🧮 algebra

1. The problem is to simplify the phrase "shorten all of these" which implies reducing or simplifying expressions or terms. 2. Since no specific expressions are given, the general

1. The problem is to find the solution to the equation or expression given in the link (link content not accessible, so please provide the exact problem statement for detailed solu

1. **State the problem:** Solve for $x$ in the equation $x + 2 = 4$. 2. **Formula and rules:** To isolate $x$, subtract 2 from both sides of the equation.

1. **State the problem:** Simplify the expression $$\frac{x^2-25}{x^2+5x} \div \frac{xy+6x-5y-30}{5x-15}$$. 2. **Rewrite division as multiplication by reciprocal:**

1. **State the problem:** We need to find the equation of an exponential function in the form $$f(x) = a b^x$$ given points on the graph and its shape. 2. **Analyze the graph:** Th

1. **State the problem:** Solve the system of linear equations: $$2x + y = 8$$

1. **State the problem:** Solve the simultaneous equations: $$a^2 - ab + b^2 = 3 \quad (D)$$

1. **State the problem:** Simplify the expression $$(2a^4 + 5)^2$$. 2. **Formula used:** To square a binomial, use the formula $$(x + y)^2 = x^2 + 2xy + y^2$$.

1. **State the problem:** Simplify the expression $$(20^4 + 5)^2 +$$ 2. **Calculate the inner term:** First, calculate $20^4$.

1. **State the problem:** We are given the quadratic function $$g(x) = 2x^2 + 4x - 5$$ and need to rewrite it in the form $$g(x) = a(x + h)^2 + k$$ where $$a, h, k \in \mathbb{Z}$$

1. **Stating the problem:** Solve the equation for 401: $ (2x - 1)^2 - (2 - x)(1 + 3x) = (x - 1)(7x - 2) $.

1. **State the problem:** Solve the simultaneous equations: $$\begin{cases} 2x + 3y - z = -4 \\ 3x + 2y + 2z = 14 \\ x - 3z = -13 \end{cases}$$

1. **Problem statement:** We have two snails, Flash and Trovão, racing. Flash moves at a constant speed of 5 cm per minute.

1. **State the problem:** Identify which expressions are equivalent to $6^3 \cdot 3^3$. 2. **Recall the property of exponents:** For any positive numbers $a$ and $b$, and exponent

1. **State the problem:** Identify which expressions are equivalent to $5^5 \cdot 5^{-2}$. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same bas

1. **State the problem:** Solve the inequality $$3x > 9$$ and graph the solution. 2. **Formula and rules:** To solve inequalities, we use the same rules as equations, but when mult

1. **State the problem:** Use the Greatest Common Factor (GCF) to write an equivalent expression for $60 + 72$ using the distributive property. 2. **Find the GCF of 60 and 72:**

1. **State the problem:** We need to find a quartic function $f(x)$ that produces a W-shaped curve opening upward with x-intercepts at approximately $x=-2$ and $x=3$, and a local m

1. **State the problem:** Use the Greatest Common Factor (GCF) to write an equivalent expression for $60 + 72$ using the distributive property. 2. **Find the GCF of 60 and 72:**

1. **State the problem:** Find the equation of the straight line in the form $y = mx + c$ given it crosses the y-axis at 16 and passes through the point $(2, 40)$. 2. **Recall the

1. **Énoncé du problème :** Simplifier l'expression suivante : $$\frac{8 \times (7 \times 5)^5 \times 5^2 \times 7^{-1}}{(7 \times 5^5 \times 7^{-2})^2}$$