🧮 algebra

1. The user asked to match choices with graphs similar to a previous example, but no specific functions or choices were provided. 2. Without explicit functions or graphs given, no

1. The problem is to find the range of the relation given by the ordered pairs: (8, -9), (5, -3), (-4, 6), (-3, -2), (6, 8), and (8, 6). 2. The range of a relation is the set of al

1. Let's analyze each function and describe its graph shape based on the given information. 2. For $f(x) = -x^3 - 2x^2 - 1$, it is a cubic function with a negative leading coeffici

1. We are given four functions $f(x)$, $g(x)$, $h(x)$, and $k(x)$ with their polynomial expressions. 2. Let's analyze each function's general shape based on degree and leading coef

1. We are given the equation $5x + 3y = -15$ and asked to find its intercepts. 2. To find the \textbf{x-intercept}, set $y=0$ and solve for $x$:

1. **State the problem:** Solve the quadratic equation $2x^2 + x^2 + 1 = 0$. 2. **Combine like terms:**

1. The question asks about the meaning of the variable $x$ given that $A = Z$ and $B = Y$. 2. However, from the statement alone, there is no direct information or equation linking

1. نبدأ بتوضيح المسألة: المعادلة المعطاة هي $$y = - \frac{1}{\sqrt{3}} x$$. 2. نلاحظ أن المعادلة تعبر عن خط مستقيم حيث قيمة \( y \) تعتمد خطيًا على \( x \) بمعامل \( - \frac{1}{\sq

1. **State the problem:** We are given that 8 men can dig a field in 9 days.

1. The problem states we start with the equation $$y = - \frac{1}{\sqrt{3}} x$$. 2. You are asked to multiply both sides by $$x$$. This means you multiply each side of the equation

1. The given equation is $kx^2 + 3x - 4 = 0$. 2. This is a quadratic equation where:

1. The problem is to find the value(s) of $k$ such that the quadratic equation $$x^2 - 2x + k = 0$$ has one repeated root. 2. A quadratic equation $ax^2 + bx + c = 0$ has a repeate

1. The problem asks us to find the value(s) of $k$ such that the quadratic equation $$x^2 - 3x + k = 0$$ has a repeated root. 2. A quadratic equation has a repeated root when its d

1. State the problem: We know 30 workers can dig a well in 180 hours. We want to find how many workers are needed to dig the same well in 60 hours. 2. Understand the relationship:

1. Find the rectangular coordinates for the polar point $(3, \frac{\pi}{2})$. - Recall conversion formulas: $x = r \cos \theta$, $y = r \sin \theta$.

1. The problem asks for the minimum value of the quadratic function whose graph is a parabola opening upwards. 2. The vertex form of a parabola is given by $$y = a(x - h)^2 + k$$ w

1. The problem states that the number $k$ is rounded to two decimal places to give $4.72$. 2. When rounding to 2 decimal places, the actual number $k$ lies within an interval that

1. The problem states the equation $$\frac{3}{4} \times 28 = \frac{1}{3} \times y$$. 2. First, simplify the left side by multiplying \(\frac{3}{4}\) by 28:

1. Θεώρηση των παραστάσεων με απόλυτες τιμές: 1.α. \(|3-\pi| + |4-\pi|\)

1. Given expressions with absolute values, rewrite without absolute values assuming $\pi \approx 3.14$: a) $|3 - \pi| + |4 - \pi|$

1. Στον πρώτο πρόβλημα, υπολογίζουμε τις τιμές των εκφράσεων:\nα. $$|3-\pi|+|4-\pi|$$ \n Υπολογίζουμε περίπου: $\pi \approx 3.1415$ \n Άρα $|3-3.1415| = 0.1415$, και $|4-3.1415| =