🧮 algebra

1. **State the problem:** Multiply $5\sqrt{3}$ by $6\sqrt{3}$. 2. **Recall the multiplication rule for radicals:** $a\sqrt{b} \times c\sqrt{d} = (a \times c) \times \sqrt{b \times

1. **State the problem:** Solve the first system of equations: $$\begin{cases} x - y = 5 \\ x - y = -2 \end{cases}$$

1. The problem is to write 6.38% as a decimal. 2. Recall that percent means per hundred, so 6.38% means 6.38 out of 100.

1. The problem is to arrange a set of numbers or expressions from the least to the greatest. 2. To do this, we first need the list of numbers or expressions to compare.

1. **State the problem:** We need to select all the squares that contain perfect squares and order them from least to greatest. 2. **Recall what a perfect square is:** A perfect sq

1. **State the problem:** Find the coordinates of the points of intersection of the curve $$4 + \frac{5}{y} + \frac{3}{x} = 0$$ and the line $$y = 15x + 10$$. 2. **Substitute** the

1. The problem asks to write the radical expression $$\sqrt[3]{r^4}$$ as an expression with a rational exponent. 2. Recall the rule for converting radicals to rational exponents: $

1. **State the problem:** Simplify the expression $$a^2 y^2 + ay + 2ay^2 + a^2 y^2 + a^2 y$$. 2. **Group like terms:** Group terms with the same variables and powers together:

1. **Problem Statement:** We want to graph the cost of travel by bus and car using the slope of a line and similar triangles to understand the break-even point where costs are equa

1. **State the problem:** Find the value of each expression:

1. **Problem:** Examine whether $x - 1$ is a factor of the polynomial $4x^3 + 3x^2 - 4x - 3$. 2. **Rule:** To check if $x - 1$ is a factor, use the Factor Theorem which states that

1. The problem asks to find 45% of 260. 2. To find a percentage of a number, use the formula: $$\text{Percentage of a number} = \frac{\text{percentage}}{100} \times \text{number}$$

1. **State the problem:** We are given the function $f(x) = 5x - 7$ and need to evaluate $f(-3)$. 2. **Recall the formula:** The function $f(x)$ means for any input $x$, the output

1. **State the problem:** We are given the function $f(x) = 5x - 7$ and need to evaluate $f(3)$. 2. **Recall the formula:** The function $f(x)$ means for any input $x$, the output

1. **State the problem:** Ada works Monday to Friday with working hours from 0800 to 1230 and 1330 to 1700 each day. We need to find the total number of hours she works in 5 days.

1. **State the problem:** Simplify the expression $$(a^3 - 2a^2) - (3a^2 - 4a^3)$$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign ov

1. **State the problem:** Simplify the expression $(5p^2 - 3) + (2p^2 - 3p^3)$. 2. **Write down the expression:**

1. **State the problem:** Graph the equation $x = -4$ by making a table of values. 2. **Understand the equation:** The equation $x = -4$ means that for every value of $y$, $x$ is a

1. **Stating the problem:** An investor receives 31000 in interest per annum from a sum of money invested partly at 10% and partly at 7% simple interest. If the amounts invested at

1. **State the problem:** Simplify the expression $5p - 3p + p$. 2. **Recall the rule:** When simplifying algebraic expressions, combine like terms by adding or subtracting their c

1. **State the problem:** Simplify the expression $$\frac{16 a^8 b^4}{8 a^3 b^2}$$. 2. **Recall the rules:**