🧮 algebra

1. The problem asks to calculate $f(-1)$, $f(0)$, and $f(2)$ for the piecewise function: $$f(x) = \begin{cases} 8x - 4 & x < 0 \\ 8x - 8 & x \geq 0 \end{cases}$$

1. **State the problem:** We need to find the equation of a line in slope-intercept form $y=mx+b$ that passes through the point $(-3,5)$ and has slope $m=-2$. 2. **Recall the slope

1. **State the problem:** We need to find the slope of a line parallel to the line given by the equation $$y = -\frac{5}{8}x + 5$$ and the slope of a line perpendicular to this lin

1. **State the problem:** Find the slope of a line parallel and perpendicular to the line given by the equation $$3y + 8x = 9$$. 2. **Rewrite the equation in slope-intercept form:*

1. **State the problem:** Find the slope of the line given by the equation $$y = -\frac{5}{4}x - \frac{7}{8}$$. 2. **Recall the slope-intercept form:** The equation of a line in sl

1. **State the problem:** Find the slope $m$ of the line given by the equation $$9x - 6y = -9.$$\n\n2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is

1. The problem is to simplify the expression $6\sqrt{3}$. 2. The expression consists of a coefficient 6 multiplied by the square root of 3.

1. **State the problem:** Find the slope of the line parallel to the line passing through the points $(-8, -4)$ and $(5, -9)$. 2. **Recall the formula for slope:** The slope $m$ be

1. **State the problem:** Find the slope of a line perpendicular to the line passing through points (9, 0) and (10, 7). 2. **Find the slope of the original line:** The slope formul

1. **State the problem:** We need to find the expression for $k(x) - h(x)$ where $k(x) = \sqrt{x+3}$ and $h(x) = x^3 + 4$. 2. **Write the expression:**

1. The problem asks why a slope was calculated. 2. In mathematics, the slope represents the rate of change between two points on a line.

1. **State the problem:** We need to find the new function rule if the total number of questions increases from 250 to 300, but the time frame (number of weeks) remains the same.

1. **State the problem:** Solve the equation $$\frac{4x-2}{2} + \frac{5}{3} = \frac{2}{3}(1-2x)$$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Simplify the expression $$\frac{\frac{4}{9} \left(4c^3 d \frac{1}{2}\right)^2}{3c^5 \frac{3}{2} d \frac{5}{2}}$$. 2. **Rewrite the expression clearly:**

1. **State the problem:** Calculate the values step-by-step based on the given expressions.

1. **State the problem:** The ratio of the leg span of the female katipō spider to that of the male is 6:1. Mature females have a leg span of 32 mm. We need to find the leg span of

1. **State the problem:** Simplify the expression $g = (5c^2 d^3)^4$. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power:

1. The problem is to determine if any of the provided options satisfy a given equation or condition by working backwards. 2. To work backwards, we substitute each option into the o

1. **State the problem:** We are given the ratio of incomes of A and B as 7:9, the ratio of their expenditures as 5:7, and both save 800 per month. We need to find A's income.

1. **State the problem:** We need to find the value of $x$ in the equation $$11 = x - 6$$. 2. **Formula and rules:** To solve for $x$, we want to isolate $x$ on one side of the equ

1. **State the problem:** We need to find the expression for the perimeter of a rectangle where the width is $k + 3$ cm and the length is $k - 9$ cm. 2. **Recall the formula for pe