🧮 algebra

1. **State the problem:** We need to find Lyla's total profit over two days, given that Monday's activity is -4 (money spent) and Tuesday's activity is 10 (money earned). 2. **Form

1. The problem is to solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. The formula used here is to isolate $x$ by eliminating the denominator and then solving the resulting lin

1. **Stating the problem:** John drives 200 km at steady speeds of 60 km/h and 100 km/h. The graph shows fuel consumption for these speeds: segment l1 ends at (25 km, 275 litres) f

1. **State the problem:** Find the zeros of the function $$g(x) = 4x^2 - 484$$. The zeros are the values of $$x$$ where $$g(x) = 0$$. 2. **Set the function equal to zero:**

1. **Problem (a):** Find the original price of an oven sold at 25% off with a sale price of 251.85. 2. The formula for discount price is:

1. **State the problem:** We need to find which expressions are equivalent to the expression $$ (x - y) \frac{5}{8} - \frac{1}{4} x + y $$. 2. **Rewrite the original expression:**

1. **Problemstellung:** Gegeben ist die Parabel $y = 0,5x^2 + 2x$. Wir sollen die Schnittpunkte mit der x-Achse bestimmen und die Parabel skizzieren. 2. **Formel und Regeln:** Die

1. **State the problem:** Determine if $y$ varies directly with $x$ given the pairs $(-2,6)$, $(1,3)$, and $(4,8)$. If yes, write the direct variation equation in the form $y = kx$

1. The problem asks to write the equations of a house-like graph composed of lines and curves using square roots, absolute values, and quadratic forms, with vertical and horizontal

1. **Stating the problem:** In a class, there are girls and 30 boys. 28 boys pass, all girls pass. The total passing students are 95% of the class. Find the number of girls and boy

1. **State the problem:** Zach paid 8 for an 8-inch diameter pizza, and Aiden paid 12 for a 12-inch diameter pizza. We need to find the percentage increase in price and size, then

1. **Problem 14:** Find the value of $k$ if the slope of the line through points $(3, 2)$ and $(8, k)$ is $\frac{3}{5}$. 2. **Formula for slope:** The slope $m$ between two points

1. **State the problem:** Simplify the expression $$\frac{4x^2 - 2x + 8x - 4}{u x^2 + 1 - u x}$$ and solve the equation $$\frac{2x^2 - 2x - 4}{u x^2 + 1 - u x} = 1$$ for $x$. 2. **

1. **State the problem:** We are given the function $f(x) = x^2 - 2x - 3$ and a table of $x$ values: 0, 1, -1, 3, -2. We need to find the corresponding $y$ values and understand th

1. **Solve the inequalities:** a) $8x \leq x^2 + 12$

1. **Solve the inequalities:** **Problem 1:** Solve $8x \leq x^2 + 12$

1. **State the problem:** Graph the system of inequalities:

1. The problem states: 1/8 of a number is 9, and we need to find the whole number. 2. Let the whole number be $x$.

1. **State the problem:** We need to find a number such that when \(\frac{3}{4}\) of it is added to 9, the result is 27. 2. **Set up the equation:** Let the number be \(x\). The pr

1. **Problem:** Find $x$ in the equation $$105^\circ + x^\circ + 40^\circ + 75^\circ = 360^\circ$$ 2. **Formula:** The sum of angles around a point is always $$360^\circ$$.

1. The problem is to understand how to factorize algebraic expressions. 2. Factorization means writing an expression as a product of simpler expressions called factors.