🧮 algebra
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.
Boat Sale Profit
1. The problem states that Jimmy made a 15% profit on the sale of a boat which originally cost N15,000.
2. To find the selling price, we need to calculate 15% of the original cost
Total Prize
1. **State the problem:**
We know the winner receives half (\(\frac{1}{2}\)) of the total prize money and gets N6,000.
Map Distance
1. **State the problem:**
Given that 1 inch on the map represents 20 miles in reality, and the distance between two towns on the map is 6 1/5 inches, find the actual distance betwe
Rational Number
1. Let's start by defining what a rational number is.
2. A rational number is any number that can be expressed as the quotient or fraction $\frac{a}{b}$, where $a$ and $b$ are inte
Gpa Calculation
1. **State the problem:** A student took 5 classes with given credit hours and received letter grades. We need to find the GPA using a 4.0 scale (A=4, B=3, C=2).
2. **List the clas
Instrument Original Cost
1. **Stating the problem:** Julie buys a flute for N306 after two discounts: first 10% for students, then an additional 15% during a sale. We need to find the original price of the
Vienadojumu Atrisi
1. Uzdevums: Atrisināt vienādojumus.
2. a) Atrisināsim vienādojumu $$\frac{4}{x} = 5 - x^2$$, izmantojot grafiku.
Write Scientific
1. The problem is to write the number $8.6 \times 10^{-3}$ as an ordinary decimal number.
2. Recall that $10^{-3}$ means $\frac{1}{10^3} = \frac{1}{1000}$.
Number Conversion
1. The problem asks us to convert the number given in scientific notation $3.46 \times 10^6$ into an ordinary number.
2. Scientific notation means we multiply $3.46$ by $10$ raised
Scientific Division
1. **State the problem:** We need to divide $4.37 \times 10^{8}$ by $7.13 \times 10^{-3}$ and express the answer in standard form to 3 significant figures.
2. **Write down the divi
Exponent Multiplication
1. The problem asks us to find the exponent in the expression $W^8 \times W = W^{\square}$.
2. Recall the rule of exponents: When multiplying like bases, add the exponents.
Solution Unique
1. Énoncé du problème : Montrer que l'équation $$\sqrt{x} - 3 = \frac{4}{x^{2}}$$ admet une unique solution.
2. Réécrivons l'équation pour faciliter l'étude : $$\sqrt{x} - 3 = \fra
Fraction Division
1. The problem is to divide two fractions: $\frac{4}{5} \div \frac{8}{7}$.
2. Dividing by a fraction is the same as multiplying by its reciprocal. So, rewrite the division as multi
Fraction Modification
1. Énoncer le problème : Modifier la fraction \( \frac{4}{7} \) en \( \frac{4}{x^2} \) dans le premier énoncé.
2. Remplacer la fraction dans l'expression originale par la nouvelle
Function Examples
1. **Linear functions:**
These are of the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
Curries Salads Ratio
1. The problem asks for the ratio of curries to salads sold by the restaurant on Thursday.
2. From the given data: On Thursday, salads sold = 12 and curries sold = 8.
Fraction Equality
1. Énonçons le problème : nous avons une fraction $\frac{4}{7}$ et une autre expression $\frac{4}{x^2}$. Vous demandez probablement à comparer ou résoudre une équation impliquant c
Ratio Chillies Quiches
1. The problem asks for the ratio of chillies to quiches sold by the restaurant on Wednesday.
2. From the graph description, the number of quiches sold on Wednesday is 20.
Equation Racine
1. Énoncé du problème :\n(a) Montrer que l'équation $\sqrt{x} - 3 = \frac{4}{7}$ possède une unique solution réelle.\n(b) Donner un encadrement à $10^{-2}$ près de cette solution.\
Determination A B
1. Énoncé du problème : On considère la fonction $$f(x) = \frac{3x^2 + ax + b}{x^2 + 1}$$ avec $$a$$ et $$b$$ réels. On veut déterminer les valeurs de $$a$$ et $$b$$ telles que la
Gpa Calculation
1. We are asked to calculate your GPA based on the given credit hours and grades.
2. Here are the data points you provided: