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To find the discriminant of the trinomial 3x² + 6x + 5, we first need to recall the formula for the discriminant, which is derived from the quadratic equation in the standard form, ax² + bx + c. The discriminant (D) is given by: D = b² – 4ac In this trinomial, the coefficients are: … Read more

To convert the expression x4 + 3x – 12 into a system of equations, we first need to isolate the variable and create relationships between multiple equations. The expressions can represent a function, and by setting it equal to zero, we can treat it as an equation: 1. First, we start by rewriting the equation: … Read more

To solve the inequality 5 < r < 3, we need to analyze its components and intervals carefully. First, let’s break this down into two parts: 5 < r: This means that r must be greater than 5. r < 3: This means that r must be less than 3. Now, let’s put these two ... Read more

The equation y = 52x represents a direct variation, which means that the value of y varies directly with the value of x. In simpler terms, if you increase x, y increases proportionally to that change, and vice versa. To visualize this, the graph of the equation will be a straight line that passes through … Read more

To prove that if 7n4 is even, then n must be even, we’ll start by analyzing the properties of even and odd numbers. 1. **Understanding Even and Odd Numbers**: A number is even if it is divisible by 2. Conversely, a number is odd if it is not divisible by 2. We know that: If … Read more

Determining the truth value of statements involves a clear understanding of the context and evidence surrounding each statement. Here’re some steps to help you identify whether a statement is true or false: Research the Facts: Look for credible sources or data that support or contradict the statement in question. Reliable information can often provide clarity. … Read more

Finding the Quotient of the Expression To determine the quotient of the expression 3x² + 4x + 15 divided by 3, we need to perform the division on each term of the polynomial. Step-by-Step Breakdown Starting with the expression: 3x² + 4x + 15 We divide each term by 3: 3x² ÷ 3 = x² … Read more

To solve the challenge of finding two whole numbers from the digits 1 to 9, while ensuring that one number is double the other, we can approach the problem step-by-step. Let’s denote the smaller number as X. Consequently, the larger number would be 2X. The digits 1 to 9 must be used exactly once in … Read more

Converting Vertex Form to Standard Form To convert the given vertex form of the function f(x) = 2(x – 2)^2 + 32 into standard form, we’ll follow a systematic approach. Step 1: Expand the Squared Term Start by expanding the squared term: (x – 2)^2 = x^2 – 4x + 4 Now substitute this back … Read more

The first ten odd numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19. To find the sum of these numbers, you can simply add them together: 1 + 3 = 4 4 + 5 = 9 9 + 7 = 16 16 + 9 = 25 25 + 11 = 36 … Read more