🧮 algebra

1. **State the problem:** Sumita and Carrie start with ribbons of the same length $x$ cm. 2. Sumita used $75.6$ cm, so she has $x - 75.6$ cm left.

1. **State the problem:** We have a mixture of gold and silver in the ratio $3:7$ by weight, and the total weight is $250g$. We need to find the weight of gold. 2. **Formula and ru

1. **Problem statement:** Solve the absolute value inequalities and express solutions in interval notation. ---

1. **Problem statement:** Solve the absolute value inequalities and express the solutions in interval notation. ---

1. **State the problem:** Reflect point $A(2,1)$ about the line $y = -x + 1$ and find the coordinates of the reflected point $A'$. 2. **Identify the line equation in standard form:

1. **Problem:** Given matrices $A = \begin{pmatrix}4 & 2 \\ 5 & 3\end{pmatrix}$ and $B = \begin{pmatrix}-5 & -2 \\ 4 & 1\end{pmatrix}$, find: a) $A^2$

1. **State the problem:** We want to factor the expression $x^2$. 2. **Recall the factoring rules:**

**Factoring $x^2$** **1. Understanding the Problem**

1. **Problem Statement:** Find the following for matrices $A$ and $B$:

1. **State the problem:** Solve the quadratic equation $x^2 + 5x + 6 = 0$. 2. **Formula and rules:** The quadratic equation is generally solved using the quadratic formula:

1. Let's clarify what it means to "cancel out zeros" in math. 2. Zeros in multiplication can make the entire product zero, but you cannot cancel zeros like you cancel common factor

1. The problem shows two ratios or fractions: $\frac{3}{5}$ and $\frac{3}{6}$, and numbers $721$ and $7$ are also given. 2. We need to understand the relationship or compare these

1. **State the problem:** Simplify or factor the quadratic expression $$x^2 - 5x + 6$$. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, we look f

1. **State the problem:** Simplify the expression $$2x^2 + 8x \times 2$$. 2. **Recall the order of operations:** Multiplication must be done before addition.

1. **State the problem:** Arelli bought a bike for $80 and sold it for 20% less. We need to find the selling price. 2. **Formula used:** To find the selling price after a percentag

1. **State the problem:** We have a pond shaped like a prism with dimensions length $= 2$ m, width $= 1$ m, and height $= 1.3$ m.

1. **State the problem:** We are given the ratio of purple cars to red cars as $89 : 53$. 2. **Goal:** Write this ratio in the form $n : 1$, where $n$ is a decimal rounded to 2 dec

1. **State the problem:** We need to evaluate the cube root of the expression $$\sqrt[3]{\frac{((24\times3600)^2 \times 6.67\times10^{-11} \times 5.97\times10^{24})}{4\pi^2}}.$$ 2.

1. **State the problem:** Solve the equation $$3d - 21(2d - 4) = -45(4d - 4)$$ for $d$. 2. **Distribute the constants inside the parentheses:**

1. Simplify $\sqrt{81} + 2\sqrt{5} + \sqrt{63} + \sqrt{45}$. 2. For $f(x) = x^2 + 4x - 2$:

1. Simplify $\sqrt{81} + 2\sqrt{5} + \sqrt{63} + \sqrt{45}$. 2. For $f(x) = x^2 + 4x - 2$: