🧮 algebra

1. **Problem:** Identify the property of real numbers illustrated by the statement $13 - 13 = 0$. 2. **Property Used:** This is the **Additive Inverse Property**, which states that

1. **State the problem:** We are given the quadratic function $$y = -x^2 + 3$$ and want to analyze its properties. 2. **Formula and rules:** This is a quadratic function in the for

1. **State the problem:** Find the turning point of the function $$y=(x+2)^2$$. 2. **Recall the formula and concept:** The turning point of a quadratic function in the form $$y=a(x

1. **State the problem:** Find the turning point of the function $y=4x^2$. 2. **Recall the formula:** The turning point of a quadratic function $y=ax^2+bx+c$ occurs at $x=-\frac{b}

1. **Problem:** Classify each number in the first set as (a) natural number, (b) integer, (c) rational number, or (d) irrational number. 2. **Recall definitions:**

1. **Problem:** Classify the numbers in the set $\{ \frac{3}{5}, -4, 0, \sqrt{2}, 52, -\frac{1}{8}, \sqrt{9} \}$ as (a) natural numbers, (b) integers, (c) rational numbers, and (d)

1. **State the problem:** Solve the equation $$\frac{6r - 5}{9r - 3} = - \frac{1}{3}$$ for $r$. 2. **Use the cross-multiplication method:** When two fractions are equal, their cros

1. **State the problem:** Lorenzo and Mariana mix yellow and blue food coloring to make green icing. Both use the same amount of yellow, but Mariana uses less blue than Lorenzo. We

1. **State the problem:** We need to compare the ratio of short-sleeved shirts to long-sleeved shirts sold last year and this year. 2. **Write the ratios:**

1. **State the problem:** We want to complete the equation $$\frac{1}{6} (36v + 24) - v = \text{[blank]} v + \text{[blank]}$$

1. **State the problem:** Solve the quadratic equation $$2x^2 + 6x - 36 = 0$$ using the quadratic formula. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$

1. **State the problem:** We need to solve the quadratic equation $$y = x^2 - 6x - 5$$ by completing the square. 2. **Recall the formula and rule:** To complete the square for an e

1. **State the problem:** Simplify the expression $$\frac{10}{5 - \sqrt{7}}$$ so that the denominator is rational. 2. **Formula and rule:** To rationalize the denominator when it c

1. **State the problem:** We need to express the fraction $$\frac{-8}{7 + \sqrt{2}}$$ in simplest form with a rational denominator. 2. **Formula and rule:** To rationalize the deno

1. **State the problem:** We need to find the value of $k$ such that $x + 2$ is a factor of the polynomial $$x^3 - 2kx^2 + 6x - 4.$$\n\n2. **Recall the Factor Theorem:** If $x + 2$

1. **State the problem:** Solve the equation $1 + 1x = 2$ for $x$. 2. **Recall the order of operations:** Multiplication comes before addition.

1. **State the problem:** We are given a parabola and need to determine its direction, vertex, axis of symmetry, and intercepts based on the graph. 2. **Direction of the parabola:*

1. **State the problem:** We are given the formula for the area of a trapezoid: $$A = \frac{(b_1 + b_2)h}{2}$$

1. **State the problem:** Two window washers start at different heights: one at 21 ft rising at 8 in./s, the other at 50 ft descending at 11 in./s. We want to find the time $t$ whe

1. **State the problem:** Find the equation of line AB given as $$y=\frac{2}{3}x - 4$$ and match it with the correct answer from the list. 2. **Recall the slope-intercept form:** T

1. **State the problem:** Fully factorise the quadratic expression $$5x^2 + 22x + 8$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two numbe