🧮 algebra

1. **State the problem:** Evaluate the expression $\log_3 27 - \log_2 4$. 2. **Recall the logarithm rules:**

1. **State the problem:** Simplify the expression $$4[x - 4(y - 2[5y + 2])]$$. 2. **Recall the distributive property:** $$a(b + c) = ab + ac$$ and the rule for simplifying inside b

1. The problem is to evaluate the expression $$\frac{\log_5 125}{\log_3 27}$$. 2. Recall the definition of logarithms: $$\log_b a = c \iff b^c = a$$.

1. **State the problem:** We need to sketch the function $$y=(x-4)(x^2+9)$$. 2. **Understand the function:** This is a product of two factors: a linear factor $x-4$ and a quadratic

1. **Find the additive inverse of $-\frac{2}{3}$**. The additive inverse of a number $a$ is the number that when added to $a$ gives zero.

1. **Problem:** Check the work for the given problems from the test. 2. **Additive inverse of $-\frac{2}{3}$:**

1. The problem is to solve a math question "do it like a grade 10" which usually means solving a typical grade 10 level algebra problem. 2. Since no specific problem is given, let'

1. **Stating the problem:** Solve the equation $x \cdot (x - 2) = 0$. 2. **Formula and rules:** The zero product property states that if $a \cdot b = 0$, then either $a = 0$ or $b

1. **Problem statement:** Solve the equation $x \cdot (x - 2) = 0$. 2. **Formula and rule:** The zero product property states that if a product of two factors is zero, then at leas

1. **State the problem:** We want to find the amount over the cost price that maximizes the revenue for the electronics store.

1. The problem asks to find the slope of the graph of a vertical line at $x=3$. 2. Recall that the slope $m$ of a line is given by the formula:

1. **State the problem:** Determine which expressions always yield an even value when $x$ is an even number. 2. **List the expressions:**

1. **State the problem:** We are given the function $$f(x) = e^x \sqrt[3]{3x t \sin x}$$ and we want to understand or analyze it. 2. **Recall the components:**

1. **State the problem:** We are given Jake's savings account balance as a function of weeks: $$b = 40n + 150$$

1. Problem: Calculate each sum, difference, product, or quotient of integers. 2. Important rules:

1. **Problem statement:** Calculate and simplify the following expressions. 2. **Part a:** $\frac{2}{8} + \frac{2}{8}$

1. The problem asks: How many roots does the function have based on the given description? 2. Roots of a function are the values of $x$ where the function crosses the x-axis, meani

1. **Stating the problem:** We need to complete the table showing the number of web shops in the Netherlands for the years 2019, 2020, and 2021, given some percentage increases and

1. **Stating the problem:** We want to find the number of web shops in 2021 and the number of clothing stores in 2021 based on the given data. 2. **Given data:**

1. **Problem 1: Simplify the expression** $3x + 5x - 2 + 4$. 2. **Step 1:** Combine like terms (terms with $x$ and constant terms separately).

1. **Problem:** Determine if the given ratios are true or false. 2. **Part a:** Is the ratio 3 : 2 the same as 2 : 3?