Which statement best describes how to determine whether f(x) = 9 – 4x² is an odd function?
To determine if the function f(x) = 9 – 4x² is an odd function, we can use the definition of odd functions. A function f is considered odd if for every x in the domain of f, the following condition holds: f(-x) = -f(x). To check this for our function, we first find f(-x): f(-x) […]
Find the remainder when f(x) = 4x³ + 20x + 50 is divided by x³
To find the remainder of a polynomial when divided by another polynomial, we can use the Remainder Theorem. For our polynomial f(x) = 4x³ + 20x + 50, we want to divide it by x³. When we divide a polynomial of degree n by a polynomial of degree m, if m < n, the remainder […]
What are the first three terms of a geometric sequence when a = 4 and r = 5?
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio. In this case, the first term (a) is 4 and the common ratio (r) is 5. The first three terms can be calculated as follows: First term: […]
What is the remainder when 3x^4 + 2x^3 + x^2 + 2x + 24 is divided by 2?
To find the remainder when the polynomial 3×4 + 2×3 + x2 + 2x + 24 is divided by 2, we can evaluate the polynomial at specific values that represent congruence classes modulo 2. First, we look at the coefficients of the polynomial: The coefficient of x4 is 3, which is congruent to 1 modulo […]
What is the sum of 3, 1421, 0, 241, 0, and 09 with correct precision?
To find the sum of the numbers 3, 1421, 0, 241, 0, and 09, we first need to add them together: 3 + 1421 + 0 + 241 + 0 + 9 = 3 + 1421 + 0 + 241 + 0 + 9 Now, performing the addition step-by-step: 3 + 1421 = 1424 1424 […]
What was the original price of the dress Kate bought for $27 with a 10% discount?
To find the original price of the dress, we can use the formula for calculating the sale price based on the original price and the discount percentage. Let X be the original price of the dress. Since the dress was on sale for 10% off, Kate paid 90% of the original price. We can express […]
What is the slope of the line that contains the points (1, 1) and (2, 8)?
To find the slope of the line that connects the points (1, 1) and (2, 8), we can use the formula for slope, which is: slope (m) = (y2 – y1) / (x2 – x1) Here, (x1, y1) = (1, 1) and (x2, y2) = (2, 8). Now, substituting the values into the formula: 1. […]
What is the equation of a vertical line passing through the point (3, 5)?
A vertical line has a constant x-value for all points on the line. To find the equation of a vertical line that passes through the point (3, 5), we simply take the x-coordinate of the point. In this case, the x-coordinate is 3. Therefore, the equation of the vertical line can be expressed as: x […]
Evaluate sin(p/4) cos(p/6) sin(p/6) cos(p/4)
To evaluate the expression sin(p/4) cos(p/6) sin(p/6) cos(p/4), we can start by using known values for the sine and cosine functions at these angles. Firstly, we know: sin(p/4) = sqrt(2)/2 cos(p/4) = sqrt(2)/2 sin(p/6) = 1/2 cos(p/6) = sqrt(3)/2 Now, substituting these values into the expression: sin(p/4) cos(p/6) sin(p/6) cos(p/4) = (sqrt(2)/2) * (sqrt(3)/2) * […]
For what value of x is sin x cos 19 where 0 < x < 90?
To solve the equation sin x = cos 19, we can use the identity that relates sine and cosine: sin x = cos (90 – x). This means we can set up the equation: cos (90 – x) = cos 19 From the properties of cosine, we know that if cos A = cos B, […]