Which equation shows the quadratic formula used correctly to solve 5x² + 3x + 4 = 0 for x?
To solve the quadratic equation 5x² + 3x + 4 = 0 using the quadratic formula, we start by recalling the formula itself. The quadratic formula is: x = (-b ± √(b² – 4ac)) / (2a) In our equation, we can identify the coefficients as follows: a = 5 b = 3 c = 4 […]
Which value is needed to create a perfect square trinomial from the expression x² + 8x?
To create a perfect square trinomial from the expression x² + 8x, we need to find the value that completes the square. A perfect square trinomial can be written in the form (x + a)², where a is a constant. To find the value, we take the coefficient of x, which is 8, divide it […]
Percentage as a Fraction in Simplest Form
To convert a percentage into a fraction, you start by writing the percentage number over 100. For instance, if you have 25%, you can write it as: 25% = 25/100 Next, the key step is to simplify the fraction. This means finding the greatest common divisor (GCD) of both the numerator (the top number) and […]
How to solve the quadratic equation x² + 5x + 3 = 0?
To solve the quadratic equation x² + 5x + 3 = 0, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a In this equation, a = 1, b = 5, and c = 3. First, we need to calculate the discriminant (b² – 4ac): b² – 4ac = 5² […]
Factor Completely: 4x² + 25x + 6 + 4x + 1 + 6 + 4x + 6x + 1 + 2x + 32x² + 2 + 2x + 62x + 1
To factor the expression completely, we first need to simplify it. We combine like terms: For the x² terms: 4x² + 32x² = 36x² For the x terms: 25x + 4x + 6 + 4x + 6x + 2x + 62x = 109x Constant terms: 1 + 1 + 1 + 2 = 5 Now […]
For a Regular 30-Sided Polygon, What is the Degree of Rotation?
The degree of rotation for a regular 30-sided polygon, also known as a triacontagon, is 12 degrees. To understand how we arrive at this, we can start by noting that a full rotation around a point is 360 degrees. Since the polygon has 30 identical sides and angles, we divide the total degrees of rotation […]
What are the solutions of 2x² + 16x + 50 = 0?
To find the solutions for the quadratic equation 2x² + 16x + 50 = 0, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a In this equation, a = 2, b = 16, and c = 50. We start by calculating the discriminant (b² – 4ac): b² = 16² […]
In a parallelogram ABCD if angle D is 125 degrees, what are the other angles?
In a parallelogram, opposite angles are equal, and the sum of the angles in any quadrilateral is 360 degrees. If angle D is 125 degrees, then angle B, which is opposite to angle D, is also 125 degrees. To find angles A and C, we can use the property that consecutive angles in a parallelogram […]
What is the sum of the first 10 terms of the sequence defined by an = 4n + 3?
To find the sum of the first 10 terms of the sequence defined by an = 4n + 3, we first need to calculate the individual terms. Let’s calculate the first 10 terms: a1 = 4(1) + 3 = 7 a2 = 4(2) + 3 = 11 a3 = 4(3) + 3 = 15 a4 […]
What are the factors of x² – 100?
The factors of the expression x² – 100 can be found by recognizing that it is a difference of squares. The difference of squares formula is given by: a² – b² = (a – b)(a + b) In this case, we can set: a = x and b = 10 (since 10² = 100) Applying […]