🧮 algebra

1. The problem is to simplify the expression $-350 + 420 - 180$. 2. We use the rule of addition and subtraction of integers: add positive numbers and subtract negative numbers step

1. **State the problem:** The temperature starts at $-12^\circ C$. It increases by $7^\circ C$ by noon and then decreases by $5^\circ C$ in the evening. We need to find the final t

1. **State the problem:** Solve the rational equation $$\frac{9}{x-7} - \frac{7}{x-6} = \frac{13}{x^2 - 13x + 42}$$. 2. **Recognize the denominator factorization:** The quadratic i

1. **State the problem:** Solve the rational equation. Since the user did not provide a specific equation, let's consider a general example: $$\frac{2x+3}{x-1} = \frac{4x-1}{x+2}$$

1. **State the problem:** Solve the equation $$\frac{9}{x-7} - \frac{7}{x-6} = \frac{13}{x^2 - 13x + 42}$$. 2. **Recognize the denominator factorization:** The quadratic in the den

1. **State the problem:** Solve the equation $$\frac{9}{x} - 7 - \frac{7}{x} - 6 = \frac{13}{x^2} - 13 + 42$$ for $x$. 2. **Rewrite and simplify the equation:** Combine like terms

1. **State the problem:** Solve the rational equation. Since the user did not specify a particular equation, let's consider a general example: $$\frac{2x+3}{x-1} = \frac{x+5}{x+2}$

1. **State the problem:** Solve the system of equations using the matrix inversion method: $$\begin{cases} x + 2y + 4z = 14 \\ 2x - y + 5z = 15 \\ -3x + 2y + 4z = 13 \end{cases}$$

1. **State the problem:** Simplify the expression $x \cdot 10 \sqrt{x^7}$. 2. **Rewrite the square root:** Recall that $\sqrt{x^7} = x^{7/2}$ because $\sqrt{x^a} = x^{a/2}$.

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + 3y + 3z = 5 \\ 3x + y - 3z = 4 \\ -3x + 4y + 7z = -7 \end{cases}$$

1. **State the problem:** Find the x-intercept of the function $$y = 2 - 5x$$. 2. **Recall the definition:** The x-intercept is the point where the graph crosses the x-axis, which

1. **Problem vii:** Find the value of $h$ such that the vertex of $f(x) = (x + 4)(x - h)$ has a positive $x$-coordinate. 2. **Step 1:** Expand the function:

1. The problem is to find the x-intercept of a function, which is the point where the graph crosses the x-axis. 2. The x-intercept occurs when the output value $y$ is zero.

1. **State the problem:** Solve the equation $y = 2 - 5x$ for $x$ when $y = 0.4$. 2. **Write the equation with the given value:** Substitute $y = 0.4$ into the equation:

1. **Stating the problem:** We are given two circle equations and need to find the center coordinates and radius for each.

1. The problem is to convert the fraction $\frac{41}{250}$ into a decimal. 2. To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom numbe

1. The problem is to convert the fraction $\frac{41}{250}$ into a decimal. 2. To convert a fraction to a decimal, divide the numerator by the denominator.

1. **Stating the problem:** Victoria creates a sequence of tiles and wants to find the rule that relates the entry number to the number of tiles used. 2. **Understanding the option

1. The problem is to convert the fraction $\frac{41}{250}$ into a decimal. 2. To convert a fraction to a decimal, divide the numerator by the denominator.

1. **Stating the problem:** We have a sequence where the number of tiles used in each entry forms a pattern: Entry 1 uses 1 tile, Entry 2 uses 4 tiles, Entry 3 uses 9 tiles, Entry

1. **Stating the problem:** We need to find the equation that represents the relationship between Roxanne's account total $A$ and the number of weeks $W$ she has been adding money