How many lines of symmetry does a regular polygon with 22 sides have?
A regular polygon with 22 sides has 22 lines of symmetry. This is because a regular polygon is symmetric around its center, and each vertex can be paired up with the vertex directly opposite it. To understand this better, consider the definition of a line of symmetry: it is a line that divides a shape […]
On a Number Line, What is the Distance Between 37 and 23?
To find the distance between two numbers on a number line, you simply subtract the smaller number from the larger number. In this case, the numbers are 37 and 23. So, we calculate: Distance = 37 – 23 When you perform the subtraction, you get: Distance = 14 This means the distance between 37 and […]
What is 5 of 500?
To find 5 of 500, you simply need to calculate 5% of 500. This is done by multiplying 500 by 0.05 (which represents 5%). Calculation: 500 × 0.05 = 25 So, 5 of 500 is 25. This means that 5 is a fraction of 500, specifically 5% of that total amount.
What is the value of x in the equation 2x – 3 + 9 = 3x + 1 + x?
How do you expand (x + 1)^3 using binomial expansion?
To expand the expression (x + 1)^3 using binomial expansion, we can use the binomial theorem, which states that: (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k In our case, a = x, b = 1, and n = 3. Let’s break this down step by step: Identify the components: a = x, b = […]
A coin is tossed three times what is the probability of getting 3 tails?
To find the probability of getting three tails when a coin is tossed three times, we need to look at the total possible outcomes and the favorable outcomes. When a coin is tossed, there are two possible results: heads (H) or tails (T). Therefore, when tossing a coin three times, the total number of outcomes […]
Find a quadratic polynomial whose zeros are 4 and 2
To find a quadratic polynomial given its zeros, we can use the fact that if a polynomial has zeros at p and q, it can be expressed in the form: f(x) = k(x – p)(x – q) Here, p = 4 and q = 2. We can substitute these values into the equation. Using k […]
Find the Value of cos 15° Using cos(a ± b) Identity
To find the value of cos 15°, we can use the cosine addition identity: cos(a ± b) = cos a cos b ∓ sin a sin b. We can express 15° as the difference of two angles that we know the cosine and sine for: 15° = 45° – 30°. Now, we can set a […]
If you roll two fair six sided dice what is the probability that the dice show the same number?
When rolling two fair six-sided dice, we want to determine the probability that the numbers on both dice match. There are a total of 6 possible outcomes for the first die (numbers 1 through 6) and 6 possible outcomes for the second die, resulting in: Total possible outcomes = 6 * 6 = 36 For […]
What is the next number in the sequence: 256, 196, 144, 100, 64, 36, 16?
The next number in the sequence is 4. This sequence consists of perfect squares of consecutive even numbers. Let’s break it down: 256 = 16^2 196 = 14^2 144 = 12^2 100 = 10^2 64 = 8^2 36 = 6^2 16 = 4^2 The pattern clearly shows that we are squaring the even numbers in […]