How to find the area of a triangle with sides a = 4, b = 7, and c = 9?
To find the area of a triangle when the lengths of all three sides are known, we can use Heron’s formula. First, we need to calculate the semi-perimeter (s) of the triangle. The semi-perimeter is half the sum of the lengths of the sides: s = (a + b + c) / 2 For our […]
Find LCM by Division Method: 48, 72, 80
To find the LCM (Least Common Multiple) of the numbers 48, 72, and 80 using the division method, follow these steps: Write the numbers in a row: 48 72 80 Divide the numbers by their smallest prime factor. In this case, we can start with 2: 48 ÷ 2 = 24 72 ÷ 2 = […]
How to Find the Lateral Area of a Triangular Prism
To find the lateral area of a triangular prism, you need to focus on the sides of the prism that connect the two triangular bases. The formula for the lateral area (LA) of a triangular prism is: LA = perimeter of the base × height of the prism Here’s how to calculate it step by […]
Which ordered pair maximizes the objective function p = 3x + 8y?
To determine which ordered pair maximizes the objective function p = 3x + 8y, we will evaluate this function at the given points: (0, 0), (2, 7), (5, 6), and (8, 1). 1. For the point (0, 0): p = 3(0) + 8(0) = 0 2. For the point (2, 7): p = 3(2) + […]
How many kilograms of tea worth 300 rupees per kg should be mixed with 10 kg of tea worth 240 per kg to produce a mixture to cost 260 per kg?
To solve this problem, we can use the concept of a mixture and weighted averages. We need to find the amount of tea (let’s denote it as x kg) priced at 300 rupees per kg that should be mixed with 10 kg of tea priced at 240 rupees per kg to achieve a new mixture […]
What is the distance between two points?
The distance between two points in a plane can be calculated using the distance formula derived from the Pythagorean theorem. For any two points, say (x1, y1) and (x2, y2), the distance (d) can be expressed as: d = √((x2 – x1)2 + (y2 – y1)2) This formula essentially forms a right triangle where the […]
What fractional part of a day do you spend sleeping if you sleep 8 hours per day?
To find out the fractional part of a day spent sleeping, we can follow a simple calculation. A full day has 24 hours. If you sleep for 8 hours each day, you can express this as a fraction of the total hours in a day. The calculation is: Fraction of the day spent sleeping = […]
Which equation has a graph that is a parabola with a vertex at (5, 3)?
To find an equation of a parabola with a specific vertex, we can use the vertex form of a quadratic equation, which is given by: y = a(x – h)² + k In this equation, (h, k) represents the vertex of the parabola. Here, the vertex is given as (5, 3), so we can substitute […]
Dividing Polynomial x^4 + 9x^2 – 9 by x^2 + 3x: What are the Quotient and the Remainder?
To divide the polynomial x4 + 9×2 – 9 by x2 + 3x, we can use polynomial long division. Firstly, we set it up similar to numeric long division: Dividend: x4 + 0x3 + 9×2 + 0x – 9 Divisor: x2 + 3x Next, we divide the leading term of the dividend by the leading […]
Which equation matches the table y = x^3, y = 4x^3?
To determine which equation matches the given table, we start by analyzing the equations provided. The two equations are: y = x3 y = 4×3 The first equation, y = x3, describes a cubic function where the output (y) is equal to the cube of the input (x). In this case, each value of x […]