🧮 algebra

1. **State the problem:** Multiply the expression $$\sqrt{5}(-7 + \sqrt{2})$$ and simplify the result. 2. **Distribute $$\sqrt{5}$$ to each term inside the parentheses:**

1. **State the problem:** Solve the inequality $$\frac{2x - 5}{x - 5} - 3 \geq 0$$. 2. **Rewrite the inequality:** Combine terms over a common denominator:

1. Find 4% of what number is 10. We set up the equation: $0.04 \times x = 10$.

1. The problem asks how many cups of butter Rama should use to make 3/4 of the cookie recipe, which requires 2/3 cup of butter. 2. To find this, we need to calculate 3/4 of 2/3, wh

1. The problem asks to sketch the curve of a function $f(x)$ and its inverse $f^{-1}(x)$ on the same Cartesian plane, along with the first bisector line $y=x$. 2. We are given tabl

1. Diberikan sistem persamaan linear: $$\begin{cases} 2x + 3y - z = 5 \\ 4x - y + 2z = 3 \\ 3x + 2y + z = 4 \end{cases}$$

1. Problem 13: Find the number $x$ such that 4% of $x$ is 10. Use the proportion $\frac{4}{100} \times x = 10$.

1. **Problem:** Solve the exponential equation $2^{x+1} = 16$. Step 1: Express 16 as a power of 2: $16 = 2^4$.

1. Problem 11: Given sets $D = \{ x \mid -2 \leq x \leq 3 \}$ and $E = \{ y \mid 1 \leq y \leq 11 \}$, and a function $f(x) = ax + b$ with $a > 0$, find $a$ and $b$ such that $f$ i

1. **State the problem:** We need to find how much cloth can be bought for 1400 using the given cost-length relationship. 2. **Analyze the data:** From the table, cost increases by

1. **State the problem:** We are given the sag formula $$l = \frac{12}{d} + d$$ where $l$ is the sag in metres and $d$ is the distance between the supports in metres. 2. We need to

1. **State the problem:** We have data points representing lengths of cloth in metres and their costs in naira. The horizontal axis scale is 2 cm to 1 metre, and the vertical axis

1. समस्या को समझें: हमें पता लगाना है कि किस राशि का 1% घटाने पर 127860 प्राप्त होता है। 2. मान लें कि राशि $x$ है। 1% घटाने का मतलब है कि राशि का 99% बचा है। इसलिए,

1. **State the problem:** Simplify the expression $$\frac{3}{8} + \left( -\frac{1}{5} + -\frac{3}{10} \right)$$. 2. **Simplify inside the parentheses:**

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