Find the Center and Radius of the Sphere x² + y² + z² – 6y – 8z = 0
To find the center and radius of the sphere given by the equation x² + y² + z² – 6y – 8z = 0, we’ll first rewrite it in the standard form of a sphere’s equation. The standard form of a sphere’s equation is (x – h)² + (y – k)² + (z – l)² […]
Find the distance between the points (2, 4) and (4, 6)
To find the distance between two points in a Cartesian plane, we use the distance formula, which is derived from the Pythagorean theorem. The formula is: d = √((x2 – x1)² + (y2 – y1)²) Here, (x1, y1) and (x2, y2) are the coordinates of the two points. For our points (2, 4) and (4, […]
Which is the probability of rolling an odd number on a fair 6 sided number cube?
To find the probability of rolling an odd number on a fair 6-sided number cube, we first need to identify the odd numbers on the cube. A standard 6-sided die has the following numbers: 1, 2, 3, 4, 5, and 6. The odd numbers in this set are 1, 3, and 5. Therefore, there are […]
What is the least common denominator of 3, 4, 4, 5, 2, 3?
To find the least common denominator (LCD) of the numbers 3, 4, 4, 5, 2, and 3, we first identify the prime factors of each number: 3: 3 4: 2 × 2 5: 5 2: 2 Next, we take the highest power of each prime number that […]
How do you find the vertex form of the quadratic function h(x) = x² + 14x + 6?
To find the vertex form of the quadratic function h(x) = x² + 14x + 6, we need to complete the square. First, we can start by rewriting the function: h(x) = x² + 14x + 6 Next, we focus on the quadratic and linear terms, which are x² + 14x. To complete the square, […]
How can we simplify the expression 6x^2 + 3 – 5x^3 + 4x^3 + 2x^2 + 16?
To simplify the expression 6x² + 3 – 5x³ + 4x³ + 2x² + 16, we start by combining like terms. 1. First, let’s identify the like terms: For the cubic terms: -5x³ + 4x³ For the quadratic terms: 6x² + 2x² The constant terms are: 3 + 16 2. Next, we combine these: Cubic […]
The circle shown below has ab and bc as its tangents if the measure of arc ac is 130 what is the measure of angle abc?
To find the measure of angle ABC, we can use a property of tangents and circles. When two tangents are drawn from a point outside the circle, the angle formed between the two tangents equals half the difference of the measures of the arcs intercepted by the angle. In our case, since AB and BC […]
What is the slope of the line through the points (3, 5) and (4, 5)?
The slope of a line is calculated using the formula: slope (m) = (y2 – y1) / (x2 – x1) In this case, we have two points: (3, 5) and (4, 5). Here, (x1, y1) = (3, 5) and (x2, y2) = (4, 5). Substituting the values into the slope formula: m = (5 – […]
How do you solve the equation for a in the equation 2a = 4?
To solve the equation 2a = 4, you need to isolate the variable a. Here are the steps to do that: Start with the equation: 2a = 4. To isolate a, divide both sides of the equation by 2: a = 4 / 2. Now perform the division: a = 2. So the solution to […]
Choose a linear function for the line represented by the point slope equation y = 3x + 2
The point-slope equation you provided is actually slightly misformatted in your question. The correct point-slope form is usually written as y – y1 = m(x – x1), where m is the slope and (x1, y1) is a specific point on the line. In your equation, y = 3x + 2, the slope m is 3, […]