🧮 algebra

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

1. The problem involves graphing the functions $y=4^x$ and $y=5^x$ on the same coordinate plane. 2. The general form of an exponential function is $y=a^x$ where $a>0$ and $a \neq 1

1. The problem is to find the value of the function or expression "f" again, but since no specific function or expression "f" was provided, we need more information to proceed. 2.

1. The problem is to solve the equations given. Since no specific equations are provided, I will demonstrate how to solve a general linear equation as an example. 2. Consider the e

1. **Problem:** Factor the trinomial $3x^2 - 5x - 12$ completely. 2. **Formula and Rules:** To factor a quadratic trinomial of the form $ax^2 + bx + c$ where $a \neq 1$, we use the

1. The problem is to solve the equations given. However, no specific equations were provided in the message. 2. To solve an equation, we typically isolate the variable on one side

1. **Problem:** Factor the quadratic trinomial $3x^2 - 5x - 12$ completely. 2. **Formula and Rules:** To factor a quadratic trinomial of the form $ax^2 + bx + c$ where $a \neq 1$,

1. The problem is to understand why the function is odd and not even. 2. Recall the definitions: