🧮 algebra

1. The problem is to find the equation of the line passing through the points (-8, -7) and (8, 7). 2. The formula for the slope $m$ of a line passing through two points $(x_1, y_1)

1. **State the problem:** We want to find out how many gallons of gas are used for every 1 mile driven if the car's fuel efficiency is 28.01 miles per gallon (mpg). 2. **Formula:**

1. **State the problem:** We need to find the fuel mileage, which is the number of miles driven per gallon of fuel used. 2. **Formula:** Fuel mileage (miles per gallon) is calculat

1. **State the problem:** Emily wants to buy turquoise stones priced at 4 or 6 each, spending no more than 30 total, and wants to give stones to at least 4 friends. 2. **Define var

1. **Problem Statement:** (a) We want to graph the relationship between the number of hours Diego works out and the number of miles he walks per week.

1. **State the problem:** Simplify the expression $3 + \sqrt{2}$. 2. **Understand the expression:** The expression consists of a rational number 3 and an irrational number $\sqrt{2

1. **State the problem:** Simplify the expression $3 + \sqrt{2}$. 2. **Understand the terms:** The expression consists of a rational number 3 and an irrational number $\sqrt{2}$.

1. **State the problem:** Solve the equation $$5 - \sqrt[3]{x^2 - 9} = 7$$ for $x$. 2. **Isolate the cube root term:** Subtract 5 from both sides:

1. **State the problem:** We are given the system of linear equations: $$x + 3y = -3$$

1. **State the problem:** Find the inverse of the function $y = -3x + 4$. 2. **Recall the formula and rule:** To find the inverse of a function, swap $x$ and $y$ and then solve for

1. **Problem:** Identify the vertical asymptote, horizontal asymptote, domain, and range of the function $$f(x) = -\frac{1}{x - 2} - 1$$ and sketch its graph. 2. **Vertical asympto

1. **State the problem:** Factor the trinomial $$2z^2 - 7z - 15$$ into the form $$(2z + A)(z + B)$$ where $A$ and $B$ are constants to be found. 2. **Recall the factoring method fo

1. **State the problem:** We analyze the function $$f(x) = \frac{2x + 2}{x^2 + 8}$$ to find its domain, intercepts, sign (positivity and negativity), asymptotes, derivatives, monot

1. The problem is to find the value of $\sqrt{36}$.\n\n2. Recall that the square root $\sqrt{x}$ is the number which when squared gives $x$.\n\n3. We know $36 = 6^2$, so $\sqrt{36}

1. **Problem Statement:** Determine the slope of the red line positioned center-right that crosses the x-axis near -240 and 30, and descends diagonally through y-axis values from a

1. **State the problem:** We need to analyze and graph the quadratic equation $$b^2 - 4b + 4 = 0$$. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c

1. **State the problem:** Solve the quadratic equation $$m^2 - 5m - 14 = 0$$ using the quadratic formula. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$

1. We are asked to solve the equation using the balance method: $24 - d = 2d - 9$. 2. The balance method means we perform the same operation on both sides to isolate the variable $

1. **Problem Statement:** We are given two exponential decay functions: $$P(t) = 20000(0.92)^t$$

1. **Problem statement:** Ein Wald hat 10 000 m³ Holz. Der Holzbestand nimmt jährlich um 200 m³ ab.

1. Vi har ekvationen $x^2 - 6x - 7 = 0$ och ska lösa den. 2. Detta är en andragradsekvation på formen $ax^2 + bx + c = 0$ där $a=1$, $b=-6$, och $c=-7$.