Two poles of height 6m and 11m stands on a plane ground if the distance between their feet is 12m find the distance between their tops
To find the distance between the tops of the two poles, we can visualize this as a right triangle. The two poles create a vertical side of this triangle where the difference in their heights forms one side, and the horizontal distance between their feet serves as the other side. The heights of the poles […]
Identify Each Function as Linear, Quadratic, or Exponential: f(x) = 4x², g(x) = 1/x, and h(x) = 32x
To classify the functions f(x), g(x), and h(x), we need to analyze their forms. 1. f(x) = 4x²: This function is quadratic because it has the form of ax², where a is a constant (in this case, 4). Quadratic functions are characterized by the x raised to the power of 2, which means the graph […]
Which expressions are equivalent to 16x^4 + 64? Check all that apply.
To find expressions that are equivalent to 16×4 + 64, we need to factor the expression. The first step is recognizing that both terms have a common factor of 16: Factoring out 16 gives us: 16(x4 + 4) Next, we can observe that x4 + 4 is a sum of squares, which does not factor […]
What are the x-intercepts of the graph of the function f(x) = x² + 5x – 36?
To find the x-intercepts of the function f(x) = x² + 5x – 36, we need to set the function equal to zero and solve for x: f(x) = 0 x² + 5x – 36 = 0 This is a quadratic equation, and we can solve it using the quadratic formula, which is: x = […]
Which is the correct formula to find the distance between two points A(B) and C(D)?
The correct formula to find the distance between two points A(x1, y1) and B(x2, y2) in a 2D Cartesian coordinate system is: D = √((x2 – x1)² + (y2 – y1)²) Here’s how the formula works: Subtract the x-coordinates of the two points to find the horizontal distance: (x2 – x1). Subtract the y-coordinates to […]
Using Synthetic Division, What is the Quotient of 2x³ + 2x + 12 ÷ (x – 2)?
To find the quotient of the polynomial 2x³ + 2x + 12 divided by (x – 2) using synthetic division, we first set up our synthetic division process. 1. Identify the coefficients of the polynomial: For 2x³ + 0x² + 2x + 12, the coefficients are [2, 0, 2, 12]. 2. Since we are dividing […]
HCF of 2 Prime Numbers
The highest common factor (HCF), also known as the greatest common divisor (GCD), of two prime numbers is always 1. Prime numbers are defined as numbers greater than 1 that have no divisors other than 1 and themselves. For example, the numbers 2, 3, 5, 7, 11, and 13 are all prime. When you take […]
If f(x) = 4x² and g(x) = 6x, which expression is equivalent to g(f(3))?
To find the expression equivalent to g(f(3)), we need to evaluate it step by step. First, we calculate f(3): f(x) = 4x² Substituting x with 3: f(3) = 4(3)² = 4(9) = 36 Now that we have f(3) = 36, we will plug this result into g(x). Next, we calculate g(36): g(x) = 6x Substituting […]
Perform the requested operation: f(x) = (x – 5) / 8, g(x) = 8x + 5. Find g(f(x)).
To find g(f(x)), we first need to determine what f(x) evaluates to given our function definition. 1. Start by calculating f(x): f(x) = (x – 5) / 8. This means that for any value of x, f(x) gives us (x – 5) divided by 8. 2. Next, we plug f(x) into g(x): g(x) = 8x […]
What is the slope of the line that passes through (2, 7) and (4, 9)?
To determine the slope of the line passing through the points (2, 7) and (4, 9), we use the slope formula: Slope (m) = (y2 – y1) / (x2 – x1) Here, (x1, y1) = (2, 7) and (x2, y2) = (4, 9). Substituting these values into the formula: m = (9 – 7) / […]