🧮 algebra

1. **Problem 1: Find $a - b$ for the linear function $f(x) = ax + b$ given the table values:** Given points: $(1, -64)$, $(2, 0)$, $(3, 64)$.

1. The problem states that for the function $f$, $f(3x) = x - 6$ for all values of $x$. We need to find $f(6)$. 2. To find $f(6)$, notice that $6 = 3 imes 2$, so we can set $3x =

1. The problem is to solve for $x$ given the expression or equation involving $x$. 2. Since the user only provided the variable $x$ without an equation, we cannot solve for a speci

1. **Problem:** Find the value of $ (2.4 \times 10^3) + (5.7 \times 10^2) $. 2. **Formula and rules:** To add numbers in scientific notation, they must have the same power of 10.

1. **State the problem:** We know that $x$ is 25% less than $y$. Given $x=17$, we want to find $y$. 2. **Understand the relationship:** Saying $x$ is 25% less than $y$ means:

1. **State the problem:** The sum of two consecutive integers is -13. If 2 is added to the smaller integer and 3 is subtracted from the larger integer, find the product of the two

1. **State the problem:** Find the sum of the arithmetic series: $$2 - \frac{4}{3} + \frac{8}{9} - \frac{16}{27} + \ldots - \frac{4096}{177147}$$

1. **Problem 1: Find the sum of all possible y-intercepts for a line passing through (9,0) with negative slope and single-digit prime y-intercept.** 2. The line equation is $y = mx

1. **State the problem:** We need to find the daily fee for renting a moving truck given that the total cost includes a daily fee plus $0.50 per mile driven.

1. The problem asks for the answer to question 4, which is: $$0 \div (-9)^2 \times 11^2$$

1. **State the problem:** We need to find the cost of Maggie's phone bill if she uses 165 minutes in October, given the cost per minute and a known bill for 120 minutes.

1. **Problem:** Subtract $-22 - (-34.41)$. 2. **Formula:** Subtracting a negative number is the same as adding its positive counterpart: $a - (-b) = a + b$.

1. **State the problem:** Solve the equation $$\frac{r + 5}{6} = \frac{r + 3}{4} + \frac{r - 1}{9}$$ for $r$. 2. **Identify the formula and rules:** To solve equations with fractio

1. The problem involves finding the midpoint and distance between two points on a coordinate plane. 2. The midpoint formula is given by $$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}

1. The problem is to solve the equation given by the user, but since no specific equation was provided, let's consider a general approach to solving algebraic equations. 2. The gen

1. **State the question:** Why is the solution written as $3 e^{2+x}$ instead of $3 e^{2} e^{x}$? 2. **Recall the exponential property:** For any real numbers $a$ and $b$, the expo

1. **State the problem:** Solve the equation $$\frac{6}{5}(2x + 1) - \frac{7}{10}(x - 7) = 1$$ for $x$. 2. **Write the equation clearly:**

1. The problem is to write an expression equivalent to $-2(4 + 6m)$ using the distributive property. 2. The distributive property states that $a(b + c) = ab + ac$. This means we mu

1. The problem asks us to identify which ratios are equivalent to $3:18$. 2. Two ratios $a:b$ and $c:d$ are equivalent if their cross products are equal, i.e., $a \times d = b \tim

1. **State the problem:** We need to find which ratios are equivalent to $4:9$. 2. **Recall the rule for equivalent ratios:** Two ratios $a:b$ and $c:d$ are equivalent if $\frac{a}

1. The problem asks us to identify which ratios are equivalent to $1:20$. 2. Two ratios $a:b$ and $c:d$ are equivalent if their cross products are equal, i.e., $a \times d = b \tim