What is the slope of the line with the equation 2x + 3y – 6 = 0?
To find the slope of the line given by the equation 2x + 3y – 6 = 0, we need to rearrange the equation into slope-intercept form, which is y = mx + b, where m represents the slope. Starting with the original equation: 2x + 3y – 6 = 0 We can isolate y: […]
Evaluate a b² for a = 2 and b = 3
To evaluate the expression a b² where a = 2 and b = 3, we start by substituting the values into the expression. First, we need to calculate b²: b² = 3² = 3 * 3 = 9. Now, we have: a b² = 2 * 9 = 18. Thus, the final result for a […]
Solve the Following System of Equations: 2x + 4y + 3z = 7, 3x + y + 4z = 12, x + 3y + 4z = 4
To solve the given system of equations, we can use methods like substitution or elimination. Here, I will demonstrate the elimination method. The equations are: 1. 2x + 4y + 3z = 7 2. 3x + y + 4z = 12 3. x + 3y + 4z = 4 Let’s first manipulate the equations to […]
An investment of $1000 today invested at 10% for two years will give a future value of?
To calculate the future value of an investment, we can use the formula for compound interest, which is: Future Value (FV) = P (1 + r)^n Where: P = principal amount (initial investment) r = annual interest rate (in decimal) n = number of years the money is invested or borrowed In this case, we […]
The diagonal of a square is x units. What is the area of the square in terms of x?
To find the area of a square in terms of its diagonal, we can use the relationship between the side length of the square and its diagonal. Let’s denote the side length of the square as s. According to the properties of squares and right triangles, the diagonal d (which is given as x) can […]
How much money is due to the vendor per day for milk supplied to the hotel?
To calculate the amount due to the vendor per day, we first need to determine the total amount of milk supplied by the vendor in a day. In the morning, the vendor supplies 32 liters of milk, and in the evening, he supplies 68 liters. So, the total milk supplied in a day is: 32 […]
Find the perimeter of an isosceles right angled triangle having an area of 5000 metre square
To find the perimeter of an isosceles right angled triangle given its area, we start with the known properties of such triangles. The area (A) of an isosceles right angled triangle can be calculated using the formula: A = (1/2) * base * height In an isosceles right angled triangle, the base and height are […]
In how many different ways can a true false test consisting of 9 questions be answered?
To determine how many different ways a true-false test consisting of 9 questions can be answered, we can approach this by recognizing that each question has 2 possible answers: true or false. For each of the 9 questions, since there are 2 independent choices (true or false), we can calculate the total number of ways […]
Given sin x = 35 and x is in quadrant 3, what is the value of tan x²?
To find the value of tan x² given that sin x = 35 and x is in the third quadrant, we first need to correct the value of sin x. Since the sine function can only have values between -1 and 1, it’s likely there was a mistake in the value provided. Assuming a more […]
How to Find the Least Common Multiple of Two Numbers
Finding the least common multiple (LCM) of two numbers is a straightforward process, and it can be done using a couple of different methods. Here, we’ll explain the step-by-step process using the prime factorization method and the relationship between the LCM and the greatest common divisor (GCD). Method 1: Prime Factorization Factor Each Number: Begin […]