To solve for x in the equation 5x + 10 = 30 + 15x, you need to isolate x on one side of the equation. Here’s a step-by-step approach: Start with the original equation: 5x + 10 = 30 + 15x Move the terms involving x to one side: Subtract 15x from both sides to … Read more
To understand what you need to divide in order to obtain the mathematical constant pi (π), it’s essential to start with its definition. Pi is defined as the ratio of a circle’s circumference to its diameter. This means that if you have a circle and you measure its circumference (the distance around the circle) and … Read more
To find the probability of getting heads on both flips when you flip a coin twice, we first need to understand the basic principles of probability. A fair coin has two sides: heads (H) and tails (T). When you flip the coin, there are two possible outcomes for each flip. So, when flipping the coin … Read more
Simplifying the Expression 1 – cos(x1)cos(x) The expression we want to simplify is 1 – cos(x1)cos(x). To do this, we’ll employ a useful trigonometric identity. Using the Product-to-Sum Identities One effective method for simplifying products of cosine functions is to use the product-to-sum identities. Specifically, we can express the product of cosines as: cos(A)cos(B) = … Read more
To evaluate the expression 1 – sin(x) – sin(x), we start by simplifying it. First, notice that the expression can be simplified as: 1 – sin(x) – sin(x) can be rewritten as 1 – 2sin(x). So the expression now simplifies to: 1 – 2sin(x) This expression expresses the value based on the sine of the … Read more
To find the solution set of the system of equations 3x + 2y = 7 and y = 3x + 11, we can use the substitution method. First, let’s start with the second equation: y = 3x + 11 This equation expresses y in terms of x, making it convenient to substitute this expression for … Read more
The commutative property of multiplication states that changing the order of the factors in a multiplication operation does not change the product. In simpler terms, if you multiply two numbers, the result will remain the same regardless of the order in which you multiply them. An example of this property can be illustrated with the … Read more
The square root of m6 can be determined by utilizing the properties of exponents in algebra. When you take the square root of a variable raised to an exponent, you apply the rule that states: √(an) = an/2 In your case, you have m6. So, applying the rule: √(m6) = m6/2 = m3 Thus, the … Read more
The expression 6x² + 7x + 10 is a quadratic equation in standard form, where: 6 is the coefficient of the x² term. 7 is the coefficient of the x term. 10 is the constant term. To analyze it, we can evaluate its properties: Shape: The graph of a quadratic function is a parabola. Since … Read more
To determine the slope of a line that is perpendicular to another given line, you must first find the slope of the original line. Every line can be represented mathematically by the equation of a line in the form of y = mx + b, where m represents the slope and b represents the y-intercept. … Read more