An athlete completes one round of a circular track of diameter 200m in 40s. What will be the distance covered and the displacement at the end of 2min 20s?
To determine the distance covered and the displacement of the athlete, we need to analyze the situation step by step. The diameter of the circular track is given as 200 meters. First, we can find the circumference (which is the distance for one complete round) using the formula: Circumference = π × Diameter Substituting the […]
Find the correct description of the graph of the compound inequality x 9 or x 10
The graph of the compound inequality can be described by examining each part of the inequality separately. First, let’s break down the inequalities: x < 3: This part indicates that all values of x that are less than 3 will be included in the graph. x > 9: This part indicates that all values of […]
Which expression is used to calculate the present value of an amount of money?
The present value (PV) of an amount of money can be calculated using the formula: PV = FV / (1 + r)^n Where: PV = Present Value FV = Future Value (the amount of money in the future) r = Interest rate (as a decimal) n = Number of periods (years, months, etc.) This formula […]
What are the x and y intercepts of the graph of y = x² + 3x + 10?
To find the x and y intercepts of the graph represented by the equation y = x² + 3x + 10, we need to calculate each intercept separately. Y-Intercept The y-intercept occurs when the value of x is 0. We can find it by substituting x = 0 into the equation: y = (0)² + […]
Find the area enclosed by graphs of y = x and y = x³
To find the area enclosed by the graphs of y = x and y = x³, we first need to determine the points where the two curves intersect. This can be done by setting the equations equal to each other: x = x³ Rearranging this, we get: x³ – x = 0 Factoring out x, […]
Is the logarithmic function the inverse of an exponential function?
Yes, the logarithmic function is indeed the inverse of an exponential function. To understand this, let’s look at what each function does. An exponential function can be expressed in the form f(x) = a^x, where a is a positive constant and x is the exponent. This function grows rapidly as x increases. On the other […]
Use the Zero Product Property to Find the Solutions to the Equation x² – 12 – 7x
To solve the equation x² – 12 – 7x = 0 using the Zero Product Property, we first need to rearrange the equation into a standard quadratic form: x² – 7x – 12 = 0 Now, we can factor this quadratic expression. We want two numbers that multiply to -12 (the constant term) and add […]
According to the Rational Root Theorem, 7/8 is a potential rational root of which function?
The Rational Root Theorem states that any rational solution of a polynomial equation, in the form of p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient. So, if we consider 7/8 as a potential rational root, we need to find a polynomial function that […]
Without Graphing, is the System Independent, Dependent, or Inconsistent: 2x + y = 9 and 3x + 4y = 8?
To determine whether the system of equations is independent, dependent, or inconsistent, we can analyze the equations algebraically. The given equations are: 1) 2x + y = 9 2) 3x + 4y = 8 First, we can express both equations in terms of one variable, say y. From the first equation: y = 9 – […]
Find the Sample Space for Tossing 2 Coins and Find the Probability of Getting Exactly 1 Head
When tossing 2 coins, we first need to determine the sample space. The sample space is the set of all possible outcomes. For 2 coins, each coin has 2 possible outcomes: heads (H) or tails (T). The outcomes when tossing 2 coins can be listed as: HH (both heads) HT (first head, second tail) TH […]