[FREE] Find the focus and directrix of the following parabola: (y-2)^2 . . . To find the focus and directrix of the given parabola, we start with the equation: (y − 2)2 = 16(x − 7) This is a parabola in the form (y − k)2 = 4p(x − h), which indicates a parabola that opens to the right Step 1: Identify the vertex The vertex form of the equation (y − k)2 = 4p(x −h) tells us that the vertex of the parabola is at the point (h,k) In our equation: h = 7 k = 2
[FREE] Simplify the expression: -2 x^3\left (8 x^4+2\right) A. -16 x^7 . . . Certainly! Let's simplify the expression step-by-step: We have the expression: −2x3(8x4 + 2) Let's distribute the −2x3 across the terms inside the parentheses: First, distribute −2x3 to 8x4: −2x3 × 8x4 = −16x3+4 = −16x7 Next, distribute −2x3 to 2: −2x3 × 2 = −4x3 Now, combine these results to get the simplified expression: −16x7 − 4x3 Thus, the simplified expression is
[FREE] Solve for $x$ in the equation $x^2 - 14x + 31 = 63$. A. $x = -16 . . . To solve the equation x2 −14x + 31 − 63 = 0, let's start by simplifying it: Combine the constant terms: 31 − 63 = −32 So, the simplified equation is: x2 −14x − 32 = 0 We will solve this quadratic equation by using the quadratic formula The quadratic formula is: x = 2a−b ± b2 −4ac For the equation x2 − 14x − 32 = 0, we identify the coefficients as: a = 1 b = −14 c = −
Answer two questions about the following rational multiplication: To solve the given rational multiplication and identify the values to exclude from the domain, let's go through the problem step by step = = Summary of Excluded Values: From our calculations, the values x = −2 and x = 7 make the denominator zero Thus, these values must be excluded from the domain Therefore, the correct options to exclude from the domains are: B (x = −2) and D (x = 7)
[FREE] Convert the equation y - 4 = 16(x - 7) to standard form . . . To convert the equation y – 4 = 16 (x – 7) to standard form, distribute the 16 and rearrange the equation so that the variables are on one side and the constant terms are on the other side Finally, combine like terms