Write the odd numbers between 36 and 53
To find the odd numbers between 36 and 53, we start by identifying the smallest odd number greater than 36, which is 37. From there, we can list the odd numbers by adding 2 repeatedly until we reach a number that exceeds 53. The odd numbers in this range are: 37, 39, 41, 43, 45, […]
Find the value of x in the equation 2 x 20 15 3 x
To solve the equation 2 x 20 = 15 – 3 x, we first need to clarify what the equation states. This is an algebraic equation where we have a variable, x, that we need to isolate in order to find its value. Let’s break down the equation step by step: Start with the original […]
What do the side lengths of a triangle add up to?
In any triangle, the sum of the lengths of the three sides is always greater than the length of the longest side. However, if you are asking about the specific total when you add the lengths of the three sides together, it simply depends on the measurements of those sides. Unlike shapes like squares or […]
Find the exact length of the polar curve r = e^(2θ) for 0 ≤ θ ≤ 2π
To find the exact length of the polar curve given by r = e^(2θ) over the interval 0 ≤ θ ≤ 2π, we can use the formula for the length of a polar curve: L = ∫ from a to b √( (dr/dθ)^2 + r^2 ) dθ 1. First, we need to calculate dr/dθ. For […]
What is the value of the radius of the following circle with an area of 154 cm²?
To find the radius of a circle given its area, we use the formula for the area of a circle: A = πr² Where A is the area, r is the radius, and π (pi) is approximately 3.14. Given that the area (A) is 154 cm², we can rearrange the formula to solve for the […]
Solve for x and y: 2x + 3y = 23 and 3x + y = 7
To solve the system of equations given by 2x + 3y = 23 and 3x + y = 7, we can use substitution or elimination methods. Here, we’ll use the substitution method for clarity. First, we can express y in terms of x from the second equation: 3x + y = 7 => y = […]
What are the zeroes of f(x) = x² – 2?
The zeroes of the function f(x) = x² – 2 can be found by solving the equation: f(x) = 0 This means we need to set the equation equal to zero: x² – 2 = 0 To solve for x, we can add 2 to both sides: x² = 2 Next, we take the square […]
What property of multiplication is used to find equivalent fractions?
To find equivalent fractions, we use the Multiplicative Identity Property of multiplication. This property states that when you multiply any number by 1, that number remains unchanged. When it comes to fractions, we can express 1 in many forms, such as a/b, where a and b are the same non-zero number. For example, if we […]
What is the probability of rolling a sum of 5 if two regular 6 sided number cubes are rolled?
To find the probability of rolling a sum of 5 with two six-sided dice, we first need to identify all the possible combinations of the two dice that would result in that sum. The possible pairs of rolls that give a sum of 5 are: (1, 4) (2, 3) (3, 2) (4, 1) So, there […]
What is the equation of the line passing through (1, 4) and parallel to y = 2x + 1?
To find the equation of a line that is parallel to another line, we first need to know the slope of the original line. The given line is y = 2x + 1, which is already in slope-intercept form (y = mx + b), where m is the slope. From the equation y = 2x […]