To find the value of x when given cos(24°) and rounding it to the nearest tenth, we need to first understand what cosine means in this context. In trigonometry, the cosine function relates the angle of a right triangle to the ratios of its adjacent side over the hypotenuse. However, if we are specifically looking … Read more
To find the factors of the polynomial x² + 100x + 0, we can start by rewriting it in a simpler form. The expression can be factored as follows: First, note that the polynomial can be expressed as: x² + 100x = x(x + 100) From this expression, we can see that the polynomial is … Read more
The equation xy = 7 is a simple linear equation with two variables, x and y. To find solutions, we can isolate one variable in terms of the other. Here are two pairs of solutions: Solution 1: If we let x = 1, then we can solve for y: y = 7 / x = … Read more
To find the factors of the quadratic expression 2x² + 3x + 54, we will use the technique of factoring by grouping or the quadratic formula if necessary. First, we can identify the coefficients from the given expression: a: 2 (the coefficient of x²) b: 3 (the coefficient of x) c: 54 (the constant term) … Read more
To find out how many tickets the theatre sells, we need to calculate two-thirds of its total seating capacity of 1200 seats. The calculation can be performed as follows: First, determine what two-thirds of the total capacity is: Two-thirds (2/3) of 1200 is calculated as: 1200 x (2/3) = 1200 x 0.6667 = 800 Therefore, … Read more
In military time, 1 AM is expressed as 0100 hours. This format represents the time using a 24-hour clock, which eliminates any confusion between AM and PM. To break it down: The first two digits (01) represent the hour, indicating it is 1 o’clock in the morning. The last two digits (00) represent the minutes, … Read more
To rewrite the equation 3x + 2y = 5 in slope-intercept form, we first need to understand what slope-intercept form is. The slope-intercept form of a linear equation is given by: y = mx + b where: m is the slope of the line, b is the y-intercept (the value of y when x = … Read more
Let’s solve the equation step by step. The equation given is: 3x + 2x + 9 – 8x + x – 14 = 0 First, we will combine the like terms: Combine all the terms that involve x: 3x + 2x – 8x + x = -2x This simplifies our equation to: -2x + 9 … Read more
To find the approximate percent change when the new number is 200 and it is 400 less than the original number, we first need to establish the original number. Since the new number (200) is 400 less than the original number, we can express this relationship mathematically as: Original Number = New Number + Decrease … Read more
To determine the value of m in the context of kite fghk, we must acknowledge some properties of kites in geometry. A kite is a quadrilateral that has two distinct pairs of adjacent sides that are equal. The diagonals of a kite intersect at right angles, with one diagonal bisecting the other. Assuming we have … Read more