🧮 algebra

1. **State the problem:** We are comparing two temperatures: Vancouver at $-1.5$ degrees and Chicago at $-5$ degrees. 2. **Understanding negative numbers:** On the number line, num

1. The problem asks for the temperatures in two cities, Berlin and Paris, based on thermometer readings. 2. Each thermometer scale ranges from -5 to 5 degrees, with zero in the mid

1. **State the problem:** Solve the quadratic equation $$20 - 12u + u^2 = 0$$. 2. **Rewrite the equation in standard form:** The standard form of a quadratic equation is $$au^2 + b

1. **State the problem:** We are given the inequalities:

1. **State the problem:** Solve the quadratic equation $$10y^2 - 11y - 6 = 0$$. 2. **Formula used:** For a quadratic equation $$ay^2 + by + c = 0$$, the solutions are given by the

1. **Stating the problem:** We need to graph the system of inequalities:

1. **State the problem:** We have a box where the height is 1 cm longer than the width, and the length is twice the width. The volume is 346 cm³. We need to find the dimensions: wi

1. **State the problem:** Joe's average running speed is 0.5 km/h greater than Bob's. In a 5-km race, Bob finishes 3 minutes (which is 0.05 hours) behind Joe. We need to find their

1. **Problem Statement:** We are given the function $f(x) = -\frac{1}{x^2 + 6x - 7}$. We need to sketch the graph, label key points, find the domain and range, equations of asympto

1. **Problem Statement:** We are given the function $f(x) = (x-2)(x-5)(x+2)$. We need to sketch the graph, label key points, find the domain and range, equations of asymptotes, end

1. **State the problem:** Determine whether the function $y=5x^5 - x^3 + 1$ is even, odd, or neither. 2. **Recall definitions:**

1. The problem is to understand and use the point-slope form of a linear equation, which is given by the formula: $$y - y_1 = m(x - x_1)$$

1. **Problem Statement:** We need to find the slopes of the missing line segments to complete the Christmas tree shape, which extends up to $y=23$. We will use the point-slope form

1. Problem: Find the x-intercept and y-intercept of the equation $4y = 2x - 1$. - To find the x-intercept, set $y=0$ and solve for $x$.

1. **State the problem:** Simplify the expression $$3(x - 5)^2 - 2(x - 5) + 4$$ by distributing and writing it as a polynomial in standard form. 2. **Recall the formula:** The squa

1. **State the problem:** We need to subtract the expression $$(x - 5)^2$$ from $$4x^2 - 7$$ and simplify the result into a polynomial in standard form. 2. **Recall the formula:**

1. **State the problem:** We need to find the result when the polynomial $(2x - 6)^2$ is subtracted from $8x$. 2. **Write the expression:** The expression is $$8x - (2x - 6)^2$$

1. **State the problem:** We need to find the result when the expression $$(x + 8)^2$$ is subtracted from $$(x + 7)$$ and write the answer as a simplified polynomial in standard fo

1. **State the problem:** We need to subtract the polynomial $(x - 3)^2$ from $7x^2$ and write the result as a simplified polynomial in standard form. 2. **Recall the formula:** Th

1. **State the problem:** Determine if the table shows a proportional relationship and find the value of $y$ when $x=\frac{3}{5}$.\n\n2. **Check proportionality:** A relationship i

1. **State the problem:** Evaluate the division of fractions $\frac{5}{4} \div \frac{3}{5}$. 2. **Recall the rule for dividing fractions:** To divide by a fraction, multiply by its