🧮 algebra

1. **State the problem:** We want to find the value of $z$ that makes each polynomial a perfect trinomial square. 2. **Recall the form of a perfect square trinomial:**

1. Problem b) Determine the dimensions and volume of the box if $x=20$. Assuming the box dimensions depend on $x$, we substitute $x=20$ into the given expressions for length, width

1. The problem asks to simplify the expression labeled as answer b. 2. Since the original expression for answer b is not provided, please provide the exact expression or problem st

1. Problem: Analyze the quadratic functions and find their key features such as y-intercept, zeros/roots, axis of symmetry, vertex, and graph orientation. 2. For $y = -x^2 - 8x - 1

1. **State the problem:** We are given two linear equations: $$y - 7x + 18 = 0$$

1. **State the problem:** Solve the system of simultaneous equations: $$3y - x = -1$$

1. **State the problem:** Solve the system of linear equations by substitution: $$7x - 2y = 27$$

1. **State the problem:** Simplify the expression \( \frac{A}{B} \) where \[ A = \frac{(p - q)^2 + 4pq}{p^3 - q^3 - 3pq(p - q)} \quad \text{and} \quad B = \frac{p^3 + q^3 + 3pq(p +

1. Riješimo jednadžbe jednu po jednu. 1) $9^{4-x} = \frac{1}{27}$

1. **Calculer $I_2 + C$, $AB$ et $ABC$.** - Matrices données :

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. Start by isolating the variable term $2x$ on one side. Subtract 3 from both sides:

1. Calculer $I_2 + C$, $AB$ et $ABC$. - $I_2$ est la matrice identité $2 \times 2$: $$I_2 = \begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$$

1. **تحديد صحة العبارات بالنسبة للعدد النسبي a غير المعدوم:** أ. الجداء 4a عدد سالب؟

1. **State the problem:** We want to analyze the polynomial function $$f(x) = x^4 - 6x^2 + 1$$. 2. **Rewrite the function:** Notice that the function is a quadratic in terms of $x^

1. **Simplify** $[(2a^3b^3 + 3a^2c)(4a^2b^3)]^2$. First, distribute inside the parentheses:

1. The problem involves calculating simple interest and understanding bearings. 2. Simple interest is calculated using the formula $$SI = P \times r \times t$$ where $P$ is the pri

1. Solve for $x$: $$2x + 5 = 15$$ 2. Simplify: $$3(2x - 4) + 5x$$

1. **State the problem:** Solve the equation $37z - 78 = 1994$ for $z$. 2. **Isolate the term with $z$:** Add 78 to both sides to get rid of the $-78$ on the left.

1. Stating the problem: Solve the equation $76 - 8z = 4$ for $z$. 2. Subtract 76 from both sides to isolate the term with $z$:

1. **Problem a:** Simplify $\left[(2a^3 b^3 + 3a^2 c)(4a^2 b^3)\right]^2$. Step 1: Distribute inside the parentheses:

1. **Problem statement:** Simplify the expression \(\left[(2a^3b^3 + 3a^2c)(4a^2b^3)\right]^2\). 2. **Distribute inside the parentheses:**