According to the number line, what is the distance between points A and B?
The distance between two points on a number line can be determined by taking the absolute value of the difference between their coordinates. If point A is located at coordinate a and point B is at coordinate b, the formula to find the distance d between them is: d = |a – b| For example, […]
What are all the common factors of 15, 45, and 90?
To find the common factors of the numbers 15, 45, and 90, we first need to determine the factors of each individual number. Factors of 15: The factors of 15 are 1, 3, 5, and 15. Factors of 45: The factors of 45 are 1, 3, 5, 9, 15, and 45. Factors of 90: The […]
What is the quotient of 6x^4 + 15x^3 + 10x^2 + 10x + 4 divided by 3x^2 + 2?
To find the quotient of the polynomial division of 6x^4 + 15x^3 + 10x^2 + 10x + 4 by 3x^2 + 2, we can use polynomial long division. 1. **Setup the division**: Write the dividend (the polynomial you are dividing) and the divisor (the polynomial you are dividing by). 2. **Divide the leading terms**: Divide […]
How to Solve the Inequality 2x + 3 < 7 + 62x?
To solve the inequality 2x + 3 < 7 + 62x, we need to isolate the variable x. Let’s break this down step by step. Start by simplifying both sides: On the left side, we have 2x + 3. On the right side, we have 7 + 62x. Next, we will get all the x […]
A man walks 10 miles in x hours. How far does he walk in one hour?
To determine how far the man walks in one hour, we need to find the rate of his walking speed. When he walks 10 miles in x hours, we can calculate his speed by dividing the total distance by the total time. The formula for speed is: Speed = Distance / Time In this case: […]
How to Find the Number of Units x That Produces the Minimum Average Cost per Unit c in the Equation c = 0.001x³ + 5x + 250?
To minimize the average cost per unit c, we first start with the given equation for total cost: c = 0.001×3 + 5x + 250 The average cost per unit (AC) is calculated by dividing the total cost by the number of units produced: AC = c/x = (0.001×3 + 5x + 250)/x = 0.001×2 […]
What is the value of x rounded to the nearest tenth if cos 24° is involved?
To find the value of x, we start by using the cosine function from trigonometry. The cosine function relates the adjacent side of a triangle to the hypotenuse. In this case, we know that: cos(24°) = adjacent / hypotenuse Assuming we’re looking for ‘x’ where adjacent represents the value we need, we can rearrange our […]
Which of the following exponential functions goes through the points (1, 6) and (2, 12)?
To determine which exponential function passes through the points (1, 6) and (2, 12), we start by using the general form of an exponential function, which is given by: f(x) = a * b^x Here, a is a constant, and b is the base of the exponential function. We know that: f(1) = 6, which […]
If HCF of Two Numbers is 1, What Could Be the Numbers?
If the highest common factor (HCF), also known as the greatest common divisor (GCD), of two numbers is 1, that means the numbers are coprime or relatively prime. This implies that they do not have any common factors other than 1. For example, the numbers 8 and 9 are coprime. The only factor they share […]
What is the y-intercept of the graph of the line given by the equation 3y + 4x = 15?
To find the y-intercept of the line represented by the equation 3y + 4x = 15, we need to determine the value of y when x is equal to 0. Here are the steps: Substitute x = 0 into the equation: 3y + 4(0) = 15 This simplifies to: 3y = 15 Now, divide both […]