Which of the following shows the complete factorization of x³ – 3x²?
To factor the expression x³ – 3x² completely, we start by identifying the common factors in the terms. In this case, both terms share a common factor of x². Factoring out x² from the expression, we get: x³ – 3x² = x²(x – 3) This means the complete factorization of the expression x³ – 3x² […]
What is a prime number between 40 and 50?
A prime number between 40 and 50 is 43. A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself. To determine which numbers between 40 and 50 are prime, we can check each one: 41: Prime (divisors are 1 and 41) 42: Not prime […]
Is the diagonal of a square equal to its sides?
No, the diagonal of a square is not equal to its sides. In fact, the diagonal is longer than each side of the square. To understand why this is the case, let’s take a closer look at a square. A square has four equal sides, and if we label the length of each side as […]
How many subsets does the set 1 2 3 have?
The set {1, 2, 3} has a total of 2n subsets, where n is the number of elements in the set. In this case, the set has 3 elements: 1, 2, and 3. To calculate the number of subsets, we use the formula: 2n = 23 = 8 This means there are 8 possible subsets […]
What are the solutions to the quadratic equation 4x² – 64?
To solve the quadratic equation 4x² – 64 = 0, we first need to rearrange the equation so that we can identify the variable terms more easily. Start by adding 64 to both sides: 4x² = 64 Next, divide both sides by 4 to simplify: x² = 16 Now, to find the solutions for x, […]
What is the slope of the line represented by the equation y = 45x + 3?
The slope of the line represented by the equation y = 45x + 3 is 45. In this equation, which is in the slope-intercept form (y = mx + b), the variable m represents the slope of the line. Here, m = 45, which means that for each increase of 1 unit in the x-direction, […]
If a theatre holds 1200 people and sells 2/3 of its seats, how many tickets does it sell?
To find out how many tickets the theatre sells, we need to calculate two-thirds of the total number of seats available. The total number of seats in the theatre is 1200. To calculate two-thirds of this amount, you can multiply 1200 by 2/3: 1200 * (2/3) = 800 This means the theatre sells 800 tickets. […]
How to Write This in Number: Eleven Thousand Eleven Hundred
To express the phrase ‘eleven thousand eleven hundred’ in numerical form, you need to break it down into its components. The term ‘eleven thousand’ refers to 11,000, while ‘eleven hundred’ refers to 1,100. Therefore, when you combine these two parts together, you add 11,000 and 1,100. Mathematically, this looks like: 11,000 + 1,100 = 12,100 […]
How do you write a remainder as a fraction in the given expression 64 ÷ 30?
To express the remainder as a fraction in the division of 64 by 30, you first need to perform the division to find out how many times 30 fits into 64 and what is left over. When you divide 64 by 30, you can see that 30 goes into 64 two times because 30 x […]
Find the HCF of 95, 105, and 115 by Continued Division
To find the Highest Common Factor (HCF) of the numbers 95, 105, and 115 using continued division, we can follow these steps: Start by dividing the largest two numbers, which are 105 and 115. Divide 115 by 105: 115 ÷ 105 = 1 (remainder 10) The process continues with the divisor (105) and the remainder […]