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To find the midpoint of a line segment defined by two endpoints, we can use the midpoint formula. The formula is as follows: Midpoint (M) = ( (x1 + x2) / 2, (y1 + y2) / 2 ) In this formula, (x1, y1) are the coordinates of the first endpoint (A), and (x2, y2) are … Read more

To find the vertex of the graph of the equation y = 4x + 22 – 5, we first need to rewrite the equation correctly. This equation can appear a bit confusing at first. Let’s consider what we have: Firstly, the equation simplifies to: y = 4x + 17 In this case, we can see … Read more

To convert the repeating decimal 3.24̅ (where ’24’ is the repeating part) into a rational number, we can follow these steps: Identify the decimal: The decimal can be expressed as 3.24242424… Separate the whole number: The integer part is 3, and we will focus on the decimal part 0.242424… Set up an equation: Let x … Read more

To find the exact length of a polar curve defined by the equation r = 0.8e^{2θ}, we need to use the formula for the length of a polar curve: L = ∫ (from α to β) √(r^2 + (dr/dθ)^2) dθ Here, r is the polar coordinate function, dr/dθ is the derivative of r with respect … Read more

To determine the radius of a circle given its area, we can use the formula for the area of a circle: A = πr² where A is the area and r is the radius. We are given that the area A is 154 cm². To find the radius, we need to rearrange the formula to … Read more

In the booster club you mentioned, there are a total of 128 members. Out of these, 18 are male members. This means that the number of male members in the club is 18. To clarify, in this situation, we simply identify that the count of male members is directly provided. Therefore, there is no need … Read more

To understand the expression h(f(x)) when h(x) is the inverse of f(x), we need to delve into the definitions of inverse functions. An inverse function essentially ‘reverses’ the effect of the original function. Specifically, if y = f(x), then we can say that x = h(y), where h is the inverse of f. Now, let’s … Read more

To find equivalent fractions, we utilize the Multiplicative Property of Equality. This property states that if you multiply both sides of an equation by the same non-zero number, the equality remains true. In the context of fractions, we can apply this property to the numerator and denominator of a fraction. For example, let’s say we … Read more

When dealing with polynomial functions that have real coefficients, a key property to remember is how complex and irrational roots behave. Given that one of the roots of the polynomial is an irrational number, in this case, √7, we need to consider whether it has a conjugate that is also a root. For any polynomial … Read more