🧮 algebra

1. **Problem statement:** There are 125 students arranged in rows such that the number of rows equals the number of students in each row. We need to find how many students are in e

1. **Problem statement:** There are 125 students arranged in rows such that the number of rows equals the number of students in each row. We need to find how many students are in e

1. **State the problem:** We are given the quadratic equation $$25x^2 + 9 = 30x$$ and asked to compute its discriminant and identify the type of solutions. 2. **Rewrite the equatio

1. **State the problem:** Mr. Chang bought 8 volleyballs and 2 nets for 1460.

1. **Problem Statement:** Evaluate each logarithm expression given. 2. **Formula and Rules:** Recall that $\log_a b = c$ means $a^c = b$.

1. **Problem 1: For the function $f(x) = 2x + 5$** 1. a) The domain of $f(x)$ is all real numbers because there are no restrictions on $x$ in a linear function.

1. **State the problem:** A photograph originally measures 16 cm by 11 cm. It is cropped by removing the same width $x$ cm from the top and left side. The area is reduced by 72 cm²

1. **Problem statement:** A photograph originally measures 16 cm by 11 cm. It is cropped by removing the same width $x$ cm from the top and left side, reducing the area by 72 cm$^2

1. **Problem Statement:** We are given three lines representing walkways in a park: $$x + y - 4 = 0$$

1. **State the problem:** Simplify the expression $$2 \times x^3 \times \sqrt{2} \times x^3 \div \sqrt[3]{9}$$. 2. **Rewrite the expression:** Group like terms and rewrite radicals

1. **State the problem:** We are given an open box with dimensions involving $x$: - Height: $25$ cm

1. **State the problem:** We want to express the quadratic expression $$q + 12x - qx^2$$ in the form $$a - b(x - c)^2$$ where $$a$$, $$b$$, and $$c$$ are expressed in terms of $$q$

1. The problem is to round the number 0.04945 to 2 significant figures (sf). 2. Significant figures are the digits in a number that carry meaning contributing to its precision.

1. **State the problem:** Expand and fully simplify the expression $$(x + 5)(x + 3)^2$$. 2. **Recall the formula:** To expand, first recognize that $$(x + 3)^2 = (x + 3)(x + 3)$$.

1. **State the problem:** Simplify the expression $$\frac{\sqrt{7 + \sqrt{7} + h}}{\sqrt{7 - \sqrt{7} + h}}$$ where $h$ is a variable. 2. **Recall the formula and rules:** To simpl

1. **State the problem:** Simplify or analyze the expression $x^2$. 2. **Formula and rules:** The expression $x^2$ means $x$ multiplied by itself: $$x^2 = x \times x$$.

1. **State the problem:** Solve the equation $$\frac{5x-8}{x+8} = -2$$ for $x$. 2. **Understand the formula and rules:** This is a rational equation where the variable $x$ appears

1. **State the problem:** We are given a quadratic function $$F(x) = x^2 + x$$ and two points $$a$$ and $$b=42$$. We want to find the Average Rate of Change (AROC) of $$F(x)$$ betw

1. The problem is to find the values of A and B, which according to your answer key are both 6.0. 2. Since the answer key gives the values directly, we assume the problem involves

1. **State the problem:** We are given the quadratic function $f(x) = -x^2 + 2x - 2$ and want to analyze it. 2. **Formula and rules:** A quadratic function is generally $f(x) = ax^

1. **State the problem:** We have 250 plants growing at a rate of 40% per month. We want to find the number of plants after 3 months. 2. **Formula used:** The exponential growth fo