What is the measure of the supplementary angle of an interior angle of a regular polygon?
The measure of the supplementary angle of an interior angle of a regular polygon can be determined by first understanding the formula for finding the measure of an interior angle. For a regular polygon, the formula for calculating the measure of an interior angle (A) is: A = [(n – 2) × 180°] / n […]
If m = x^2 + 3 and n = x + 5x + 9, which expression is equivalent to mn = x?
To find the expression equivalent to mn, we first need to simplify m and n based on the given equations. Starting with m: m = x2 + 3 Next, let’s simplify n: n = x + 5x + 9 = 6x + 9 Now, we can find the product mn: mn = (x2 + 3)(6x […]
If a translation of t2 7 x y is applied to dabc what are the coordinates of b?
In order to find the new coordinates of point B after the translation, we need to understand what the translation means. The translation t2 7 x y indicates that we will be shifting each point of the shape DABC by 7 units along the x-axis and along the y-axis. Let’s start by identifying the coordinates […]
How do you solve the equation 2x + 4 = 18?
To solve the equation 2x + 4 = 18, follow these steps: Subtract 4 from both sides: This helps to isolate the term with x. So we get: 2x + 4 – 4 = 18 – 4 This simplifies to: 2x = 14 Divide both sides by 2: Now, we can isolate x by dividing […]
How to Find the Median of an Even Set of Numbers
Finding the median of an even set of numbers is a straightforward process. The median is the middle value of a data set when it has been ordered from least to greatest. When dealing with an even number of observations, there isn’t a single middle value. Instead, you need to follow these steps: Organize the […]
Find a Positive Angle Less Than 2π That Is Coterminal with the Given Angle
To find a positive angle less than 2π that is coterminal with a given angle, we need to subtract or add multiples of 360° (for degrees) or 2π (for radians) until we land within the desired range. For 425 Degrees: 1. First, we subtract 360° from 425°: 425° – 360° = 65° 2. Since 65° […]
How to Calculate the Volume of a Prism with a Rhombus Base?
To find the volume of a prism, you can use the formula: Volume = Base Area × Height In this case, we have a prism with a height of 12 units and a rhombus as the base. To proceed, we first need to calculate the area of the rhombus. The area of a rhombus can […]
Find the equation of an ellipse that circumscribes another ellipse x² + 4y² = 4
To find the equation of an ellipse that circumscribes another ellipse, we need to start by identifying the parameters of the given ellipse. The equation of the ellipse given is: x² + 4y² = 4 This can be rewritten in standard form by dividing the entire equation by 4: \( \frac{x²}{4} + \frac{y²}{1} = 1 […]
Find the Length of the Curve: r(t) = cos(4t)i + sin(4t)j + 4ln(cos(t))k, where 0 ≤ t ≤ π/4
To find the length of the given curve, we first need to determine the parameterization of the curve and then use the arc length formula. The arc length L of a curve defined by a vector function r(t) from a to b is given by the formula: L = ∫_a^b ||r'(t)|| dt where r'(t) is […]
What is the greatest number which can be made using each of the digits 53147?
To find the greatest number that can be formed using the digits 5, 3, 1, 4, and 7, we need to arrange these digits in descending order. This means we start with the highest digit and work our way down to the lowest. The digits in descending order are: 7, 5, 4, 3, and 1. […]