How Many Squares Make Up the Surface of a Cube?
A cube has a total of 6 squares that make up its surface. This is because a cube has six faces, and each face is a square. Each square is identical in size and shape, and they are all arranged perpendicular to each other. If you visualize a standard dice, you can see that it […]
What is the value of b² – 4ac for the following equation 2x² + 2x + 1 = 0?
To find the value of b² – 4ac, we first need to identify the coefficients a, b, and c from the quadratic equation in the standard form ax² + bx + c = 0. For the equation 2x² + 2x + 1 = 0: a = 2 b = 2 c = 1 Now, we’ll […]
What is the equation of the line whose y intercept is 3 and slope is 1?
To find the equation of a line given the y-intercept and the slope, you can use the slope-intercept form of the equation: y = mx + b In this formula, m represents the slope of the line and b represents the y-intercept. From the question, we know: The slope (m) is 1. The y-intercept (b) […]
How many 4 card hands are possible with a 52 card deck?
To determine how many 4 card hands can be formed from a standard 52 card deck, we need to use the concept of combinations. In mathematical terms, a combination is a way of selecting items from a larger pool where the order does not matter. The formula for combinations is given by: C(n, r) = […]
What is the common ratio of the sequence 2, 6, 18, 54?
The common ratio of the sequence 2, 6, 18, 54 can be found by dividing any term in the sequence by the previous term. Starting from the first two terms: Common ratio = 6 ÷ 2 = 3 Now, let’s verify using the next terms: Common ratio = 18 ÷ 6 = 3 Common ratio […]
How many cubic units is a box that is 3 units high, 3 units wide, and 2 units deep?
To find the volume of a box, you can use the formula for the volume of a rectangular prism, which is: Volume = Height × Width × Depth. In this case, the dimensions of the box are: Height = 3 units Width = 3 units Depth = 2 units Now, plug the values into the […]
How do you solve the equation 3x² + 18x + 15 = 0 by completing the square?
To solve the equation 3x² + 18x + 15 = 0 by completing the square, follow these steps: Divide the entire equation by 3: This makes the calculations easier. Dividing each term gives us: x² + 6x + 5 = 0 Rearrange the equation: Move the constant term to the other side: x² + 6x […]
What is Trigonometric Identity?
Trigonometric identities are equations involving trigonometric functions that are true for all values of the variables where both sides of the identity are defined. These identities are fundamental in mathematics, especially in fields such as geometry, calculus, and physics. One common example of a trigonometric identity is the Pythagorean identity: sin²(θ) + cos²(θ) = 1 […]
Find the Vertex, Focus, Directrix, and Focal Width of the Parabola x = 4y²
To analyze the parabola given by the equation x = 4y², we first reformat it to identify its key characteristics. This form indicates that we have a horizontally oriented parabola. Vertex: The vertex of this parabola is at the origin, which is the point (0, 0). Focus: For a parabola, the distance from the vertex […]
What is the expression in factored form x² + 14x + 48?
To factor the expression x² + 14x + 48, we want to find two numbers that multiply to 48 (the constant term) and add up to 14 (the coefficient of the x term). Upon inspection, the numbers 6 and 8 work since: 6 × 8 = 48 6 + 8 = 14 We can now […]