What is the value of x in the equation 2x + 3y = 36 when y = 6?
To find the value of x in the equation 2x + 3y = 36, we start by substituting the given value of y. Since we know that y = 6, we can replace y in the equation: 2x + 3(6) = 36 Next, we calculate 3(6), which equals 18. Substituting that back into the equation […]
Use the Intermediate Value Theorem to Show that There is a Root of the Equation x^5 – 2x^4 – x – 3 = 0 in the Interval [-2, 3]
To apply the Intermediate Value Theorem, we first need to define the function based on the given equation: f(x) = x5 – 2×4 – x – 3 Now, let’s evaluate the function at the endpoints of the interval [-2, 3]. First, we calculate f(-2): f(-2) = (-2)5 – 2(-2)4 – (-2) – 3 f(-2) = […]
How Does the Length of the Hypotenuse in a Right Triangle Compare to the Lengths of the Legs?
In a right triangle, the hypotenuse is the longest side, which is opposite the right angle. It can be measured against the lengths of the two legs of the triangle using the well-known Pythagorean theorem. This theorem states that the square of the length of the hypotenuse (c) is equal to the sum of the […]
Which is greater, 29 or 0?
When comparing the two numbers 29 and 0, it is clear that 29 is greater. This is because in mathematics, any positive number is always greater than zero. To illustrate this further, think of the number line where numbers increase from left to right. Zero is located to the left of 29, confirming that 29 […]
What is the common ratio of the geometric sequence below 625, 125, 25, 5, 1?
To find the common ratio of a geometric sequence, you can divide any term by the previous term. In this case, we can calculate the common ratio using the first two terms of the sequence. The first term is 625 and the second term is 125. We calculate the common ratio (r) as follows: r […]
Which of the Following is an Odd Function?
To determine which of the following functions is an odd function, we first need to understand what an odd function is. An odd function is one that satisfies the condition: f(-x) = -f(x) for all x in its domain. This means that the graph of the function is symmetric with respect to the origin. Now, […]
How to Find the Diameter of a Circle Using the Circumference
To find the diameter of a circle using its circumference, you can use a simple formula derived from the relationship between these two measurements. The circumference (C) of a circle is given by the formula: C = π × d where π (pi) is a constant approximately equal to 3.14, and d is the diameter […]
What is the difference between a relation and a function?
A relation is any set of ordered pairs, where each pair consists of an input (typically called the domain) and an output (called the range). A function, on the other hand, is a specific type of relation that follows a unique rule: each input in the domain is associated with exactly one output in the […]
A soccer team played 160 games and won 65 percent of them. How many games did it win?
To find out how many games the soccer team won, we can calculate 65 percent of the total games played. First, we convert the percentage into a decimal by dividing by 100. So, 65 percent becomes 0.65. Next, we multiply the total number of games (160) by the decimal value (0.65): 160 games * 0.65 […]
Which expression is equivalent to i²³³ 1 1 i i?
To simplify the expression i²³³ 1 1 i i, we start by recalling the properties of the imaginary unit i, where i = √(-1). The powers of i cycle every four terms: i1 = i i2 = -1 i3 = -i i4 = 1 To evaluate i²³³, we can determine its equivalent by calculating the […]