What is the Rule for Subtracting Integers?
Subtracting integers follows a simple rule that can be understood through a few key concepts. When you subtract one integer from another, you’ll want to keep in mind the signs (positive or negative) of the integers involved. Here’s the basic rule: to subtract an integer, you will actually add its opposite. This means that instead […]
Find the Area of the Following Figure Attached
To find the area of the given figure, we first need to identify the shape and any dimensions provided. Assuming the figure is a polygon, such as a rectangle, triangle, or circle, we will use the appropriate formula for each shape. For a rectangle, the area can be calculated using the formula: Area = length […]
What is the value of y in triangle MRN created when an equilateral triangle is folded in half?
When an equilateral triangle is folded in half, it creates two congruent right triangles. In the case of triangle MRN, the folding creates a right triangle where the original triangle’s base becomes one leg of the right triangle, and the height forms the other leg. The hypotenuse is the original side of the equilateral triangle. […]
What is the probability of randomly choosing a white chip, not replacing it, and then randomly choosing another white chip?
To determine the probability of choosing two white chips in succession from a bag containing 4 white chips and 6 black chips, we can follow these steps: Initially, there are a total of 10 chips in the bag (4 white and 6 black). 1. **Probability of the first white chip**: The probability of drawing a […]
A box has sides of 10 cm, 82 cm, and 35 cm. What is its volume?
To calculate the volume of a box (or rectangular prism), you can use the formula: Volume = length × width × height In this case, the dimensions of the box are: Length = 82 cm Width = 10 cm Height = 35 cm Now, plug the values into the formula: Volume = 82 cm × […]
Which number comes next in this series 1, 64, 1, 32, 1, 16, 1, 8, 1, 4, 1, 2?
The next number in the series is 1. This series alternates between the number 1 and a sequence of decreasing powers of 2. The pattern is as follows: 1 (constant) 64 (which is 26) 1 (constant) 32 (which is 25) 1 (constant) 16 (which is 24) 1 (constant) 8 (which is 23) 1 (constant) 4 […]
Evaluate the Summation of 20 times 05 to the n minus 1 power from n equals 3 to 12
To evaluate the summation of the expression 20 * 0.5^(n – 1) from n = 3 to n = 12, we start by setting up the summation: ∑ (from n=3 to n=12) 20 * 0.5^(n – 1) This means we will calculate the value for each integer n from 3 to 12 and then sum […]
Use the Rational Root Theorem to List All Possible Rational Roots for the Equation x^3 – 2x + 9 = 0
The Rational Root Theorem states that any rational solution, or root, of a polynomial equation can be expressed as a fraction p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. For the given polynomial equation x^3 – 2x + 9 = 0, let’s identify the […]
What is the simplest form of the quotient 4 sqrt 810 / 4 sqrt 2?
To simplify the expression 4 sqrt 810 / 4 sqrt 2, we start by canceling out the common factor of 4 in the numerator and the denominator: 4 sqrt 810 / 4 sqrt 2 = sqrt 810 / sqrt 2 Next, we can use the property of square roots that states: sqrt(a) / sqrt(b) = […]
How many solutions does the linear system 6x + 2 and 12x + 2y = 4 have?
To determine how many solutions the linear system has, we first need to analyze the equations given. The equations seem to be linear, but let’s clarify the system. If we assume that the equations are meant to be: 6x + 2 = 0 12x + 2y = 4 We can rearrange these equations to find […]