Using the graph of f(x) = log2(x), approximate the value of y in the equation 2^(2y) = 5
To approximate the value of y in the equation 2^(2y) = 5 using the graph of f(x) = log2(x), we first need to isolate y. Start by rewriting the equation: Taking the logarithm base 2 of both sides gives us: 2y = log2(5) Next, we can solve for y: y = (1/2) * log2(5) Now, […]
Find the values of the 30th and 90th percentiles of the data 129, 113, 200, 100, 105, 132, 100, 176, 146, 152
To find the 30th and 90th percentiles of the given data set, we first need to organize the data in ascending order: Sorted Data: 100, 100, 105, 113, 129, 132, 146, 152, 176, 200 Next, we can use the formula for finding the percentile: P = (n + 1) * (percentile / 100) where n […]
What is a term in a polynomial?
A term in a polynomial is a single mathematical expression that can be a constant, a variable, or a combination of both multiplied by coefficients. Terms are separated by addition (+) or subtraction (–) operators. For instance, in the polynomial 3x² + 5x – 2, there are three terms: 3x², 5x, and -2. Each term […]
Which of the following is a subset of 1, 3, 5, 7, 9, 135, 27, 3?
To determine which of the options is a subset of the given set {1, 3, 5, 7, 9, 135, 27}, we need to understand what a subset is. A subset is a set where all its elements are also contained in another set. For example, if we consider the set {1, 3, 5}, every element […]
If c is a zero of even multiplicity for a function f, how does the graph of f behave at c?
If c is a zero of even multiplicity for the function f, the graph of f touches the x-axis at c but does not cross it. This behavior arises because a zero of even multiplicity means that the function has a factor of the form (x – c)n where n is an even number. Consequently, […]
How do you find an equation of the line having the given slope and containing the given point m = 8, y = 4, x = 5?
To find the equation of a line given the slope (m) and a point on the line (x, y), you can use the point-slope form of a linear equation, which is: y – y1 = m(x – x1), where (x1, y1) is the given point and m is the slope. In your case, the slope […]
Find a Cartesian Equation for the Curve and Identify it: r = 7 cos(8θ)
To convert the polar equation r = 7 cos(8θ) into a Cartesian equation, we start by using the relationships between polar and Cartesian coordinates. The standard transformations are: x = r cos(θ) y = r sin(θ) r² = x² + y² From the given equation, we can multiply both sides by r (noting that this […]
Identify the vertex for the graph of y = 3x² + 12x + 5
To find the vertex of the quadratic function given by the equation y = 3x² + 12x + 5, we can use the vertex formula. The vertex of a parabola in the form y = ax² + bx + c is found using the formula: x = -b / (2a) In this equation, a = […]
What is the simplified form of 3 over 2x minus 5 21 over 8 x squared minus 14x minus 15?
To simplify the expression 3/(2x) – 5(21/(8x² – 14x – 15)), we will start by factoring the quadratic expression in the denominator. The expression 8x² – 14x – 15 can be factored. We need two numbers that multiply to 8 imes -15 = -120 and add to -14. These numbers are -20 and 6. We […]
The Sum of Two Numbers is 18 and Their Difference is 4. Find the Numbers.
To find the two numbers, we can set up a system of equations based on the information given in the question. Let’s denote the two numbers as x and y. According to the problem: The sum of the two numbers: x + y = 18 The difference of the two numbers: x – y = […]