🧮 algebra

1. **State the problem:** Evaluate each expression from problems 8 to 11 and identify which expressions in problem 12 have negative values. 2. **Recall the rules:**

1. **State the problem:** We need to find out how many floors will be cleaned in a week. 2. **Identify the information needed:** To solve this, we need to know how many floors are

1. **State the problem:** We need to find how long it takes the window cleaner to clean all the windows on the Q1 building, which has $78$ floors and $32$ windows per floor, with $

1. **State the problem:** Find the roots and the vertex of the quadratic function $$y = -x^2 - 20x - 19$$. 2. **Formula for roots:** The roots of a quadratic $$ax^2 + bx + c = 0$$

1. **State the problem:** We need to find the roots and the vertex of the quadratic function $$y = -x^2 - 9x + 79$$. 2. **Formula for roots:** The roots of a quadratic $$ax^2 + bx

1. **State the problem:** Find the roots and vertex of the quadratic function $$y = -x^2 - 9x + 79$$. 2. **Recall the formulas:**

1. **State the problem:** We need to find the roots and the vertex of the quadratic function $$y = x^2 - 7x - 109$$. 2. **Formula for roots:** The roots of a quadratic equation $$a

1. **State the problem:** Find the roots and vertex of the quadratic function $$y = x^2 + 14x - 72$$. 2. **Formula for roots:** Use the quadratic formula $$x = \frac{-b \pm \sqrt{b

1. **State the problem:** Find the roots and vertex of the quadratic function $$y = -x^2 - 10x + 11$$. 2. **Formula for roots:** Use the quadratic formula $$x = \frac{-b \pm \sqrt{

1. **State the problem:** We need to find the minimum value of the quadratic function $$f(x) = x^2 - 10x + 22.8$$ to the nearest hundredth. 2. **Recall the formula for the vertex o

1. **State the problem:** We are asked to expand and simplify the expression $(x+y)(7x+2y-1)$ and verify if it equals $7x^2+2xy+2y^2-x-y$.

1. **Problemstellung:** Wir wollen ein lineares Gleichungssystem mit zwei Unbekannten lösen. Ein solches System hat die Form: $$a_1x + b_1y = c_1$$

1. **State the problem:** We need to find the numerical length of the segment $SU$ given expressions for $ST$, $SU$, and $TU$. 2. **Recall the segment addition postulate:** If poin

1. **State the problem:** We have a line segment $QS$ with point $R$ between $Q$ and $S$. We know the lengths $RS = 2x - 1$, $QR = 5x + 3$, and the total length $QS = 5x + 10$. We

1. **State the problem:** Simplify $$\frac{-3(j^{-3}a^{4})^{-3}}{3j^{4}a^{8}}$$ so that all exponents are positive. 2. **Recall the exponent rules:**

1. **State the problem:** Simplify the fraction $$\frac{(2j^3p)^{-1}}{10j^6}$$ so that all exponents are positive. 2. **Recall the rule for negative exponents:** $$a^{-n} = \frac{1

1. **State the problem:** Simplify the expression $$\frac{10h^{10}}{(-5h^{5}q)^{3}}$$ to its simplest form using only positive exponents. 2. **Apply the exponent to the denominator

1. **State the problem:** Simplify the expression $$\frac{2(p^{2})^{-4}}{2r^{-2}}$$ to its simplest form. 2. **Recall the rules:**

1. **State the problem:** Solve the equation $$-4(z - 12) = 42$$ for the variable $$z$$. 2. **Use the distributive property:** Multiply $$-4$$ by each term inside the parentheses.

1. **State the problem:** Simplify the fraction $$\frac{(3t^{-1})^{-3}}{4t^{7}j}$$ so that all exponents are positive. 2. **Recall the exponent rules:**

1. **State the problem:** Simplify the expression $$\frac{(3t^{-1})^{-3}}{4t^{7}j}$$ so that it contains only positive exponents. 2. **Recall the exponent rules:**