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Finding the Value of X in Parallelogram RSTU In a parallelogram, there are certain properties that help us find unknown variables, such as the value of x in this case. Properties of a Parallelogram Opposite sides are equal in length. Opposite angles are equal. Consecutive angles are supplementary (they add up to 180 degrees). The … Read more

To find an equivalent form of the compound inequality 44 < 2x < 88, we need to isolate the variable x. We can do this by dividing all parts of the inequality by 2. Here’s the step-by-step breakdown: Start with the original compound inequality: 44 < 2x < 88. Divide each part of the inequality … Read more

To evaluate the expression x + 3y using the given values, we start by substituting the values of x and y into the expression. We know that x = 3 And y = 2 Now we can substitute these values into the expression: x + 3y = 3 + 3(2) Next, we calculate the value … Read more

To determine how far a man walks in one hour if he walks 10 miles in x hours, we can use a simple calculation. The distance he covers in one hour can be found by dividing the total distance by the total time taken. Here’s the formula: Distance per hour = Total distance / Total … Read more

The angles in a quadrilateral always add up to 360 degrees. This rule applies regardless of the type of quadrilateral, whether it’s a square, rectangle, trapezoid, rhombus, or any other four-sided shape. To understand why this is the case, consider the process of dividing a quadrilateral into two triangles. By drawing a diagonal line from … Read more

To find the solution to the system of equations: 1. 3x + 2y + z = 7 2. 5x + 5y + 4z = 3 3. 3x + 2y + 3z = 1 we will use the method of substitution or elimination. Let’s start with the first equation (1) and express z in terms of … Read more

To find the centroid of the region bounded by the curves y = x³, y = 10, and y = 0, we first need to identify the area of the region and then calculate the coordinates of the centroid. Step 1: Identify the Curves y = x³ is a cubic function that increases from the … Read more

To find all the zeros of the polynomial function f(x) = x^4 – 32x^2 + 144 given that 2i is a zero, we can follow these steps: Use the Given Zero: Since 2i is a zero, its complex conjugate, -2i, must also be a zero because the coefficients of the polynomial are real. Factor the … Read more

Estimating Maximum Error in Surface Area To determine the maximum error in the surface area of a sphere, we can use differentials. First, we need to establish a relationship between the measurements of the circumference and the surface area. Step 1: Formulas The circumference (C) of a sphere is given by the formula: C = … Read more

An equilateral triangle is a special type of triangle where all three sides are of equal length. Because all the sides are the same, all three internal angles are also equal, measuring 60 degrees each. This symmetry gives the equilateral triangle its distinct appearance. Visually, an equilateral triangle appears as a perfectly balanced shape. When … Read more