How many months have 31 days?
There are seven months that have 31 days: January, March, May, July, August, October, and December. This pattern can be remembered using the rhyme: ‘Thirty days hath September, April, June, and November; all the rest have thirty-one, except for February alone, which has twenty-eight days clear, and twenty-nine in each leap year.’ This means that […]
How to Find the Area of a Regular Hexagon with Side Length 10
To find the area of a regular hexagon, you can use the formula: Area = (3√3/2) × side² In this case, the side length is given as 10. Plugging this value into the formula to calculate the area, we get: Area = (3√3/2) × 10² Area = (3√3/2) × 100 Area = 150√3 Now, if […]
Which of the following is the conjugate of 10 + 3i?
The conjugate of a complex number is formed by changing the sign of its imaginary part. For the complex number 10 + 3i, the conjugate is 10 – 3i. This means we keep the real part the same (which is 10) and change the sign of the imaginary part (from +3i to -3i).
A polygon has an angle sum of 360 and each angle measures 90. What is the polygon?
The polygon you are describing is a quadrilateral, specifically a square or a rectangle. In geometry, the sum of the interior angles of a polygon can be calculated using the formula: Angle Sum = (n – 2) × 180 where n is the number of sides. For a polygon with an angle sum of 360 […]
What is the sum of the angles in a rhombus?
The sum of the angles in a rhombus is 360 degrees. A rhombus is a type of quadrilateral, which means it has four sides. In any quadrilateral, the sum of all interior angles is always 360 degrees. This rule applies to all four-sided shapes, whether they are squares, rectangles, trapezoids, or rhombuses. In the case […]
How Do You Graph the Inequality 6x + 3y ≤ 12?
To graph the inequality 6x + 3y ≤ 12, you will first need to convert the inequality into an equation to find its boundary line. This means you will set 6x + 3y = 12. 1. **Find the intercepts**: – To find the x-intercept, set y = 0: 6x + 3(0) = 12 → 6x […]
What is the prime factorization of 30?
The prime factorization of 30 is 2 × 3 × 5. To find the prime factorization, we start by dividing 30 by the smallest prime number, which is 2. This gives us: 30 ÷ 2 = 15 Next, we take the result, 15, and check if it can be divided by any prime number. The […]
The polygons are similar but not necessarily drawn to scale. Find the value of x.
To find the value of x in the larger polygon, we can use the property of similar polygons that states that the ratios of corresponding sides are equal. The side lengths of the larger polygon are x, 3, 8, and 16. The side lengths of the smaller polygon are 25, 2, 4. Since the polygons […]
How do you write an equation in slope-intercept form of the line through the point (6, 1) with slope m = 4?
To find the equation of a line in slope-intercept form, we can use the formula: y = mx + b where m represents the slope of the line and b is the y-intercept. In this case, the slope m is given as 4, and we have a point on the line, which is (6, 1). […]
The rectangles in the figure below are similar; find the value of x
To find the value of x in similar rectangles, we can use the concept that the ratios of corresponding sides of similar figures are equal. Assuming we have two rectangles where the ratio of their lengths and widths can be represented as follows: For the first rectangle: width = a, length = b For the […]