🧮 algebra

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

1. **State the problem:** We need to identify and list the holes, vertical asymptotes, and horizontal asymptotes of a rational function. A rational function is a ratio of two polyn

1. **State the problem:** Simplify the expression $$\left(\frac{2v^{-3} \cdot u^{2} v^{-1}}{2u^{3} v^{4}}\right)^{-2}$$. 2. **Combine terms in the numerator:** Multiply the powers

1. **State the problem:** Simplify the expression $\left(2v - 3 \cdot u^{2}v - 12u^{3}v^{4}\right)^{-2}$. 2. **Rewrite the expression inside the parentheses:** Note that the expres

1. **State the problem:** Solve algebraically for all values of $x$ in the equation $$2x^3 - 14x^2 + 2x - 14 = 0.$$\n\n2. **Factor out the greatest common factor (GCF):** Notice ea

1. We are asked to factor the expression: $$32a^2b^2 - 48ab + 18$$. 2. First, identify the greatest common factor (GCF) of all terms.

1. **State the problem:** Simplify the expression $$2(a + b)^2 - x(a + b)$$. 2. **Recall the formulas:**