What is the value of p in the equation x² = 12y?
To find the value of p in the equation x² = 12y, we start by relating it to the standard form of a parabola. The general formula for a parabola that opens upwards is given as x² = 4py. In our case, we have the equation x² = 12y. By comparing this to the standard […]
What is the formula for volume of a rectangular prism?
The formula for the volume of a rectangular prism is V = l × w × h, where V is the volume, l is the length, w is the width, and h is the height of the prism. To understand this better, think of a rectangular prism as a box. The length is how long […]
If in a histogram the area of the rectangle is proportional to its frequency, can we say that the lengths of the rectangles are also proportional to the frequencies?
In a histogram, the area of each rectangle (or bar) represents the frequency of that interval or class. If we say that the area of the rectangle is proportional to its frequency, it means that if the area increases or decreases, the frequency does the same. However, to determine if the lengths of the rectangles […]
Which Calculation Can Be Used to Find the Value of Y in the Equation y³ = 27?
To find the value of y in the equation y³ = 27, we can use the method of taking the cube root of both sides of the equation. The cube root is the opposite operation of cubing a number. Here’s how the calculation works: Start with the equation: y³ = 27 Now, to solve for […]
What value of x is in the solution set of 3x + 4 = 5x – 2?
To solve the equation 3x + 4 = 5x – 2, we start by looking to isolate the variable x. We want to get all the terms involving x on one side of the equation and the constant terms on the other side. First, let’s subtract 3x from both sides: 3x + 4 – 3x […]
What is 30 as a fraction in the lowest terms?
To express 30 as a fraction in its lowest terms, we can write it as 30/1. This is because any whole number can be represented as a fraction by placing it over 1. Next, we check if this fraction can be simplified. The greatest common divisor (GCD) of 30 and 1 is 1, which means […]
It’s 2 PM: How Many Degrees Are in the Angle Between the Hour and Minute Hand?
To find the angle between the hour and minute hands of a clock at 2 PM, we can break it down step by step. The minute hand at 2 PM is pointing at 12, which is the 0-degree mark. The hour hand, pointing at 2, is at 2 on the clock face. Each hour represents […]
Solve for x: 3x + 3 – 2 = 14
To solve for x in the equation 3x + 3 – 2 = 14, we start by simplifying the left side of the equation. First, combine the constants: 3 – 2 = 1 This simplifies our equation to: 3x + 1 = 14 Next, we want to isolate the term with x. To do this, […]
Given y = 2x + 32, choose the standard form of the given quadratic equation.
To convert the equation y = 2x + 32 into standard form, we first recognize that the equation currently represents a linear expression rather than a quadratic one. A quadratic equation typically takes the form y = ax2 + bx + c. However, if we assume you want to express this equation as a quadratic […]
You Roll a Six Sided Die: What is the Probability of Rolling a 5 or a Number Greater Than 3 and a Number Less Than 5?
To determine the probabilities for each of the scenarios when rolling a six-sided die, we will first identify the possible outcomes. A standard six-sided die has six faces, numbered from 1 to 6. Case A: Rolling a 5 or a Number Greater Than 3 The numbers that are 5 or greater than 3 on the […]