devyy When rolling a pair of fair dice, each die has 6 faces, resulting in a total of 36 possible outcomes (6 faces on the first die multiplied by 6 faces on the second die). The probabilities of rolling specific sums can be calculated based on these outcomes. Here’s a breakdown of the probabilities for sums … Read more
Factoring the Expression: 9x² + 12x + 4 To express the quadratic expression 9x² + 12x + 4 in factored form, we will follow these steps: Step 1: Identify the Coefficients In the expression ax² + bx + c, the coefficients are: a = 9 b = 12 c = 4 Step 2: Multiply a … Read more
To convert the decimal 0.375 into a fraction, follow these steps: Identify the place value: The decimal 0.375 has three decimal places. This means it is in the thousandths place. Write it as a fraction: You can express 0.375 as 375/1000, since 375 is in the thousandths. Simplify the fraction: To simplify 375/1000, find the … Read more
To determine what needs to be added to the expression 3x + 7 to equal the expression x2 + 4x + 1, we can set up the equation: 3x + 7 + ? = x2 + 4x + 1 To isolate the unknown (let’s call it k), we rearrange the equation: k = (x2 + … Read more
To write the equation of a line given the slope and the y-intercept, you can use the slope-intercept form of a linear equation, which is expressed as: y = mx + b In this formula: y represents the dependent variable (the output of the function), x is the independent variable (the input), m is the … Read more
When a number is raised to the power of 1, it simply means that the number remains unchanged. Mathematically, this can be expressed as: a1 = a Where a is any real number. This property holds true for all numbers, whether they are integers, fractions, or decimals. For example: If you take the number 5, … Read more
To find the first five terms of the sequence defined by the formula a(n) = 1 + 4n, we need to substitute the values of n starting from 0 up to 4. Here’s how the calculation works: For n = 0: a(0) = 1 + 4(0) = 1 + 0 = 1 For n = … Read more
The divisor represented by the synthetic division notation you provided, which is written as 5 5 x 5 x 5, is referring to a polynomial being divided by the binomial (x – 5). In synthetic division, the coefficients of the polynomial are aligned with the value being used as the divisor, which in this case … Read more
The perimeter of a triangle is simply the sum of the lengths of all its sides. For triangle LMN, you would need to know the lengths of sides LM, LN, and MN. To calculate the perimeter, you can use the following formula: Perimeter (P) = LM + LN + MN Here’s a step-by-step guide on … Read more
A polygon is a flat shape consisting of straight lines that are joined to form a closed chain or circuit. Let’s examine the potential candidates to determine whether they are polygons: Triangle: Yes, a triangle has three straight sides and is a polygon. Rectangle: Yes, a rectangle has four straight sides and is a polygon. … Read more