🧮 algebra

1. The problem asks what happens to the coordinates of the point $p(2,3)$ when the transformation $y = -f(x)$ is applied. 2. The original point is $p(2,3)$, where $x=2$ and $y=3$.

1. **State the problem:** Calculate the student's final grade based on the weighted categories. 2. **Identify the weights and scores:**

1. **State the problem:** Multiply the expressions $$(9 - \sqrt{3})(-4 - \sqrt{5})$$ and simplify the result. 2. **Apply the distributive property (FOIL):**

1. **State the problem:** Multiply $$\sqrt{14p^5} \cdot \sqrt{3}$$ assuming $$p \geq 0$$ and simplify the result. 2. **Use the property of square roots:** $$\sqrt{a} \cdot \sqrt{b}

1. **State the problem:** Solve the rational inequality $$\frac{2x - 5}{x - 5} - 3 < 0$$. 2. **Rewrite the inequality:** Combine the terms on the left-hand side over a common denom

1. Let's state the problem: We want to understand the properties of two parallel lines, say $l_1$ and $l_2$, especially focusing on their gradients (slopes). 2. By definition, two

1. The problem is to solve the inequality $x^2 - 4x + 3 < 0$. 2. First, factor the quadratic expression: $$x^2 - 4x + 3 = (x - 1)(x - 3).$$

1. The original problem is to change the inequality from $>$ to $<$. 2. If the original inequality is $a > b$, changing it to $a < b$ means we are reversing the direction of the in

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,