Distance covered by Ship […]
The difference of x and a number is 6. What is the other number?
To find the other number, we start with the equation describing the relationship given in the question. If we let that unknown number be represented by ‘y’, the relationship can be written as: x – y = 6 From this equation, we can express ‘y’ in terms of ‘x’: y = x – 6 This […]
How do I find a vector that has the same direction as (4, 6, 4) but with a length of 6?
To find a vector that points in the same direction as the vector (4, 6, 4) but has a length of 6, you can follow these steps: Calculate the length (magnitude) of the original vector: The magnitude of a vector (x, y, z) is given by the formula: Magnitude = √(x² + y² + z²) […]
How fast must the train travel the next 100km so that the average speed is 70km/h for the whole journey?
To find out how fast the train must travel for the next 100 km to achieve an average speed of 70 km/h for the entire journey, we first need to understand how average speed is calculated. The average speed is given by the formula: Average Speed = Total Distance / Total Time Let’s assume the […]
How to Find f(g(x)) for Given Functions f(x) and g(x)?
To find f(g(x)), we need to start by identifying the functions f(x) and g(x) based on the given information: f(x) = 4x + 6 g(x) = 5x^2 Now, let’s break down the steps to perform the operations: Step 1: Substitute g(x) into f(x). This means we will replace every instance of x in f(x) with […]
Is the Lateral Surface Area of Cone A Exactly Equal to the Lateral Surface Area of Cylinder B?
This statement is false. To understand why, let’s break down the formulas for the lateral surface areas of both shapes. The lateral surface area of a cone is given by the formula: Acone = πrl where r is the radius of the base of the cone and l is the slant height. On the other […]
What is the equation of a circle with center at (4, 9) and diameter of 10 units?
The equation of a circle is generally given by the formula: (x – h)² + (y – k)² = r², where (h, k) is the center of the circle and r is the radius. In this case, the center of the circle is at the point (4, 9). The diameter of the circle is 10 […]