How many solutions exist for the given equation 3x² – 22x?
To determine how many solutions exist for the equation 3x² – 22x = 0, we start by factoring the equation. First, we can factor out an x from the expression: 3x(x – rac{22}{3}) = 0 From this factored form, we can set each factor equal to zero: 1. 3x = 0 2. x – rac{22}{3} […]
What is a letter that is used in place of a numeral?
In mathematics and various contexts, a letter that is used in place of a numeral is often referred to as a variable. Variables can represent numbers that might change or be unknown in a given situation. For example, in the equation x + 2 = 5, the letter x is a variable that stands in […]
What is the greatest common factor of 4xy² and 20x²y⁴?
To find the greatest common factor (GCF) of the terms 4xy² and 20x²y⁴, we need to identify the factors of each term. First, let’s break down each term into its prime factors: 4xy²: 4 can be factored as 2 × 2, so: 4xy² = 2 × 2 × x × y² 20x²y⁴: 20 can be […]
What are the possible values of x in the equation 12x = 50?
To solve for the values of x in the equation 12x = 50, we need to isolate x. We can do this by dividing both sides of the equation by 12. Starting with the equation: 12x = 50 Now, divide both sides by 12: x = 50 / 12 This simplifies to: x = 4.1667 […]
What is the measure of arc EF in circle H?
To find the measure of arc EF in circle H, we first need to understand that the measure of an arc is determined by the central angle that subtends the arc at the center of the circle. If we have the measure of the central angle corresponding to arc EF, the measure of the arc […]
The multiplication property of equality could be used to solve which of the following equations?
The multiplication property of equality states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal. This property can be applied to any equation where you need to isolate a variable by removing a coefficient through multiplication. For example, consider the equation: 1. 2x = 10: […]
Are Rational Numbers and Irrational Numbers Part of the Set of Real Numbers?
Yes, both rational numbers and irrational numbers are included in the set of real numbers. To clarify, rational numbers are those that can be expressed as the quotient of two integers, where the denominator is not zero. Examples of rational numbers include 1/2, -3, and 0.75. On the other hand, irrational numbers cannot be expressed […]
Which point is on the line that passes through (0, 6) and is parallel to the given line (12, 8), (6, 6), (2, 8), (6, 0)?
To find a point on the line that passes through (0, 6) and is parallel to the given line, we first need to determine the slope of the given line. We can do this by using the points provided. The coordinates of the given points are (12, 8), (6, 6), (2, 8), and (6, 0). […]
Which equation can be simplified to find the inverse of y = 5x² + 10?
To find the inverse of the equation y = 5x² + 10, we need to follow a few steps to rearrange the equation in terms of x. First, replace y with x: x = 5y² + 10 Next, isolate the term with y: x – 10 = 5y² Now, divide both sides by 5: (x […]
How to Find the Length of a Segment in a Circle
To find the length of a segment in a circle, you need to understand what a segment is. A segment is the area of a circle that is ‘cut off’ from the rest of the circle by a chord. The length of the segment can be determined using a formula that involves the radius of […]