🧮 algebra

1. The problem is to graph the function $y = x^2$. 2. The formula for this function is $y = x^2$, which is a quadratic function representing a parabola.

1. **State the problem:** Simplify the expression $$\frac{x + 5}{x - 4} - \frac{8x + 13}{x^2 - 3x - 4}$$. 2. **Factor the denominator:** Notice that $$x^2 - 3x - 4$$ can be factore

1. **State the problem:** Add and simplify the rational expressions $$\frac{6}{x+5} + \frac{x+65}{x^2-25}$$. 2. **Identify the denominators:** The denominators are $x+5$ and $x^2-2

1. **Problem:** Simplify the expression $4\sqrt{3} \cdot 2\sqrt{3} - 5\sqrt{27}$. 2. **Recall the rules:**

1. **State the problem:** Solve the inequality $7x - 2 > 6x - 5$. 2. **Isolate the variable terms on one side:** Subtract $6x$ from both sides:

1. **State the problem:** Solve the equation $$\frac{1}{2} + x - \frac{3}{4} = -0.75$$ for $x$. 2. **Rewrite the equation:** Convert decimals to fractions for consistency. Note tha

1. The problem asks to identify the type of function $f(x)$ based on the given table values: | $x$ | $f(x)$ |

1. The problem is to analyze the function $y=2^x$. 2. This is an exponential function where the base is 2 and the exponent is the variable $x$.

1. Masalah yang akan kita bahas adalah tentang fungsi invers. 2. Fungsi invers dari suatu fungsi $f(x)$ adalah fungsi yang membalikkan efek dari $f(x)$, sehingga jika $y=f(x)$, mak

1. **State the problem:** We need to find the greatest possible width of a rectangle whose area is more than 126 cm² and length is 18 cm. 2. **Formula:** The area $A$ of a rectangl

1. El problema es factorizar y simplificar la expresión $4x^2 - 20x - 11$. 2. La fórmula para factorizar un trinomio cuadrático $ax^2 + bx + c$ es buscar dos números que multiplica

1. **State the problem:** A bakery sells 250 loaves of bread per day at price 20 each. For every 0.25 increase in price, 10 fewer loaves are sold. We want to find the price that ma

1. **Problem statement:** Given the function $f(x) = \frac{2x + 2}{x - 1}$ with $x \neq 1$, find (1) $f^{-1}(3)$ and (2) express $f^{-1}(p) = kp + d$ and determine $k$ and $d$. 2.

1. **State the problem:** We are given the quadratic function $$y = x^2 + 2x$$ and need to analyze it. 2. **Recall the standard form:** A quadratic function is generally written as

1. **State the problem:** Solve the equation $$15 \cdot \log_3(2x - 5) - 2 \cdot \log_3 4 = \log_3 x - 1$$ for $x$. 2. **Recall logarithm properties:**

1. **State the problem:** Simplify or factor the quadratic expression $x^2 - 7x + 10$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers

1. **State the problem:** Simplify or factor the quadratic expression $X^2 + 5X + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers

1. **State the problem:** We are given two functions: $$k(x) = \frac{6x+5}{7x-9}$$

1. The problem asks to find answers for parts b to f, but since only the first question or problem is to be solved, I will solve part b completely. 2. Without the original problem

1. **State the problem:** Lucy exercises weekly with two types of activities: cardiovascular work ($x$ hours) and weight training ($y$ hours).

1. **State the problem:** We need to graph the quadratic function $$f(x) = 5x^2 + 10x - 5$$ and plot its vertex and another point on the parabola. 2. **Recall the vertex formula:**