If f(x) = 7 – 4x and g(x) = 12x, what is the value of f(g(5))?
To find the value of f(g(5)), we need to calculate g(5) first and then use that result to evaluate f. Starting with g(x): g(x) = 12x Substituting 5 into g: g(5) = 12 * 5 = 60 Now that we have g(5), we can find f(g(5)) or f(60): f(x) = 7 – 4x Substituting 60 […]
What is the x coordinate of the vertex of the parabola whose equation is y = 3x² + 9x?
To find the x-coordinate of the vertex of the parabola given by the equation y = 3x² + 9x, we can use the formula for the vertex of a parabola in standard form, which is y = ax² + bx + c. The x-coordinate of the vertex can be calculated using the formula: x = […]
How do you simplify the expression 5x² + 3x + 4 – 5x² + 5x – 1?
To simplify the expression, we start by combining like terms. The given expression is: 5x² + 3x + 4 – 5x² + 5x – 1 First, observe that the terms 5x² and -5x² cancel each other out: (5x² – 5x²) + 3x + 5x + 4 – 1 = 0 + 3x + 5x + […]
Express the product of 2x², 7x, 10, and x⁵ in standard form
To express the product of the terms 2x², 7x, 10, and x⁵ in standard form, we start by multiplying all the coefficients and combining the powers of x. First, multiply the coefficients: Coefficients: 2, 7, and 10 The product of the coefficients is: 2 * 7 * 10 = 140 Next, we combine the exponents […]
Find the General Solution of the Given Differential Equation: cos(x) dy/dx + sin(x) y = 1
To solve the differential equation cos(x) dy/dx + sin(x) y = 1, we can rearrange it into a standard form. The equation can be expressed as: dy/dx + (sin(x)/cos(x)) y = 1/cos(x) This form resembles a first-order linear ordinary differential equation: dy/dx + P(x) y = Q(x) where: P(x) = sin(x)/cos(x) = tan(x) Q(x) = […]
Which of the following quadratic equations has the solution set 12, 5? Select all that apply.
To determine which quadratic equations have the solution set {12, 5}, we first need to recognize the properties of quadratic equations and their roots. A quadratic equation can be expressed in the standard form: ax² + bx + c = 0 According to Vieta’s formulas, if the roots of the quadratic equation are r₁ and […]
Find 10 Partial Sums of the Series: Σ (from n=1 to ∞) 16/(3^n)
To find the first 10 partial sums of the series Σ (from n=1 to ∞) 16/(3^n), we first identify that this is a geometric series. A geometric series is a series of the form Σ (from n=0 to ∞) a*r^n, where a is the first term and r is the common ratio. In our case: […]
What is the surface area of a cylinder with a base radius 4 and height 5?
To find the surface area of a cylinder, we use the formula: Surface Area = 2πr² + 2πrh Where r is the radius of the base, and h is the height of the cylinder. In this case, the base radius (r) is 4, and the height (h) is 5. Plugging these values into the formula […]
In the equation a pr² p π is a?
The equation a pr² p π represents the mathematical expression related to the area of a circle. Here, ‘p’ is typically used to denote a constant (like the density or pressure in physics) and ‘r’ stands for the radius of the circle. When we look at the components: a: This may represent a variable that […]
Find the Image Vertices for a Dilation with Center (0,0) and a Scale Factor of 4
To find the image vertices after a dilation, we need to apply the dilation transformation to each of the original vertices. A dilation with a center at (0,0) and a scale factor of 4 means that each vertex will be moved away from the origin by a factor of 4. The formula for dilating a […]