🧮 algebra

1. Problem: Evaluate the expression $2x+3$ when $x=4$. Formula: Substitute $x=4$ into $2x+3$.

1. **Problem statement:** Find the two possible values of $m$ using the area of the triangle formed by the lines, and then find the acute angle between these two lines.

1. **State the problem:** We are given three functions: $f(x) = 3x + 2$, $g(x) = 7 - 2x$, and $h(x) = x - 5$. We need to find and simplify the composite functions $f \circ g (x)$ a

1. **Aufgabe 10a: Bestimme den Scheitelpunkt von** $f(x) = -2(x-3)^2 + 6$. - Die Scheitelpunktform einer Parabel ist $f(x) = a(x-d)^2 + e$ mit Scheitelpunkt $S(d|e)$.

1. **Exercice 5.1** **Problème :** Étudier la fonction $f(x) = x^3 - 5x^2 + 4$.

1. **Simplify** $\left(\frac{81}{16}\right)^{-\frac{3}{4}}$. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$.

1. The problem asks: Which number is not equal to a recurring decimal? 2. A recurring decimal is a decimal number where one or more digits repeat infinitely after the decimal point

1. The problem asks us to identify which number is not equal to a recurring decimal. 2. A recurring decimal is a decimal number that has one or more repeating digits or a repeating

1. The problem is about understanding the concept of piecewise functions and their continuity. 2. A piecewise function is defined by different expressions depending on the input va

1. **Stel het probleem vast:** We willen het gewicht berekenen van een L-vormig houten bureaublad met een dikte van 3 cm en een dichtheid van 0,75 kg per dm³. 2. **Gegeven afmeting

1. **State the problem:** Divide 5.5 in the ratio $\frac{1}{2} : \frac{1}{3}$. 2. **Understand the ratio:** The ratio parts are $\frac{1}{2}$ and $\frac{1}{3}$. To divide 5.5 in th

1. **Problem statement:** (a)(i) Express $y = -x^2 - 7x - 15$ in the form $y = -(x + p)^2 + q$.

1. **State the problem:** Simplify the expression $(-6x-3)-(2x-5)$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to the second grou

1. **Problem:** Bestimmen Sie die Gleichung der Parabel (quadratischen Funktion), die durch den Ursprung geht und im Punkt S(-2|1) ihren Scheitelpunkt hat. 2. **Formel:** Die Schei

1. **Stel het probleem vast:** Een fietser rijdt een berg op en legt een horizontale afstand van 35 km af. De werkelijke afstand die hij heeft gereden (de schuine afstand langs de

1. Das Problem lautet: Löse die Gleichung $2x + 3 = 7$ nach $x$ auf. 2. Die verwendete Formel ist die lineare Gleichung $ax + b = c$, wobei $a$, $b$ und $c$ Konstanten sind.

1. **Stating the problem:** We have a grid of equations with numbers 2, 3, 9, and empty circles connected by plus and equals signs. The goal is to find the missing numbers in the e

1. **State the problem:** We are given the quadratic function $f(x) = -2x^2 + 3x - 25$ and need to analyze it. 2. **Find the domain:** The domain of any quadratic function is all r

1. The problem is to evaluate $\log_3\left(\frac{81}{27}\right)$.\n\n2. Recall the logarithm rule: $\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)$.\n\n3. Apply the rule: $

1. **State the problem:** Expand and simplify the expression $$(a - 4x)\left(\frac{1}{2}a + 3x\right)$$. 2. **Formula used:** Use the distributive property (FOIL method) to multipl

1. **State the problem:** Simplify the expression $\frac{3}{4} - \frac{1}{4} + \frac{5}{4} \times \frac{2}{5}$.\n\n2. **Recall the order of operations:** Multiplication comes befor