🧮 algebra

1. **Problem 1: Calculate the total cost of a meal including tax** The meal costs $45 and the tax rate is 8%. We want to find the total cost including tax.

1. **State the problem:** Solve the inequality $$5 + 2(6b - 10) > -b + 8 - 7$$ for $b$ and write the answer in simplest form. 2. **Expand and simplify both sides:**

1. **State the problem:** Solve the inequality $$9 + 3(-3t + 10) \leq 6t + 8 - 4$$ for $t$ and write the answer in simplest form. 2. **Apply the distributive property:** Multiply $

1. Stating the problem: Solve the system of linear equations: $$-5 + 3x = 16$$

1. **Stating the problem:** We want to understand and solve the equation $$\frac{\sqrt{2}}{2} = \frac{2x + 9}{\sqrt{x^2 + 74.3}}$$ and the equivalent transformations given. 2. **Or

1. **Problem statement:** The line $l$ passes through the point $(4, 2)$ and forms a triangle with the coordinate axes with area 25 square units. The line cuts the x-axis at $(x_1,

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