🧮 algebra

1. The problem is to simplify the expression $\sqrt[4]{\frac{16}{9}}$. 2. Recall that the fourth root of a fraction is the same as the fraction raised to the power of $\frac{1}{4}$

1. **State the problem:** Solve the system of equations by substitution and check each solution. Given:

1. **State the problem:** Solve the exponential equation $$e^x + e^{-x} = 6$$. 2. **Rewrite the equation:** Let $$y = e^x$$. Then $$e^{-x} = \frac{1}{y}$$.

1. Mari kita tentukan rumus suku ke-n, suku ke-8, dan jumlah 8 suku pertama dari deret pertama: 2 + 6 + 18 + \cdots 2. Deret pertama adalah deret geometri karena setiap suku dipero

1. **Exercice 5**: Trouver toutes les matrices $B = \begin{pmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{pmatrix}$ telles que $AB = 0_{2}(\mathbb{R})$ avec $A = \begin{pmatrix}

1. Problem 2: Find the unknown sides of rectangles given one side and area. (a) Given breadth $= (x - y)$ m and area $= (x^2 - y^2)$ m$^2$.

1. The problem is to simplify or factor the quadratic expression $6x^2 - 2x - 8$. 2. First, look for the greatest common factor (GCF) of all terms: $6x^2$, $-2x$, and $-8$. The GCF

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