To find the area of a triangle, you can use the following formula: Area = (base × height) / 2 In this case, you have: Base = 9 inches Height = 14 inches Now, plug in the values: Area = (9 inches × 14 inches) / 2 Calculating this: Area = (126 inches²) / 2 … Read more
To evaluate the double integral d = ˆ{x^2 + 6y} dA, where the region of integration is bounded by y = x, y = x^3 and x = 0, we first need to determine the limits of integration by finding the points of intersection of the curves. 1. **Finding Points of Intersection:** To find where … Read more
The area of a trapezoid can be calculated using the following formula: Area = (1/2) * (b1 + b2) * h Where: b1: Length of the first base (the top side of the trapezoid). b2: Length of the second base (the bottom side of the trapezoid). h: Height of the trapezoid (the perpendicular distance between … Read more
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