🧮 algebra

1. The problem is to analyze the function $f(x) = -(x+1)^2 + 16$ and understand its graph. 2. This is a quadratic function in vertex form: $f(x) = a(x-h)^2 + k$, where $(h,k)$ is t

1. **Stating the problem:** Create a similar problem to the given one: For $$y = \frac{2x - 1}{x^2 - x - 6}$$ find all asymptotes, state the domain and range, find the intercepts,

1. **Stating the problem:** Abhasra sold half of her comic books, then bought 17 more, and now has 32. We need to find how many comic books she started with. 2. **Define the variab

1. **Problem:** Evaluate each power without using a calculator. 2. **Key formula:** For any positive number $a$ and rational exponent $\frac{m}{n}$, we use the rule:

1. **Menyatakan masalah:** Diketahui setiap pekerja menyelesaikan $\frac{2}{5}$ bagian tugas pada pagi hari dan $\frac{3}{8}$ bagian pada sore hari. Ada 10 pekerja. Kita diminta me

1. Problem: Given $a = 19 + 8 \sqrt{3}$, find the value of $\sqrt{a} + \frac{1}{\sqrt{a}}$. 2. Formula and rules: To find $\sqrt{a} + \frac{1}{\sqrt{a}}$, we can use the identity:

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} x^2 - 4x + 3, & x \neq 0 \\ 3, & x = 0 \end{cases}$$

1. **State the problem:** We need to determine if the cubic equation $x^3 - 3x^2 - x + 4 = 0$ has a root in a given interval (though the interval is not specified, we will analyze

1. المشكلة: نريد إيجاد المقلوب (résiproque) لعدد معين. 2. تعريف المقلوب: المقلوب لعدد $a$ هو العدد الذي إذا ضربناه في $a$ يعطي 1.

1. The problem is unclear as "gof" is not a standard mathematical expression or function notation. 2. If you meant the composition of functions, such as $g \circ f$, it means apply

1. Muammo: 1-tokcada 80 ta non, 2-tokcada 95 ta non bor. Nonlar qo'shildi va umumiy son 15% ga oshdi. So'ngra sotildi va 20% ga kamaydi. Nonlarning umumiy soni necha foizga o'zgarg

1. We are asked to find the inverse of the function $$f(x) = -1 - \frac{1}{5}x$$ and then graph both the function and its inverse. 2. To find the inverse, start by replacing $$f(x)

1. **State the problem:** We know that 10% of a number is 22. We need to find 5%, 20%, 25%, 55%, and 75% of the same number. 2. **Formula and explanation:** Percentage means "per h

1. Masalani tushuntirish: Sizda boshlang'ich qiymat $24000$ va yangi qiymat $19200$ berilgan. Siz kamayish foizini topmoqchisiz. 2. Formulani eslatib o'tamiz: Kamayish foizi quyida

1. **State the problem:** Solve for $m$ in the equation $m - n \log_3 2 = 10 \log_9 6$. 2. **Recall logarithm properties:**

1. Muammo: 42 foiz 672 ga teng bo'lgan sonni toping. 2. Formulani eslatib o'tamiz: foizni son sifatida ifodalash uchun foizni 100 ga bo'lamiz. Ya'ni, $42\% = \frac{42}{100} = 0.42$

1. The problem is to simplify or understand the expression with the entire quantity $2t-5$ under the square root, which is written as $\sqrt{2t-5}$. 2. The square root function $\s

1. **State the problem:** We need to find the total number of spectators at a soccer match given that 60% are men, the rest are women and children, the number of children is \(\fra

1. Let's start by understanding what a variation table is. It shows how a function's value changes as the input changes, often indicating increasing or decreasing behavior. 2. Supp

1. **Stating the problem:** You want to solve a variation table where you have 3 given values but one value is missing. 2. **Understanding variation tables:** Variation tables show

1. **State the problem:** Determine the nature of the roots of the quadratic equation $x^2 + x - 1 = 0$. 2. **Recall the formula:** The discriminant $\Delta$ of a quadratic equatio