🧮 algebra

1. **Problem A: Multiply and simplify** Given expressions:

1. **Problem ①:** A farm stand sells oranges in 3-lb bags for 3.75. We want to find an equation for cost $c$ in terms of pounds $p$. Since a 3-lb bag costs 3.75, cost per pound is

1. Multiply and simplify $$\frac{9r^3 - 54r^2}{9r^2 + 45r} \cdot \frac{9r^2 + 9r}{9r^3 - 54r^2}$$ Factor expressions:

1. **Multiply and simplify** A1. Multiply \(\frac{9r^3 - 54r^2}{9r^2 + 45r} \cdot \frac{9r^2 + 9r}{9r^3 - 54r^2}\).

1. The problem asks to identify the type of point the function $f(x) = x^2$ has at $x=0$. 2. Recall the function $f(x) = x^2$ is a parabola opening upward.

1. Problem 5: Find the values of constant $k$ for which $(2k-1)x^2 + 6x + k + 1 = 0$ has real roots. 2. For real roots, discriminant $\Delta \geq 0$.

1. Problem statement. The price of a pen was 2 less in February than in March and 2 more in April than in March.

1. Stating the problem: Solve the equation $$(2x^2 - 3x)^2 - 2x^2 + 3x = 2.$$\n\n2. Expand the square term: $$(2x^2 - 3x)^2 = (2x^2)^2 - 2\times 2x^2 \times 3x + (3x)^2 = 4x^4 - 12

1. We are asked to find the term independent of $x$ in the expansion of $\left(\frac{1}{2x} - \frac{x^2}{3}\right)^9$. 2. Consider the general term in the binomial expansion of $(a

1. The problem states: The variable $x$ and $y$ are inversely proportional, which means $$x \propto \frac{1}{y}$$

1. First, write down the problem clearly: Calculate $\frac{7}{2} \div (2 - (-2))$. 2. Simplify inside the parentheses: $2 - (-2) = 2 + 2 = 4$.

1. The problem asks for the x-coordinate where the curve $y = x^2 - 6x + 7$ has a local minimum. 2. Since this is a quadratic function with leading coefficient $1 > 0$, it opens up

1. **Problem statement:** Given the prices of pens and the amounts sold in February and April, we need to find expressions for the number of pens sold and calculate quantities base

1. The problem is to find the value of $|1|$. 2. The absolute value function $|x|$ gives the distance of $x$ from zero on the number line, so it is always non-negative.

1. The problem states a quadratic function $f(x) = ax^2 + bx + 2$ has a critical point at $(1,4)$. 2. A critical point occurs where the derivative of $f(x)$ equals zero.

1. **State the problem:** We have an increasing function $f$ on its domain. We want to know which of the following functions is not necessarily increasing on its domain. 2. **Analy

1. The problem asks for the value of the 4th root of -81, which means finding a number $x$ such that $$x^4 = -81.$$ 2. Recall that raising any real number to the 4th power results

1. The problem is to compute the value of the expression $$\frac{1}{12} + \frac{2}{6} - \frac{2}{8}$$. 2. First, find a common denominator for the fractions. The denominators are 1

1. The problem asks to solve or simplify an expression using BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction). Since no specific expression for "question 2.

1. The problem is to divide the polynomial $x^3 - 2$ by $x^2 + 1$ using long division. 2. Set up the long division: divide the first term of the dividend $x^3$ by the first term of

1. Given $f(x) = x^2 + 3x - 4$: 1. a) Find $f(0)$: