🧮 algebra

1. The problem is to graph the piecewise function $$f(x) = \begin{cases} 2x + 8 & 0 \leq x \leq 2 \\ (x - 4)^2 + 8 & 2 < x < 7 \\ 17 & 7 \leq x \leq 10 \end{cases}$$ over the domai

1. **State the problem:** We are given the expression $-5 + \frac{7x}{4}$ and a table of values for $x$ and the expression's value. We need to identify which algebraic expression f

1. The problem asks to write an equivalent expression to $x - 6y + 5$. 2. Let's analyze each choice:

1. **Stating the problem:** We are given a graph of a function $f(x)$ with points and behavior described, and we need to find an equation that fits this curve. 2. **Analyzing the g

1. **State the problem:** Solve the system of equations using elementary row operations: $$\begin{cases} x_1 + 2x_2 = -2 \\ 3x_1 + 5x_2 = -8 \end{cases}$$

1. **State the problem:** A cell phone plan costs 4.97 per month plus 0.03 per minute. We need to find the charge for 60 minutes, write the cost equation, and find the minutes for

1. **Problem:** Simplify the expression $$\left(x^{2} + 3x\right)^{2} - 2\left(x^{2} + 3x\right) - 8$$. 2. **Formula and rules:** Recognize this as a quadratic in terms of the expr

1. **Problem:** Masa, $t$, yang diambil oleh Ben berjalan ke sekolah berubah secara songsang dengan punca kuasa dua laju jalannya, $s$. Diberi $t=35$ minit apabila $s=4$ km/j. Cari

1. **State the problem:** We need to find what percent of the nonfiction book sales were travel books. 2. **Identify the data:** The frequencies of nonfiction book sales are:

1. **State the problem:** Solve for $x$ in the equation $$\sqrt{x + 4!} + \sqrt{x} = 12.$$ 2. **Recall the factorial:** $4! = 4 \times 3 \times 2 \times 1 = 24$. Substitute this in

1. The problem asks to find what percent of the animals listed are mammals. 2. The formula to find percentage is:

1. **Problem 8:** Given that $R$ varies directly as the square of $S$ and inversely as $T$, with $R=21$ when $S=6$ and $T=3$. Find $T$ when $R=18$ and $S=4$. 2. **Formula:** Since

1. El problema es evaluar la expresión: $1 - 1 + 2^{2/7} + \frac{2}{9} \times \frac{3}{14} \times \left(-\frac{1}{2}\right) - \sqrt{\frac{2}{3}} \times \frac{1}{24} - \sqrt[3]{-3}

1. **Problem Statement:** We are given three modular functions in the form $y = |ax + b|$ with vertices at $(1,0)$ and different slopes for each function: $f(x)$ with slopes $\pm 2

1. Given that $ST^{1/3} = k$, where $k$ is a constant, determine the true statement about the variation of $S$ and $T$. 2. Given $w \propto \frac{x^m}{y^n}$ such that $w$ varies di

1. **Problem Statement:** Find the intercepts of the function $f$ given the graph points: $(-4,0)$, $(-2,-1)$, $(0,1)$, $(2,-1)$, $(4,0)$.

1. Diberi bahawa g = 2 apabila h = 27. Ungkapkan g dalam sebutan h jika (a) g berubah secara songsang dengan h.

1. **State the problem:** We have a cuboid water tank where volume $V$ varies directly as height $h$ and base area $A$. Given $V=90$ when $h=2$ and $A=30$, find the new height if v

1. **Stating the problem:** Mr Lim saved 30000 for 5 years and received interest of 6000. Interest $I$ varies directly as principal $P$ and time $t$. Find the interest if he saves

1. **State the problem:** Simplify the expression $$\frac{1}{x-1} - \frac{3x+3}{x^2 + x - 2} + \frac{1}{x+2}$$. 2. **Factor denominators:** Note that $$x^2 + x - 2 = (x-1)(x+2)$$.

1. **Problem statement:** Write equations for the modular functions $f(x)$, $g(x)$, and $h(x)$ given their graphs with vertices at $(-4,0)$, $(0,0)$, and $(3,0)$ respectively. 2. *