🧮 algebra

1. **State the problem:** Find the gradient $m$ of the line passing through points $A(-7, 2)$ and $B(2, 8)$. 2. **Formula:** The gradient formula is $$m = \frac{y_2 - y_1}{x_2 - x_

1. **State the problem:** We are given two equations:

1. **State the problem:** We have four parabolas given by $y = Ax^2$, $y = Bx^2$, $y = Cx^2$, and $y = Dx^2$. We need to determine for each coefficient $A$, $B$, $C$, and $D$ wheth

1. **State the problem:** We are given the function $y = 2x - 2$ and a set of $x$ values: $-2, -1, 0, 1, 2$. We need to find the corresponding $y$ values or $f(x)$ values for these

1. **State the problem:** We need to find the value of $b - 6$ given the equation $2(b - 6)\3 = 4$. 2. **Rewrite the equation:** The expression $2(b - 6)\3$ means $\frac{2(b - 6)}{

1. **State the problem:** Simplify the expression $$\sqrt{81y^6}$$. 2. **Recall the formula:** The square root of a product is the product of the square roots: $$\sqrt{a b} = \sqrt

1. **State the problem:** We need to order the following expressions from least to greatest: $$\frac{8}{9}, \infty, \int_1^4 x\,dx, \frac{6\pi}{6}, e^4, \log_2(20), \sum_{i=1}^5 i,

1. The problem appears to involve the expression $$\frac{3x}{2}$$. 2. We need to understand or simplify the expression $$\frac{3x}{2}$$.

1. **State the problem:** Given $x + y = \sqrt{3}$ and $x^2 + y^2 = 5$, find:

1. **State the problem:** We need to find $xy$ given different conditions involving $x+y$, $x-y$, $x^2+y^2$, and $(x-y)^2$. 2. **Recall the formula:**

1. **State the problem:** Calculate the value of the expression $\frac{82}{3} \times 33 + 12$. 2. **Recall the order of operations:** Multiplication and division are performed from

1. نبدأ بكتابة المسألة: $$8 \times (2^4 - 3) + 8$$. 2. نحسب الأس أولاً: $$2^4 = 16$$.

1. We willen de uitdrukking $\log_3(27x^2)$ vereenvoudigen. 2. Gebruik de logaritmische regel: $\log_b(mn) = \log_b(m) + \log_b(n)$.

1. **State the problem:** We are given the sequence $1$, $2$, $4$, $7$ and need to find the pattern or formula that generates this sequence. 2. **Analyze the sequence:** Look at th

1. **State the problem:** We want to describe the transformation of the function $f(x) = x^2$ when it changes to $g(x) = (x + 2)^2$ and identify which graph corresponds to this tra

1. **Probleemstelling:** We starten met de functie $$y = 2x - x^2$$ en passen vier transformaties toe: horizontale verschuiving, horizontale uitrekking, spiegeling om de y-as, en v

1. **State the problem:** We need to sketch the graph of the function $$y = |x - 2a|$$ where $$a$$ is a positive constant. 2. **Recall the absolute value function:** The graph of $

1. **Stating the problem:** Simplify the expression $$\frac{S^{m+2}}{3.5^{m+1}} \div (S^{m+2} \cdot S)$$. 2. **Rewrite the expression:** The division by a product can be rewritten

1. **State the problem:** Solve the equation $$3|-8x| + 8 = 80$$ for $x$. 2. **Isolate the absolute value term:**

1. **State the problem:** Solve the equation $$3(x - 1) = 2x + 9$$ for $$x$$. 2. **Apply the distributive property:** Multiply $$3$$ by each term inside the parentheses.

1. **State the problem:** We need to find the values of $x$ that satisfy the equation $$(x - m)(x + n) = 0$$. 2. **Recall the zero product property:** If the product of two factors