🧮 algebra

1. لنبدأ بفهم المعطيات في السؤال. لدينا طول ٦٢ متر وطول آخر ٣٦ متر، ومطلوب حساب الجبر الناتج المرتبط ب ك س م.

1. **State the problem:** Simplify the expression $\sqrt{20} - \sqrt{5}$. 2. **Factor each square root:**

1. We are asked to simplify the expression \(\sqrt{75} + \sqrt{12}\).\n2. Start by simplifying each square root separately.\n\n\(\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \

1. Stating the problem: Simplify the expression $\sqrt[3]{27} - \sqrt{3}$.\n\n2. Evaluate each root separately:\n- $\sqrt[3]{27}$ is the cube root of 27. Since $27 = 3^3$, we have

1. Stated problem: Simplify the expression $2\sqrt{18} + 4\sqrt{2}$. 2. Simplify the square root $\sqrt{18}$. Since $18 = 9 \times 2$, we can write:

1. The problem is to simplify the expression $5\sqrt{12} - 3\sqrt{3}$.\n\n2. First, simplify the square root terms. Note that $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt

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.