🧮 algebra

1. Stating the problem: Solve the equation $$11 - \frac{5}{18} = u - 5 \frac{2}{18}$$ for $u$. 2. Simplify the mixed fraction on the right side: $$5 \frac{2}{18} = 5 + \frac{2}{18}

1. **State the problem:** Simplify the expression $$\frac{\sqrt[3]{8x^6}}{\sqrt[3]{125}}$$. 2. **Rewrite the cube roots as powers:** Recall that $$\sqrt[3]{a} = a^{\frac{1}{3}}$$,

1. The problem is to graph the function $y = x^3 - x^2$. 2. First, identify the key features of the function: intercepts and extrema.

1. Solve $\frac{2}{3}x = \frac{1}{2}$. Multiply both sides by the reciprocal of $\frac{2}{3}$, which is $\frac{3}{2}$:

1. State the problem: Simplify the expression and find the value of $$\frac{2x^2 - 8}{4x}$$. 2. Factor the numerator: $$2x^2 - 8 = 2(x^2 - 4)$$.

1. The problem is to simplify the expression $\left(\frac{2}{3} - \frac{1}{3}\right) \times \frac{1}{6}$.\n\n2. First, subtract the fractions inside the parentheses: $\frac{2}{3} -

1. The **domain** of a function is the set of all possible input values (usually $x$) for which the function is defined. 2. To find the domain, identify values that make the functi

1. **State the problem:** We need to graph the line with slope $\frac{3}{4}$ passing through the point $(-5, -1)$. 2. **Recall the point-slope form of a line:** The equation of a l

1. The problem is to evaluate the square root of 29, written as $\sqrt{29}$.\n\n2. Since 29 is not a perfect square, $\sqrt{29}$ is an irrational number.\n\n3. To approximate $\sqr

1. **State the problem:** We are given two functions: $$f(x) = 2x^3 + 2$$

1. **State the problem:** We are given two functions: $$f(x) = -3x - 3$$

1. **State the problem:** We are given two functions: $$f(x) = -2x^2 - 3$$

1. The problem asks to find the values of $X$ and $Y$. 2. However, no equations or expressions involving $X$ and $Y$ are provided.

1. The problem states a man spends fractions of his monthly salary on different expenses: rent, food, and books. We need to find the total fraction spent and the fraction left. 2.

1. **State the problem:** Simplify the expression $$\frac{6np}{18p}$$. 2. **Factor and cancel common terms:** The numerator is $$6np$$ and the denominator is $$18p$$.

1. Stwierdzenie problemu: Znajdź macierz $X$ spełniającą równania macierzowe. 2. Zadanie 6a: Mamy równanie

1. **State the problem:** Simplify the expression $$\frac{8x^2 + 3x^6 + 7x}{3x}$$. 2. **Rewrite the expression:** We can split the fraction into the sum of three fractions:

1. **Stating the problem:** Simplify the expression \( \frac{8x^2 + 34_6}{3x} \) and then multiply by \( x + 7x \). 2. **Interpreting the expression:** The numerator is \(8x^2 + 34

1. **State the problem:** Find the domain and range of the function $$f(x) = 3 \cos^{-1}\left(\frac{1}{2x - 1}\right) - 2.$$\n\n2. **Find the domain:** The function involves the in

1. **Problem:** Sketch and analyze the function $y=2x-3$. - This is a linear function with slope 2 and y-intercept -3.

1. **State the problem:** Find the area of the region bounded by the parabola $$y^{2} = 2x - 2$$ and the line $$y = x - 5$$. 2. **Rewrite the parabola equation:**