🧮 algebra

1. Le problème demande de trouver une équation du second degré pour modéliser une situation où une personne a payé 180 pour un certain nombre de bouteilles, mais pour 200, elle aur

1. The problem is to find an approximate solution to the equation $$x^3 - 3x + 1 = 0$$ using the iterative formula $$x_{n+1} = - \frac{1}{x_n^2 - 3}$$ starting with $$x_1 = 0.5$$.

1. **State the problem:** Solve the quadratic equation $x^2 - 7x + 11 = 0$ and then find the integer values of $x$ that satisfy the inequality $x^2 - 7x + 11 < 0$. 2. **Recall the

1. **State the problem:** Solve the simultaneous equations for real numbers $p, q \neq 0$: $$4p + q = 10$$

1. **State the problem:** We need to write an equation for the total cost $C$ of using a computer for $t$ minutes at an internet cafe. 2. **Given information:**

1. **State the problem:** Simplify the expression $$\frac{5y^2 - 35y}{49 - y^2}$$ and find the restrictions on the variable $y$. 2. **Factor numerator and denominator:**

1. **State the problem:** Solve the equation $$\frac{3x - 16}{3} = \frac{5x + 7}{4}$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by t

1. The problem is to express the ratio $x : \sqrt{2}$ as an equation with another equivalent ratio. 2. Recall that two ratios $a : b$ and $c : d$ are equal if $\frac{a}{b} = \frac{

1. The problem asks which relationship represents a function with a greater rate of change than the given function. 2. The given function's slope (rate of change) is approximately

1. **State the problem:** Find the greatest common factor (GCF) of the two terms $16x^{4}y^{3}$ and $12x^{2}y^{7}$. 2. **Recall the formula and rules:**

1. **State the problem:** Tanisha has a cell phone plan with a base charge of 25 per month that includes 500 international minutes. For every minute over 500, she pays 2 per extra

1. **State the problem:** Simplify the expression $$[(4a^4)(2a^3)]^2$$. 2. **Use the product rule for exponents:** When multiplying terms with the same base, add the exponents: $$a

1. **State the problem:** We have two lines defined by the equations: $$r: x + y = 2$$

1. The problem asks us to write an equation for Fawzia's salary $S$ after $n$ years at the company based on the graph. 2. From the graph, we see the salary increases linearly start

1. **State the problem:** Solve the equation $$a^3 + a^2 = 42a$$ for all values of $a$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero:

1. **State the problem:** Solve the equation $$x^{\frac{7}{3}} = 128$$ for $x$. 2. **Recall the formula:** To solve for $x$ when it is raised to a fractional power, use the propert

1. **State the problem:** Factor the quadratic expression $$16x^2 - 40xy + 25y^2$$. 2. **Recognize the form:** This is a quadratic trinomial in terms of $x$ and $y$. It resembles a

1. The problem is to solve part (c) of number 6. Since the exact problem statement is not provided, please provide the full problem or the expression for part (c) of number 6. 2. G

1. The problem asks for the solution to a system of two linear equations represented by two lines on a graph. 2. The solution to a system of linear equations is the point where the

1. The problem is to simplify the expression \( (C) \) which appears to be a single variable or constant. 2. Since \( C \) is just a symbol representing a constant or variable, the

1. The problem is to identify the key features of a polynomial function. 2. Key features of a polynomial function include its degree, leading coefficient, intercepts (x- and y-inte