What are the coordinates of the vertex for f(x) = 3x² + 6x + 3?
The vertex of a quadratic function in the form f(x) = ax² + bx + c can be found using the formula for the x-coordinate of the vertex, which is given by x = -b / (2a). In this case: a = 3 b = 6 c = 3 Plugging in the values: x = […]
What are the dimensions of a square lawn with a path of 4m wide covering an area of 78 square meters?
To find the dimensions of the square lawn, we start by letting the side length of the lawn be x meters. Since the path is 4 meters wide on three sides of the lawn, the effective side length of the area that includes both the lawn and the path can be described as: On one […]
How to Find the Missing Angle of a Right Triangle
To find the missing angle of a right triangle, you can use the knowledge that the sum of all angles in any triangle is 180 degrees. Since one of the angles in a right triangle is always 90 degrees, you can easily find the missing angle by subtracting the sum of the known angles from […]
Which of the following best defines 4 to the power of 2 over 3?
To understand what 4 to the power of 2 over 3 means, we first need to break it down into simpler parts. The expression can be written mathematically as 4^(2/3). This expression involves two operations: exponentiation and the concept of a root. The 2 in the exponent signifies that we will first square 4, and […]
Classify the Following Expression by Degree and Term: x²y, 7xy, xyz, x
To classify the expressions x²y, 7xy, xyz, and x by their degree and terms, we need to analyze each term individually. x²y: This term has two variables (x and y). The degree of this term is calculated by adding the exponents of its variables: 2 (from x²) + 1 (from y) = 3. So, this […]
What is the value of the discriminant for the quadratic equation 0 x 2 x2?
The discriminant of a quadratic equation is a value that helps to determine the nature of the roots of the equation. A quadratic equation is typically written in the form ax² + bx + c = 0, where a, b, and c are coefficients. In your question, the equation is not written in standard form, […]
What is the significance of a normal distribution with a mean of 50 and a standard deviation of 4?
A normal distribution with a mean of 50 and a standard deviation of 4 describes a symmetric, bell-shaped curve where most of the observations cluster around the mean. In this scenario, the mean (or average) value is 50, indicating the center of the distribution. The standard deviation of 4 indicates how much the values vary […]
What is the maximum error in estimating the radius of a sphere given a circumference of 84 cm?
To estimate the maximum error in the radius of a sphere when the circumference is measured, we can use differentials. The formula for the circumference (C) of a sphere is given by: C = 2πr where r is the radius of the sphere. We can rearrange this formula to solve for the radius: r = […]
Which function has real zeros at x = 3 and x = 7 and is cubic?
To find a cubic function that has real zeros at x = 3 and x = 7, we start by recognizing that a cubic function can have up to three real zeros. Since we only have two specified zeros, we can introduce a third zero, which can be any real number, including possibly being a […]
The regular hexagon has a radius of 4; what is the approximate area of the hexagon?
To find the area of a regular hexagon, we can use the formula: Area = (3√3 / 2) × r² where r is the radius of the hexagon. In this case, the radius is 4. Substituting the value of the radius into the formula, we get: Area = (3√3 / 2) × (4)² Calculating the […]