Prove that if n is a positive integer then n is even if and only if 7n + 4 is even
To prove that a positive integer n is even if and only if 7n + 4 is even, we will break this down into two parts: the ‘if’ part and the ‘only if’ part. If n is even, then 7n + 4 is even Suppose n is an even positive integer. By definition, this means […]
Which point is an x-intercept of the quadratic function f(x) = x^2 – 4x?
To find the x-intercepts of the quadratic function f(x) = x^2 – 4x, we need to determine the points where the function crosses the x-axis. This happens when f(x) equals zero. We can set up the equation: x^2 – 4x = 0 Next, we can factor the equation: x(x – 4) = 0 From this […]
What is the commutative property of addition?
The commutative property of addition states that the order in which two numbers are added does not change the sum. In simpler terms, if you have two numbers, say a and b, you can add them in any order, and you will get the same result. Mathematically, this is expressed as: a + b = […]
How many 1 cm squares would it take to construct a square that is 2 m on each side?
To determine how many 1 cm squares are needed to cover a square that is 2 meters on each side, we first need to convert the dimensions of the larger square into the same units as the smaller squares. Since 1 meter equals 100 centimeters, a square that is 2 meters on each side is […]
Make a mapping diagram for the relation 2, 6, 0, 3, 1, 5, 5, 0
To create a mapping diagram for the relation given by the numbers 2, 6, 0, 3, 1, 5, 5, 0, we need to first understand what a mapping diagram represents. A mapping diagram visually shows how elements from one set (the domain) relate to elements in another set (the range). In our case, let’s treat […]
How to Find the X and Y Intercepts of a Parabola
To find the x and y intercepts of a parabola, you need to follow these steps: X-Intercepts The x-intercepts are the points where the parabola crosses the x-axis. To find them, set the y value of the parabola’s equation to zero and solve for x. For example, if you have a parabola given by the […]
What is the mass of 656 pints of blood if the density of blood is 1060 g/ml?
To find the mass of 656 pints of blood given its density, we need to follow a few steps. First, we need to convert pints to milliliters because the density is provided in grams per milliliter (g/ml). 1 pint is approximately 473.176 milliliters. Therefore, to convert 656 pints to milliliters: 656 pints × 473.176 ml/pint […]
Which of the following terms appear in the expansion of xy10? The letter ‘a’ in each term represents a real constant.
In the expansion of the expression xy10, we can look for the different terms that arise from its expansion using the binomial theorem. However, this particular expression isn’t a binomial in the traditional sense of having two addends. It consists of two variables: x and y. For the sake of expansion, if we consider xy10 […]
How do you solve the equation x² – 16x + 60 = 12 by completing the steps?
To solve the equation x² – 16x + 60 = 12, we first need to rewrite it in standard form. This means we will set the equation to zero. 1. **Rearranging the equation**: Subtract 12 from both sides: x² – 16x + 60 – 12 = 0 This simplifies to: x² – 16x + 48 […]
What is the 50th term of the sequence that begins 4, 2, 8, 14?
To find the 50th term of the sequence, we first need to identify the pattern in the given numbers: 4, 2, 8, 14. Let’s examine the differences between consecutive terms: 2 – 4 = -2 8 – 2 = 6 14 – 8 = 6 We see that the first term decreases by 2, but […]