A square has an area of 400 square miles. What is the length of each side of the square?
To find the length of each side of a square when you know the area, you can use the formula for the area of a square: Area = side × side In this case, we know the area of the square is 400 square miles. Let’s denote the length of each side as s. Therefore, […]
Evaluate the limit lim h → 0 of √(4h² + h)
To evaluate the limit lim h → 0 of √(4h² + h), we start by substituting h with 0 in the expression. When we do this, we have: √(4(0)² + (0)) = √(0) = 0 So, the limit is: 0 This limit tells us about the behavior of the function as h approaches 0. Essentially, […]
In the diagram, if SR is 42 and QR is 10, what is the perimeter of parallelogram PQRS?
The perimeter of a parallelogram can be calculated using the formula: Perimeter = 2 × (length + width). In parallelogram PQRS, we can identify the lengths of sides SR and QR. Given that SR measures 42 units (as it is opposite to PQ), and QR measures 10 units (as it is opposite to PS), we […]
How do you solve the following system 4x + 2y = 3 and 3x + y = 6?
To solve the system of equations 4x + 2y = 3 and 3x + y = 6, we can use the substitution or elimination method. Here, I’ll show you how to solve it using the elimination method. 1. First, arrange the equations: Equation 1: 4x + 2y = 3 Equation 2: 3x + y = […]
Find the length of the hypotenuse of a right triangle whose legs are 8 and 15 units in length
To find the length of the hypotenuse in a right triangle, we use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, the legs of the triangle are 8 units and 15 units. […]
Find an explicit rule for the nth term of the sequence 3, 12, 48, 192
The sequence 3, 12, 48, 192 appears to be increasing rapidly. To find an explicit rule for the nth term, we first look for a pattern in the ratios of consecutive terms. If we divide each term by its predecessor, we get: 12 ÷ 3 = 4 48 ÷ 12 = 4 192 ÷ 48 […]
Find the Slope of the Curve at the Indicated Point
To find the slope of a curve at a specific point, we need to determine the derivative of the function that describes the curve. The derivative gives us the slope of the tangent line to the curve at any given point. Follow these steps: Identify the function: Let’s denote the function as f(x). Differentiate the […]
If A and B are Independent Events with P(A) = 0.4 and P(B) = 0.6, What is P(A ∩ B)?
To find the probability of the intersection of two independent events A and B, we can use the formula: P(A ∩ B) = P(A) × P(B) Given that: P(A) = 0.4 P(B) = 0.6 Now, substituting the values into the formula: P(A ∩ B) = 0.4 × 0.6 = 0.24 Therefore, the probability of both […]
How do you simplify (x + 3)/9 divided by (x + 12)/6?
To simplify the expression (x + 3)/9 ÷ (x + 12)/6, we first need to understand that dividing by a fraction is the same as multiplying by its reciprocal. So, we can rewrite the expression: (x + 3)/9 × 6/(x + 12) Now, we’ll multiply the fractions: =(x + 3) × 6 / (9 × […]
What is the standard equation for a circle with center (10, 6) and radius 6?
The standard equation of a circle can be expressed as: (x – h)2 + (y – k)2 = r2 In this equation, (h, k) represents the coordinates of the center of the circle, and r is the radius. For a circle with center at (10, 6) and radius 6, we can substitute these values into […]