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To find the angles M1 and M3 in a kite, even when the diagram is not drawn to scale, you need to apply some basic properties of kites and the geometric relationships that apply to them. Here’s how you can do it step by step: Understand the Properties of a Kite: A kite is a … Read more

To calculate the sales tax rate, you can use the following formula: Sales Tax Rate = (Sales Tax / Cost of Item) x 100% In this case, the cost of the shirt is $3,499, and the sales tax is $210. Plugging these values into the formula gives us: Sales Tax Rate = ($210 / $3,499) … Read more

When reflecting a point across the x-axis, we only change the sign of the y-coordinate. The x-coordinate remains the same. For the point (1, 6): The x-coordinate is 1. The y-coordinate is 6. After reflection, it becomes -6. Thus, the new coordinates after reflection across the x-axis will be: (1, -6) So, the coordinates of … Read more

Finding the x-coordinates of the solutions To solve for the x-coordinates of the solutions to the system of equations given by: x² + y² = 36 y = x + 6 we can substitute the second equation into the first. Here are the steps: Start with the first equation: x² + y² = 36. Next, … Read more

To find the equation of a line that is perpendicular to the given line and passes through the specified point, follow these steps: Step 1: Determine the slope of the original line The given line’s equation is in the slope-intercept form: y = mx + b, where m is the slope. Here, the slope of … Read more

The conjugate of a complex number is obtained by changing the sign of its imaginary part. A complex number is typically written in the form a + bi, where a is the real part and b is the imaginary part. For the complex number 6 + 7i, the real part is 6 and the imaginary … Read more

The axis of symmetry for a quadratic function is a vertical line that runs through the vertex of the parabola represented by the equation. For the general form of a quadratic equation, y = ax² + bx + c, the axis of symmetry can be found using the formula: x = -rac{b}{2a} In your case, … Read more

To determine the value of g(f(2x)), we start with the definitions of the functions given: Function f(x) = 4×2 Function g(x) = 5x We will first calculate f(2x): f(2x) = 4(2x)2 = 4(4×2) = 16×2 Next, we take this result and substitute it into the function g(x): g(f(2x)) = g(16×2) = 5(16×2) = 80×2 Therefore, … Read more

The quadratic equation you’re looking at is given by: 0x² + 6x + 8 = 0 However, it’s important to point out that the term ‘0x²’ essentially means that the equation is not a quadratic equation in the conventional sense, as any expression multiplied by zero yields zero, which leads us to focus on the … Read more

To convert grams and milligrams to kilograms, we need to remember the following unit conversions: 1 kilogram (kg) = 1,000 grams (g) 1 kilogram (kg) = 1,000,000 milligrams (mg) Now, let’s break down the conversion: 1. **Convert grams to kilograms:**       87 grams = 87 / 1,000 = 0.087 kilograms. 2. **Convert milligrams … Read more