If f(g(x)) = 3x² + 2x + 1 and g(x) = 2x + 2, what is f(x)?
To find f(x), we first need to express f in terms of g(x). We’re given that f(g(x)) = 3x² + 2x + 1. Knowing that g(x) = 2x + 2, we can substitute g(x) into the equation. Let’s set y = g(x), which gives us: y = 2x + 2. We can solve for x […]
Which of the following is an equivalent form of the compound inequality 44 < 2x < 88?
To solve the compound inequality 44 < 2x < 88, we can break it down into two separate inequalities: 44 < 2x and 2x < 88. Starting with the first inequality, we divide both sides by 2: 44/2 < x ⇒ 22 < x Now, let’s solve the second inequality: 2x < 88 Again, dividing […]
Use the Number Line and Add the Following Integers
To add integers using a number line, you first need to understand where each integer lies on the line. Let’s take an example to illustrate this. Suppose we want to add 3 + 2. Start at the number 3 on the number line. Since we are adding 2, move two spaces to the right from […]
In the kite AC 10 and BD 6, what is the area of kite ABCD?
To find the area of kite ABCD, we can use the formula for the area of a kite, which is given by: Area = (d1 × d2) / 2 where d1 and d2 are the lengths of the diagonals. In this case, we know: Diagonal AC (d1) = 10 Diagonal BD (d2) = 6 Now, […]
What is the vertex of the function f(x) = 1/2 x² + 3x + 2?
To find the vertex of the quadratic function f(x) = 1/2 x² + 3x + 2, we can use the vertex formula. For a quadratic function in the form f(x) = ax² + bx + c, the x-coordinate of the vertex can be found using the formula: x = -b/(2a) In this function, the coefficients […]
What is the vertex of the absolute value function defined by f(x) = |x – 2| + 4?
The vertex of the absolute value function f(x) = |x – 2| + 4 can be determined by analyzing the expression inside the absolute value and the constant added to it. In this case, the function is defined as f(x) = |x – 2| + 4. The expression inside the absolute value, x – 2, […]
In which quadrant is the number 14 + 5i located on the complex plane?
The complex number 14 + 5i is located in the first quadrant of the complex plane. In the complex plane, the x-axis represents the real part of the complex number and the y-axis represents the imaginary part. Here, the real part is 14, which is positive, and the imaginary part is 5, which is also […]
Explain How to Write an Equivalent Expression Using the Associative Property for 2 + 11y
The associative property allows us to group numbers in different ways when adding or multiplying, without changing the outcome. This means we can rearrange the terms in an expression to create an equivalent expression. For the expression 2 + 11y, we can apply the associative property by grouping the terms. While addition is straightforward, we […]
Which number line represents the solution to 25 < 12x < 65 < 32x?
To solve the inequality 25 < 12x < 65 < 32x, we will break it down into two parts: the first part is 25 < 12x, and the second part is 65 < 32x. Step 1: Solve the first inequality (25 < 12x) Divide both sides by 12: x > 25/12 Calculating 25/12 gives us […]
What is the area of a triangle with a base length of 4 units and a height of 5 units?
To find the area of a triangle, you can use the formula: Area = (Base × Height) / 2 In this case, the base length is 4 units and the height is 5 units. Plugging these values into the formula gives: Area = (4 × 5) / 2 Area = 20 / 2 Area = […]