How can I write 9 as a fraction with 7 in the denominator?
To express the number 9 as a fraction with 7 in the denominator, you can represent 9 as a fraction by placing it over 1, giving you 9/1. From there, you want to create a fraction that has 7 as its denominator. To do this, you can multiply both the numerator and denominator of 9/1 […]
The side length of an equilateral triangle is 6 cm. What is the height of the triangle?
To find the height of an equilateral triangle, we can use the Pythagorean theorem. In an equilateral triangle, the height splits the triangle into two right-angled triangles. Each of these right triangles has: A hypotenuse equal to the side length of the triangle (6 cm). One leg that is half of the base (which is […]
Which of the following is a factor of 500x^3 108y^{18} 6 5x^3y^6 25x^2 15xy^6 9y^2?
To determine which of the options is a factor of the expression 500×3 108y18 6 5x3y6 25×2 15xy6 9y2, we need to factor the coefficients and variables carefully. First, let’s analyze the coefficients: 500 can be factored into 22 × 53. 108 can be factored into 22 × 33. 6 can be factored into 2 […]
Find the sum of 7a³ + 14a + 12 and 6a³ + 12a² + 7
To find the sum of the two expressions, we need to combine like terms. The expressions given are: 7a³ + 14a + 12 6a³ + 12a² + 7 Now, let’s add them together: (7a³ + 14a + 12) + (6a³ + 12a² + 7) Next, we identify and combine like terms: For the a³ terms: […]
If f(x) = 3x and g(x) = 13x, which expression could be used to verify that g(x) is the inverse of f(x)?
To verify that g(x) is the inverse of f(x), we need to show that f(g(x)) = x and g(f(x)) = x. First, let’s calculate f(g(x)). We know that g(x) = 13x, so we substitute this into f(x): f(g(x)) = f(13x) = 3(13x) = 39x. Now, we need to find g(f(x)). We know that f(x) = […]
How to Multiply Fractions with Whole Numbers and Mixed Numbers
To multiply fractions with whole numbers and mixed numbers, you can follow these simple steps: Step 1: Convert Mixed Numbers to Improper Fractions If you have a mixed number, such as 2 1/3, convert it into an improper fraction. To do this, multiply the whole number by the denominator and add the numerator. For 2 […]
The area of a square game board is 144 sq in. What is the length of one of the sides of the board?
To find the length of one side of a square when you know the area, you simply take the square root of the area. In this case, the area is 144 square inches. So, you calculate the square root of 144: √144 = 12 This means that each side of the square game board measures […]
What are two angles in a plane which share a common vertex and a common side but do not overlap?
In geometry, the two angles you are referring to are known as adjacent angles. These angles are formed when two rays (or lines) originate from the same point. To elaborate, adjacent angles have the following characteristics: They share a common vertex, which is the point where the two lines meet. They share a common side, […]
Using the Completing the Square Method to Rewrite f(x) = x² – 4x + 1 in Vertex Form
To rewrite the quadratic function f(x) = x² – 4x + 1 in vertex form, we can use the completing the square method. The vertex form of a quadratic function is given by f(x) = a(x – h)² + k, where (h, k) is the vertex of the parabola. Let’s follow these steps: Start with […]
What Do the Angles in a Triangle Add Up To?
In any triangle, the sum of the interior angles always equals 180 degrees. This rule holds true for all types of triangles, whether they are scalene, isosceles, or equilateral. To understand why this is the case, you can visualize or even draw a triangle and then extend one of its sides. By doing so, you’ll […]