When 92 3 is written in the simplest radical form, which value remains under the radical?
To express 923 in its simplest radical form, we need to factor the number 923 into its prime factors and simplify the radical. First, we can break down 923. We find that: 923 is divisible by 7 (since 923 / 7 = 131). This means: 923 = 7 × 131 Next, we check if either […]
A card is drawn from a well shuffled deck of 52 cards. Find P(drawing a face card or a 4).
To solve this problem, we first need to identify how many face cards and 4s are in a standard deck of 52 cards. A standard deck has 12 face cards (3 ranks: Jack, Queen, King; each rank has 4 cards) and 4 cards that are numbered 4 (one for each suit: hearts, diamonds, clubs, spades). […]
What is the slope of the line represented by the equation y = 12x + 14?
The slope of the line represented by the equation y = 12x + 14 is 12. To explain this, we need to look at the equation in the context of the slope-intercept form, which is: y = mx + b In this equation, m represents the slope of the line, and b is the y-intercept […]
What Does a Scalene Triangle Look Like?
A scalene triangle is a type of triangle where all three sides are of different lengths, and as a result, all three angles are also different. Unlike equilateral triangles, which have equal sides and angles, or isosceles triangles, which have at least two equal sides, scalene triangles stand out due to their lack of symmetry. […]
Triangle ABC is a Right Triangle: What is the Relationship Between Angles A and B?
In a right triangle, one angle measures exactly 90 degrees. In Triangle ABC, if we assume angle C is the right angle, this means that the sum of angles A and B must equal 90 degrees as well. This is derived from the fundamental property of triangles that states that the sum of all interior […]
How to Solve the Equation 3x² + 5x + 2 = 0 by Completing the Square Method?
To solve the equation 3x² + 5x + 2 = 0 by completing the square, we start by rearranging the equation in a form that makes it easier to complete the square. First, we can factor out the coefficient of x² from the first two terms: Step 1: Factor out 3: 3(x² + (5/3)x) + […]
What is the Finance Charge on an $8,000 Loan with a Monthly Payment of $162.80 for 60 Months?
To determine the finance charge on a loan, we first need to calculate the total amount paid over the life of the loan and then compare that with the principal amount borrowed. The total amount paid over 60 months (5 years) with monthly payments of $162.80 is: Total Payments = Monthly Payment × Number of […]
Which equation is an example of the commutative property of multiplication?
The commutative property of multiplication states that changing the order of the factors does not change the product. An example of this property can be illustrated with the equation: 3 × 5 = 5 × 3 In both cases, whether you multiply 3 by 5 or 5 by 3, the result is 15. This demonstrates […]
Given the exponential equation 3^x = 27, what is the logarithmic form of the equation in base 10?
The exponential equation 3x = 27 can be converted into logarithmic form. To do this, we need to recognize that the logarithm is the inverse operation of exponentiation. First, we can express 27 as a power of 3: 27 = 33. Therefore, we can rewrite the original equation as: 3x = 33 Now, since the […]
Divide 724 by 3548 and Reduce the Quotient to the Lowest Fraction
To divide 724 by 3548, we start by performing the division: 724 ÷ 3548 = 0.2042 (approximately). Next, to express this result as a fraction, we write it as: 724/3548. Now, to reduce this fraction to its lowest terms, we need to find the greatest common divisor (GCD) of the two numbers, 724 and 3548. […]