🧮 algebra

1. The problem asks to identify the polynomial equation $p(x)$ for a graph with zeros at $x=-3$, $x=-\frac{1}{2}$, and $x=3$, with the graph behavior described at each zero. 2. Fro

1. We are given the function $f(x) = \frac{3}{2 - 7x}$ and need to determine its inverse function $f^{-1}(x)$ from the options. 2. To find the inverse, start by setting $y = \frac{

1. The problem asks us to find an equation for the polynomial $p(x)$ whose graph behaves like a cubic function passing through points (0,0) and (2,0). 2. From the graph description

1. **Stating the problem:** We are given a polynomial \(p\) graphed on an \(x y\) coordinate plane. It passes through zeros at \(-3.5, 0\), \(0, 0\), and \(3, 0\).

1. The problem asks to simplify the expression $2x - x$. 2. Both terms have the variable $x$, so we can combine them by subtracting the coefficients: $2 - 1 = 1$.

1. The problem is to simplify the expression $-1 \times x$. 2. Multiplying $-1$ by $x$ means taking the opposite (negative) of $x$.

1. The given expression is $2 + 16 \div 2 + 6 = 4$ and we want to place one set of brackets to make this equation true. 2. First, let's understand the original expression without b

1. **State the problem:** We have digits 1, 2, 3, 4, 8 and need to fill in the blanks in the equation $$\frac{\_}{7} = \frac{\_\_}{\_\_}$$

1. **Problem:** Find the point on the curve $y = \sqrt{x} + 3$ closest to the origin $(0,0)$. 2. The distance squared from the origin is $D^2 = x^2 + y^2 = x^2 + (\sqrt{x} + 3)^2 =

1. The problem asks us to simplify the given polynomials: $$x^3 - 3a^2 + 3a - 1$$

1. **State the problem:** Given $a = \frac{16}{3}$ and $b = \frac{7}{3}$, find the value of $\frac{a^3 + b^3}{a + b} \times ab$. 2. **Recall the algebraic identity:** The sum of cu

1. We start by simplifying the first expression: $$25^2 - 50 \cdot 21 + 21^2$$ 2. Calculate each term:

1. We start with the given equation: $a = \frac{1}{a} + 2$. 2. Multiply both sides by $a$ to eliminate the denominator:

1. The problem presents two tables of numbers with some missing entries and requires understanding and interpreting the values given. 2. First table analysis (2 rows, 6 columns):

1. The problem involves transformations of the curve $y = f(x)$ with a turning point at $(-6,-4)$ and a graph transformation of $y = g(x)$ to $y = 2g(x)$. 2. (a)(i) For $y = f(x) +

1. The problem asks how to solve part b and sketch its graph. 2. Since part b is not explicitly given, let's clarify or define the function or equation for part b.

1. **Stating the problem:** We are given a function $y=f(x)$ with one turning point at $(-6,-4)$. We need to find the coordinates of the turning point for the transformed functions

31. Find $f \circ g$ and $g \circ f$ and their domains for $f(x)=x^2$ and $g(x)=\sqrt{1-x}$. 1. Compute $f \circ g$: \\ $f(g(x)) = (\sqrt{1-x})^2 = 1-x$.

1. We are asked to find the composite function $$f \circ g \circ h$$ for two sets of functions. **Problem 35:**

1. The problem asks for the possible values of the remainder when a positive integer is divided by 4. 2. When dividing by 4, the possible remainders are the integers from 0 up to o

1. We are asked to expand and simplify the expression **$(3a + 4b)(3a - 1b)$**. 2. Use the distributive property (FOIL method) to multiply each term: