🧮 algebra

1. The problem is to evaluate the expression $6 \div 2(1 + 2)$.\n\n2. According to the order of operations (PEMDAS/BODMAS), we first solve expressions inside parentheses.\n\n3. Cal

1. **State the problem:** Evaluate the expression $$6 \div 2(1 + 2)$$. 2. **Apply the order of operations (PEMDAS/BODMAS):**

1. **State the problem:** We are given a function that models the credit left on a prepaid phone card after making calls. The function is:

1. **State the problem:** We need to find the height of the plant after 20 months given the function $$H(x) = 8.00 + 0.08x$$ where $H(x)$ is the height in meters and $x$ is the num

1. **State the problem:** We want to solve the equation $$2x^2 + 3x = 4$$ using an iterative method and find the solution near $$x = -2$$ correct to 4 significant figures. 2. **Rew

1. **State the problem:** We have a parabolic arch represented by the polynomial $$p(x) = -0.0025x^2 - 0.025x + 136$$. (i) Write the coordinates of point A (the highest point on th

1. **State the problem:** We are given two points on the function $n(x)$: $n(1.36) = 0.9131$ and $n(1.37) = 0.9147$. We want to approximate $n(1.367)$ and $n(1.356)$ using linear i

1. **State the problem:** Solve the system of linear equations: $$\frac{2}{3}x + y = -2$$

1. **Problem:** Find the intersection point of the lines $y=3x+1$ and $y=-x-3$. 2. **Formula and rules:** To find the intersection, set the two equations equal: $$3x+1 = -x-3$$

1. The problem is to understand the shape of the graph of the function $$g(x) = (x + 4)^3 + 3$$. 2. This is a cubic function shifted horizontally and vertically. The base cubic fun

1. **State the problem:** We have the function $g(x) = 6x^2 - 1$.

1. Problemet: Vi har en funktion givet ved $$f(x) = -4x + 5$$ og en tabel med nogle værdier for $x$ og $f(x)$, hvor et tal mangler. Vi skal finde det manglende tal. 2. Formel: Funk

1. **State the problem:** Solve the cubic equation $$n^3 - 3n - 2 = 0$$ to find the exact roots. 2. **Recall the formula and approach:** For cubic equations of the form $$n^3 + an^

1. **State the problem:** Calculate the sum of the fractions $\frac{2}{-9} + \frac{-8}{9}$ and $\frac{9}{32} - \frac{-5}{-8}$.\n\n2. **Calculate the first expression:** $\frac{2}{-

1. **Problem:** Calculate $-\frac{5}{16} + \frac{7}{4}$. 2. **Formula:** To add fractions, use the formula $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a,b,c,d$ are in

1. The problem involves understanding the expression with a minus sign next to the 9 and the number 2, resulting in -8, not 8. 2. Let's clarify the expression: if you have $9 - 2$,

1. Calculate $-\frac{2}{7} + \frac{9}{7}$. Since denominators are the same, add numerators:

1. Problema: Multiplicar monomios por monomios. 2. Regla: Para multiplicar monomios, multiplicamos los coeficientes y sumamos los exponentes de las variables iguales.

1. **Simplify** $\frac{5}{63} = \frac{5 \times 8}{9 \times 7} = \frac{5}{7}$ - The original fraction is $\frac{5}{63}$.

1. Énoncé du problème : Simplifier les fractions suivantes au maximum : $$\frac{21}{14}, \frac{36}{42}, \frac{24}{-22}, \frac{-15}{-18}, \frac{-25}{55}, \frac{25}{200}$$

1. **State the problem:** Simplify the expression $$\frac{10(p^3 q^2 r^0)^{-3}}{(8p^{-3} q^5 r^3)^{-2}}$$. 2. **Recall the rules:**