🧮 algebra

1. We are asked to divide the polynomial $2x^2 + x - 3$ by $x - 1$. 2. Polynomial division formula: $$\frac{\text{Dividend}}{\text{Divisor}} = \text{Quotient} + \frac{\text{Remaind

1. **State the problem:** Florence has a rectangular field 40 m long and 25 m wide. She reduces both length and width by 20%. We need to find the percentage reduction in the area.

1. The problem is to evaluate the expression $5^2 - 2^2$. 2. Recall the formula for squaring a number: $a^2 = a \times a$.

1. **State the problem:** Solve the inequality $x^2 \le 100$. 2. **Recall the rule:** For any real number $x$, $x^2 \le a^2$ implies $-a \le x \le a$ when $a \ge 0$.

1. **State the problem:** We have six math expressions to evaluate and then match their results to letters on a decoder ring to find the passcode. 2. **Evaluate each expression ste

1. The problem asks to convert the mixed number $2 \frac{1}{2}$ into an improper fraction. 2. A mixed number consists of a whole number and a fraction. To convert it to an improper

1. **State the problem:** Simplify each expression and then order the results from least to greatest. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multipl

1. The problem asks to convert the mixed number $4 \frac{3}{4}$ into an improper fraction, which is a fraction greater than one. 2. Recall the formula to convert a mixed number $a

1. The problem is to analyze the function $f(x) = \log x$ and understand its domain, range, and behavior. 2. The logarithmic function $f(x) = \log x$ is defined only for positive v

1. The problem is to solve the division of two fractions: $\frac{2}{3} \div \frac{6}{9}$.\n\n2. The formula for dividing fractions is: \n$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b

1. **State the problem:** Mrs. Sanchez spent 19.14 on filters and will receive a 5% rebate. We need to find the final price after applying the rebate. 2. **Formula:** The final pri

1. **State the problem:** We want to find the visual composition $g(f(9))$ using the given graphs of $f$ and $g$. 2. **Identify $f(9)$ from the graph:** From the piecewise linear g

1. **State the problem:** We need to evaluate the composition $g(f(9))$, which means first find $f(9)$ and then find $g$ of that result. 2. **Analyze $f(x)$:** From the description

1. The problem asks which functions have graphs with symmetry to the left of the vertex and axis of symmetry. 2. The given function is $f(x) = (x - 1)^2 + 1$. This is a parabola wi

1. The problem gives a table showing the relationship between teaspoons of powder and number of scoops for different colors. 2. We observe from the table that the number of scoops

1. Problema: Rasti funkcijos $f(x) = 8 - 4|\tan(6x)|$ didžiausią reikšmę. 2. Formulė ir taisyklės: Funkcijos didžiausia reikšmė bus tada, kai išraiška $-4|\tan(6x)|$ bus kuo mažesn

1. **State the problem:** Solve the equation $$-2(x + 3) = 6x + 8$$ for $x$. 2. **Apply the distributive property:** Multiply $-2$ by each term inside the parentheses.

1. **State the problem:** Solve the equation $$-2(x + 3) = 6x + 8$$ for $x$. 2. **Apply the distributive property:** Multiply $-2$ by both $x$ and $3$:

1. **State the problem:** Solve the inequality $$\frac{x - 11}{2} > 3x + 5.5$$ for $x$. 2. **Write down the inequality:**

1. **State the problem:** Solve the inequality $$8x + 120 < 4x - 64$$ for $x$. 2. **Isolate the variable terms:** Subtract $4x$ from both sides to get all $x$ terms on one side.

1. The problem asks for the axis of symmetry of a parabola with vertex at the point $(5,0)$. 2. The axis of symmetry of a parabola given by a quadratic function is a vertical line