How do you simplify √24 + 3√45 – 2√20?
To simplify the expression √24 + 3√45 – 2√20, we start by simplifying each square root term individually. 1. **Simplifying √24:** √24 can be broken down into √(4 × 6), which further simplifies to √4 × √6. Since √4 = 2, we have: √24 = 2√6 2. **Simplifying √45:** √45 can be expressed as √(9 […]
Solve 5/x + 8 = 3/x for x and determine if the solution is extraneous or not
To solve the equation 5/x + 8 = 3/x, we first eliminate the fractions by multiplying both sides of the equation by x (assuming x ≠ 0): x(5/x + 8) = x(3/x) This simplifies to: 5 + 8x = 3 Next, we isolate the variable x by moving 5 to the right side: 8x = […]
Can You Conclude That A = B If A and B Are Two Sets with the Same Power Set?
No, you cannot conclude that set A is equal to set B just because they have the same power set. The power set of any set is the set of all possible subsets of that set. While it is true that two sets having the same power set implies that they have the same number […]
Identify All Solutions of √(x + 10) – 4 = x
To solve the equation √(x + 10) – 4 = x, we start by isolating the square root. We can do this by adding 4 to both sides: √(x + 10) = x + 4 Next, we square both sides to eliminate the square root: x + 10 = (x + 4)² Expanding the right […]
Find the Exact Value Using a Half Angle Identity for sin(5π/12)
To find the exact value of sin(5π/12), we can use the half-angle identity. The half-angle formula states: sin(θ/2) = ±√((1 – cos(θ)) / 2) First, let’s rewrite 5π/12 in a way that our half-angle formula can be applied. Notice that: 5π/12 = π/3 + π/4 Now, we can find sin(5π/12) as: sin(5π/12) = sin(π/3 + […]
How to Write a Decimal as a Fraction
Writing a decimal as a fraction is a straightforward process. Here’s how to do it step by step: Identify the Decimal: First, take a look at the decimal you want to convert. For example, let’s take 0.75. Count the Decimal Places: Next, determine how many digits are after the decimal point. In our example, 0.75 […]
How do you find the equation of the circle with a diameter defined by the endpoints (7, 3) and (7, 5)?
To find the equation of a circle given the endpoints of its diameter, you first need to determine the center and the radius of the circle. 1. **Find the center of the circle**: The center is the midpoint of the diameter. We can calculate the midpoint (M) using the following formula: M = ((x1 + […]
Identify the vertex for the graph of y = 2x² + 12x + 3
To find the vertex of the quadratic function represented by the equation y = 2x² + 12x + 3, we can use the vertex formula or complete the square. The vertex of a parabola given in the form y = ax² + bx + c can be found using the formula for x-coordinate of the […]
How do you find the vertex of y = 3x² + 6x + 4?
To find the vertex of the quadratic equation y = 3x² + 6x + 4, we can use the vertex formula derived from the standard form of a parabola. The vertex (h, k) can be found using the formula: h = -b / (2a) In our equation, the coefficients are: a = 3 b = […]
What is the future value of $10,000 on deposit for 5 years at 6% simple interest?
To calculate the future value of a deposit with simple interest, we can use the formula: Future Value = Principal + (Principal × Rate × Time) In this case: Principal (P): $10,000 Rate (R): 6% (or 0.06 as a decimal) Time (T): 5 years Now we can plug the values into the formula: Future Value […]