What is the equation of a horizontal line passing through the point (3, 8)?
The equation of a horizontal line passing through a specific point can be easily determined. For a horizontal line, the y-coordinate remains constant regardless of the x-coordinate. In this case, we want a horizontal line that passes through the point (3, 8). Since the y-coordinate of the point is 8, the equation of the horizontal […]
Find the value of x in 400015x 25000, show your work
To solve for x in the equation 400015x = 25000, we need to isolate x. Here’s how you can do it: Start with the original equation: 400015x = 25000. To isolate x, divide both sides of the equation by 400015: x = 25000 / 400015. Now, let’s perform the division: Using a calculator, you will […]
How can we simplify the expression a²a³?
To simplify the expression a²a³, we can use the rule of exponents which states that when multiplying two terms with the same base, we can add their exponents together. In our case, the base is ‘a’. The exponents are 2 and 3. According to the rule: a² * a³ = a^(2+3) Now, simply add the […]
The sum of two positive numbers is 16. What is the smallest value of the sum of their squares?
To find the smallest value of the sum of the squares of two positive numbers whose sum is 16, let’s denote the two numbers as x and y. We know from the problem that: x + y = 16 We need to minimize the expression for the sum of their squares: S = x2 + […]
Suppose fx is a function such that if p q then fp fq; which statement best describes fx?
To understand the statement given regarding the function fx, we need to analyze the relationship defined by the condition ‘if p q then fp fq’. This can be broken down into logical components. Essentially, this implies that when certain conditions p and q are met, the function’s outputs for those conditions, fp and fq, will […]
If the sum of two numbers is 21 and their difference is 5, then find the numbers.
To find the two numbers, we can set up a system of equations based on the information given. Let the two numbers be x and y. We have the following equations: x + y = 21 (Equation 1: the sum of the numbers) x – y = 5 (Equation 2: the difference of the numbers) […]
If the tangent line to y = f(x) at (5, 4) passes through the point (0, 3), find f(5) and f'(5)
To solve this problem, we first need to understand the information provided about the tangent line. We know that the tangent line to the curve y = f(x) at the point (5, 4) can be expressed using the point-slope form of a line. 1. **Identifying the Point on the Tangent Line**: The point (5, 4) […]
What are the possible rational zeros of f(x) = 2x³ + 15x² + 9x + 22?
To find the possible rational zeros of the polynomial function f(x) = 2x³ + 15x² + 9x + 22, we can use the Rational Root Theorem. This theorem states that any rational solution, expressed as a fraction p/q, has p as a factor of the constant term and q as a factor of the leading […]
The volume of a fish tank is 50 cubic feet; if the density is 0.5 fish over feet cubed, how many fish are in the tank?
To determine how many fish can fit in the tank, you need to multiply the volume of the tank by the density of fish per cubic foot. Here’s how to calculate it: Volume of the tank: 50 cubic feet Density of fish: 0.5 fish per cubic foot Now, multiply the volume by the density: Number […]
What is the area under the standard normal distribution curve between z = 0 and z = 2.16?
To find the area under the standard normal distribution curve between z = 0 and z = 2.16, we can use the standard normal distribution table, also known as the Z-table. The Z-table gives us the area to the left of a given z-score. For z = 0, the area is 0.5000, as it is […]