🧮 algebra

1. **State the problem:** Monique works for $h$ hours as a lifeguard earning 12 per hour and also earns 20 for dog sitting. We need to find an expression representing her total ear

1. The problem asks for the total amount of money Eric saves based on hours worked making sandwiches ($s$) and delivering orders ($d$). 2. The expression given is $$\frac{1}{2}(10s

1. The problem asks to find 2 possible equations that correspond to the given 2x2 grid where each box contains the value $\frac{1}{5}$. The grid has arrows and numbers 5, +, 4, -,

1. **State the problem:** Simplify the expression $$\frac{\sqrt{12} - \sqrt{3}}{\sqrt{12} + \sqrt{3}}$$ step by step. 2. **Recall the formula:** To simplify a fraction with radical

1. The problem asks why the expression $\frac{x+15}{3}$ was rewritten as $\frac{x}{3} + 5$ in Example 1. 2. Recall the property of division over addition: $$\frac{a+b}{c} = \frac{a

1. The problem asks to verify if part b, which is $(f \circ g)(1) = 4$, is correct. 2. Recall the definition of composition of functions: $$(f \circ g)(x) = f(g(x))$$

1. **State the problem:** Solve the system of linear equations: $$x - 2y = 12$$

1. The problem is to find the equation of an exponential function in the form $$f(x) = a b^x$$ given the values: $$f(0) = -3, f(1) = -4, f(2) = -\frac{16}{3}, f(3) = -\frac{64}{9}$

1. **State the problem:** We need to find the equation of an exponential function in the form $f(x) = a(b)^x$ given points from the graph. 2. **Identify known points:** From the gr

1. **State the problem:** Solve the equation $x - 2x + 17 = -2x + 17 = 180^\circ$ for $x$. 2. **Rewrite the equation:** The problem gives two expressions:

1. **State the problem:** We are given the equation $2x + y = 4$ and a point $(3, -2)$. We want to check if the point satisfies the equation.

1. **Stating the problem:** We have a geometric figure with line segments forming kite shapes and a central square. We will find the equations of 5 selected line segments in slope-

1. **State the problem:** We have a piggy bank with a total amount $T$. The problem states that one quarter of the total amount plus 5 equals one third of the total amount. 2. **Wr

1. The problem is to find the cube root of 64, written as $\sqrt[3]{64}$. 2. The cube root of a number $x$ is a value $y$ such that $y^3 = x$.

1. The problem is to find the square root of $-254$. 2. Recall that the square root of a negative number involves imaginary numbers because no real number squared gives a negative

1. **State the problem:** Solve the quadratic equation $$3x^2 - 20x - 13 = -6$$ by factoring. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to z

1. The problem asks to use ratios to solve the previous question, but since the previous question is not provided, let's explain how to solve problems using ratios in general. 2. A

1. Problem: Find the equation of the parabola with vertex (3,1) and passing through point (4,0). 2. Formula: The vertex form of a parabola is $$y = a(x - h)^2 + k$$ where $(h,k)$ i

1. The problem is to evaluate the expression "6 more than 9 times x" when $x=16$. 2. The expression can be written as $$9x + 6$$ where $x$ is the variable.

1. **State the problem:** Solve the equation $$\frac{3x}{2} - x = \frac{x}{6} - \frac{4}{3}$$ for $x$. 2. **Rewrite the equation:** To solve for $x$, first get all terms involving

1. **State the problem:** We need to find the number of people $n$ who can participate in each activity for exactly 29 dollars. 2. **Write the equations:**