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To solve the equations h = 5x + 3 and j = 2x, we need to find the values of h and j in terms of x first. Then we’ll look to find the total h + j and check if it equals 2. Let’s break it down step-by-step: Substituting for j: From the second … Read more

To solve the given problem, we will use the concept of related rates, which is a key idea in calculus. We have two functions, x(t) and y(t), that are dependent on a parameter t. The task includes finding the rates of change of these functions at specific points. a) Finding dy/dt when dx/dt = 3 … Read more

Solving the Equation: 7/8 – 1/x = 3/4 To solve the equation 7/8 – 1/x = 3/4, let’s break it down step by step. Step 1: Isolate the Fraction First, we want to isolate the fraction involving x. To do this, we can subtract 3/4 from both sides of the equation: 7/8 – 1/x – … Read more

To find the value of x in the equation 3xy = 18 when y = 27, we can begin by substituting the value of y into the equation. So, substituting y = 27 in the equation: 3x(27) = 18 This simplifies to: 81x = 18 Next, we need to isolate x. We do this by … Read more

To calculate the total volume of the figures with the given volumes of 15 cm³, 33 cm³, 45 cm³, and 54 cm³, you simply need to add all of these volumes together. Here’s a detailed breakdown of the calculation: Start with the individual volumes: Volume 1: 15 cm³ Volume 2: 33 cm³ Volume 3: 45 … Read more

Converting a ratio into a fraction is a straightforward process that can be broken down into a few simple steps. A ratio compares two quantities, showing how much of one thing there is compared to another. Here’s how you can do it: Understand the Ratio: A ratio is typically presented in the form A:B, where … Read more

A polynomial with a degree of 4 is an expression that includes a variable raised to the fourth power, along with non-negative integer powers of that variable, and possibly constant terms. The general form of such a polynomial can be expressed as: P(x) = ax4 + bx3 + cx2 + dx + e In this … Read more

Understanding Parallelograms and Their Properties Parallelograms are a special category of quadrilaterals, which are polygons with four sides. They have two pairs of opposite sides that are both equal in length and parallel. However, not all properties that apply to one type of parallelogram apply universally to all parallelograms. Here are some key characteristics of … Read more

To calculate how much Wendy takes home after taxes, we first need to determine how much is deducted for taxes. Wendy’s total pay is $42,300, and 19% of this amount is taken for taxes. Here’s how we can calculate it step-by-step: Calculate the amount deducted for taxes: Convert the percentage from a percentage to a … Read more

To find the equation of a circle, we use the standard form of the circle’s equation, which is: (x – h)2 + (y – k)2 = r2 Where: (h, k) is the center of the circle. r is the radius of the circle. In your case, the center of the circle is given as (2, … Read more