How to Find the Center and Radius of a Circle?
To find the center and radius of a circle, you typically need the equation of the circle or information about its diameter or circumference. If you have the equation of the circle, it usually appears in the standard form: (x – h)² + (y – k)² = r² In this equation, (h, k) represents the […]
What is the axis of symmetry for f(x) = 2x² + 4x + 5?
The axis of symmetry for a quadratic function in the standard form f(x) = ax² + bx + c can be found using the formula: x = -b / (2a) In this case, the coefficients are: a = 2 b = 4 c = 5 Plugging in the values of a and b into the […]
Find the Value of x Rounded to the Nearest Tenth
To determine the value of x, we need more context or information about the specific problem, such as a triangle, angle measurements, or equations relating to x. However, with the mention of ’25,’ it seems we might be dealing with a relationship where x is part of a set or calculated dimension. If we assume […]
How do I solve for y in the equation x + 3y = 6 and 2x + y = 10?
To solve for y in the system of equations, we have the following two equations: Equation 1: x + 3y = 6 Equation 2: 2x + y = 10 We can use the substitution or elimination method. For this explanation, we’ll use the substitution method. First, let’s solve Equation 1 for x: x = 6 […]
Find the height of a square pyramid that has a volume of 8 cubic feet and a base length of 2 feet, 6 feet, 16 feet, 12 feet, and 4 feet
To find the height of a square pyramid, we can use the formula for the volume of a pyramid, which is given by: V = (1/3) * B * h where V is the volume, B is the area of the base, and h is the height. In this case, the volume V is 8 […]
How do I write an equation for the translation of y = 5x with asymptotes x = 6 and y = 7?
To find the equation that represents the translation of the line y = 5x with given asymptotes, we start by identifying how translation works in mathematical terms. The original equation, y = 5x, is a straight line passing through the origin with a slope of 5. However, to incorporate the asymptotes x = 6 and […]
Solve the system using elimination: 2x + 2y = 8 and x + 2y = 1
To solve the system of equations using the elimination method, we start with the two equations: 1) 2x + 2y = 8 2) x + 2y = 1 First, let’s align both equations for clarity: Equation 1: 2x + 2y = 8 Equation 2: x + 2y = 1 Our goal is to eliminate one […]
What is the x coordinate of the point that lies on the line 5x + y – 7 = 0 when the y coordinate is 13?
To find the x coordinate of the point lying on the line described by the equation 5x + y – 7 = 0 when the y coordinate is 13, we need to substitute 13 for y in the equation and solve for x. Substituting y = 13 into the equation: 5x + 13 – 7 […]
Which of the following must be true for an expression to be a difference of two squares?
In order for an expression to qualify as a difference of two squares, it must be in the form of a2 – b2. This means that there are two square terms being subtracted from each other. This expression can also be factored into the product of two binomials as follows: (a – b)(a + b). […]
Find the slope and y-intercept of the line 18x + 4y = 112
To find the slope and y-intercept of the line given by the equation 18x + 4y = 112, we need to rearrange the equation into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Here are the steps: Start with the original equation: 18x […]