What values of a and b make the equation true √648 = √(2a + 3b)?
To solve the equation √648 = √(2a + 3b), we first need to simplify the left side. We can express 648 as a product of its prime factors: 648 = 2^3 * 3^4 This means: √648 = √(2^3 * 3^4) = √(2^2 * 3^4 * 2) = 2 * 3^2 * √2 = 18√2. So, […]
If tan x = 3 and cos x = 1/2, what is the value of sin x?
To find the value of sin x based on the given values of tan x and cos x, we can use the definition of tangent and the Pythagorean identity. First, recall that: tan x = sin x / cos x We are given: tan x = 3 and cos x = 1/2 Using the tangent […]
The point P(10, 2) is on the terminal side of an angle x. Find the exact values of each trigonometric function.
To find the exact values of each trigonometric function for the angle whose terminal side passes through the point P(10, 2), we first need to determine the radius (r) of the right triangle formed by this point and the origin (0, 0). The radius can be calculated using the Pythagorean theorem: r = √(x2 + […]
Find a Quadratic Model for the Set of Values 2, 20, 0, 4, 4, 20
To find a quadratic model for the given values: (2, 20), (0, 4), (4, 4), and (20), we will use the standard form of a quadratic equation, which is: y = ax² + bx + c Here, (x, y) represents the points we have. Our goal is to determine the coefficients a, b, and c. […]
Find the value of y in the formula y = 5a + 3b + c if a = 12, b = 4, and c = 8
To find the value of y in the formula y = 5a + 3b + c, we need to substitute the given values for a, b, and c into the equation. Given: a = 12 b = 4 c = 8 Now, let’s substitute these values into the formula: y = 5(12) + 3(4) + […]
The sum of 3 consecutive even numbers is 270. What is the first number in this sequence?
To find the first number in a sequence of three consecutive even numbers that sums up to 270, we can start by expressing the numbers mathematically. Let’s denote the first even number as x. Since we are looking for consecutive even numbers, the next two numbers can be represented as x + 2 and x […]
Find the area of a square park whose perimeter is 320 m
To find the area of a square park, we first need to determine the length of one side of the square using the given perimeter. The formula for the perimeter (P) of a square is: P = 4 × side Given that the perimeter is 320 meters, we can set up the equation: 320 = […]
What is the y-intercept of the graph of the function f(x) = x² + 3x + 5?
To find the y-intercept of a function, we need to evaluate the function at x = 0. This means we will substitute 0 for x in the equation f(x) = x² + 3x + 5. So, we calculate: f(0) = (0)² + 3(0) + 5 = 0 + 0 + 5 = 5. Thus, the […]
Choose the Correct Classification of 2×4 8×5 2×2 5
To classify the numbers 2×4, 8×5, 2×2, and 5 correctly, we need to evaluate each expression and understand its significance. First, let’s calculate the values of the expressions: 2×4 = 2 * 4 = 8 8×5 = 8 * 5 = 40 2×2 = 2 * 2 = 4 5 = 5 This gives us […]
Let gx be the reflection of fx = x² + 3 on the x-axis. What is the function rule for gx?
To find the function rule for gx, we need to understand what it means to reflect a function across the x-axis. The original function is given as f(x) = x² + 3. When we reflect a function over the x-axis, we negate the output values of the function. This means we will take f(x) and […]