🧮 algebra

1. **State the problem:** We have a rectangular garden with a square flower bed of side length $x$ meters in one corner. The lawn surrounds the flower bed, and the total lawn area

1. **State the problem:** We have a triangle with base length $x - 8$ cm and height $2x$ cm. The area is given as 20 cm$^2$. We need to find the values of the base length and heigh

1. The problem is to simplify the expression $\left(2x + \frac{1}{3x}\right)^2 \times \left(2x + \frac{1}{3x}\right)^3$. 2. Notice that both terms have the same base $\left(2x + \f

1. **State the problems:** (a) Factorize the expression $$a^4 - 6a^2 + 1$$.

1. Masalah ini meminta kita untuk menentukan nilai dari bilangan berpangkat 143_. 2. Namun, informasi yang diberikan tidak lengkap karena tidak ada angka atau ekspresi yang jelas s

1. Masalah ini meminta kita menentukan nilai dari bilangan berpangkat tertentu. 2. Namun, Anda belum memberikan bilangan atau pangkat yang spesifik.

1. **Problem (a): Factorise completely** the expression $$8xy - 28y - 6x + 21$$. 2. Group terms to factor by grouping:

1. **State the problem:** Simplify the expression $$\frac{6x}{5t} \div \frac{3x^2 y}{10 t^2 s}$$. 2. **Rewrite the division as multiplication by the reciprocal:**

1. **State the problem:** Solve the absolute value inequality $$\frac{4|x + 9|}{5} < 8$$ and find the intervals for $x$. 2. **Isolate the absolute value expression:** Multiply both

1. **State the problem:** Solve the absolute value inequality $$\frac{|2x - 5|}{7} \geq 10$$ for $x$. 2. **Isolate the absolute value:** Multiply both sides by 7 to get rid of the

1. **State the problem:** Solve the absolute value inequality $$\frac{|x + 9|}{4} > 2$$ and find the values of $$x$$ that satisfy it. 2. **Isolate the absolute value expression:**

1. **State the problem:** Solve the absolute value inequality $$\frac{|x - 3|}{2} > 6$$ and find the solution intervals for $x$. 2. **Isolate the absolute value:** Multiply both si

1. **State the problem:** Solve the absolute value inequality $$|4x - 4| > 48$$. 2. **Recall the definition:** For an absolute value inequality $$|A| > B$$ where $$B > 0$$, the sol

1. The problem shows a pattern with three numbers and a circled number in the middle, producing a result on the right side of the arrow. 2. Given the example: $2\ (4)\ 9 \to 40$, w

1. State the problem: Calculate the value of the expression $3 \cdot (73) - 0.2 \cdot (19)$.\n\n2. Multiply the numbers inside the parentheses by their coefficients:\n$$3 \cdot 73

1. **State the problem:** Solve the absolute value equation $$|x - 5| = 7$$. 2. **Understand the absolute value:** The equation $$|x - 5| = 7$$ means the distance between $$x$$ and

1. **State the problem:** Solve the absolute value equation $$|2x - 4| + 3 = 15$$ for $x$. 2. **Isolate the absolute value:** Subtract 3 from both sides:

1. The problem is to simplify the expression $\frac{3}{ }$, which appears incomplete. 2. Since the denominator is missing, we cannot perform any division or simplification.

1. **State the problem:** Solve the absolute value equation $$|4x - 12| = 16$$. 2. **Understand absolute value:** The equation $$|A| = B$$ means $$A = B$$ or $$A = -B$$, where $$B

1. **Problem Statement:** For each quadratic function, find the vertex, axis of symmetry, range, maximum or minimum, intervals of increasing and decreasing, and intercepts. ---

1. **State the problem:** Solve the compound inequality $$18r + 6 < 24 \text{ OR } 7r - 9 > 12.$$\n\n2. **Solve the first inequality:** $$18r + 6 < 24.$$\nSubtract 6 from both side