🧮 algebra

1. State the problem: Evaluate $2c + 3d$ when $c = 3$ and $d = 6$. 2. Substitute the given values into the expression: $2c + 3d = 2\cdot 3 + 3\cdot 6$.

1. Let's clarify what a straight line across means in the context of algebra. Typically, a straight horizontal line is represented by $y = c$, where $c$ is a constant. 2. This mean

1. The problem is to draw the line given by the equation $y=2$ on a Cartesian coordinate plane. 2. The equation $y=2$ represents a horizontal line where the $y$-value is constantly

1. The problem is to simplify the expression $\sqrt{x}9$. 2. Note that multiplication is implied between $\sqrt{x}$ and $9$, so the expression can be rewritten as $9\sqrt{x}$.

1. The original curve is given by $y = f(x)$ and it has a minimum point at coordinates $(5, -4)$. 2. The new curve is $y = f(x + 7)$, which represents a horizontal shift of the ori

1. The problem is to write down the coordinates, typically meaning to represent points in a plane or space using their coordinate values. 2. Coordinates are usually expressed as pa

1. The original curve is given by $y = f(x)$, which has a minimum point at the coordinates $(5, -4)$. This means the function $f(x)$ reaches its minimum value of $-4$ when $x = 5$.

1. Problem: Given the graph of $y=f(x)$ with points $A, B, C, D, E$ and the transformation $g(x)=f(x)+2$, find the coordinates of the image points $A', B', C', D', E'$. 2. Explanat

**Problem:** A gardener has two adjacent square plots with sides $x$ m and $y$ m, and the total boundary perimeter is 22 m. 1. **Show that $y = 11 - 2x$**

1. Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. 2. It involves expressions, equations, and formulas where letters repres

1. The problem asks to solve for the logarithm of the product $2 \times 103$. 2. We use the logarithm product property: $\log(ab) = \log a + \log b$.

1. The problem asks to evaluate $2 \times 103$ using a logarithm table. 2. First, calculate the logarithm of each number: $\log(2)$ and $\log(103)$.

1. **Stating the problem:** Factorise the expression $$2ab + 3b$$. 2. **Identify common factors:** In both terms, the variable $$b$$ appears as a common factor.

1. **State the problem:** Expand and simplify the expression $$3(2x + 1) + 2(x + 3)$$. 2. **Expand each term:** Use the distributive property $$a(b+c) = ab + ac$$.

1. **State the problem:** Factorize the expression $7ab + a$ completely. 2. **Identify common factors:** Look for the greatest common factor (GCF) between the two terms. The terms

1. **State the problem:** Sam invested 7175 for 4 years and received 8250. We need to find the simple interest rate per annum, rounded to two decimal places. 2. **Recall the formul

1. **State the problem:** Expand the expression $$(m + 5)(m - 8)$$. 2. **Apply the distributive property (FOIL method):**

1. **State the problem:** Expand and simplify the expression $$3(2x + y) + 4(x + 2y)$$. 2. **Expand the parentheses:** Multiply each term inside the parentheses by the factor outsi

1. Stated problem: Simplify the expression $5(x + y) + 3(x - y)$. 2. Distribute the constants inside each parenthesis:

1. We are given the quadratic equation $$x^2 + bx + 24 = 0$$ and one root is $$1\frac{1}{2} = \frac{3}{2}$$. 2. The quadratic equation can be written as $$x^2 + bx + 24 = 0$$. If $

1. ננסח את הנתונים עבור חומר ב'. ההכמות קטנה בצורה מעריכית לפי הנוסחה: $$Q(t)=Q_0(1-r)^t$$ כאשר $r$ הוא שיעור הירידה השנתי. 2. נתון כי מ-300 גרם נשארו 120 גרם לאחר 4 שנים: