🧮 algebra

1. **State the problem:** We need to find the principal amount $P$ given the simple interest $I=18$, the rate $r=6\%$, and the time $t=3$ months. 2. **Formula:** The simple interes

1. The problem asks to describe the transformations to obtain the graph of $g(x) = 6^{x - 7}$ from the graph of $f(x) = 6^x$. 2. Recall the general rule for horizontal shifts in ex

1. The problem asks to graph the function $$y = 2^x$$ over the interval $$[-4,4]$$. 2. The function $$y = 2^x$$ is an exponential function with base 2, which means it grows rapidly

1. **State the problem:** Find the vertical asymptotes of the function $$f(x) = \frac{x^2 + 5}{(x^2 - 25)(x^2 - 64)}.$$\n\n2. **Recall the rule for vertical asymptotes:** Vertical

1. **State the problem:** Find the horizontal asymptote(s) of the function $$f(x) = \frac{5x^2 + 4x + 4}{4x^2 + 5x - 3}$$. 2. **Recall the rule for horizontal asymptotes:**

1. The problem is to graph the piecewise function: $$f(x) = \begin{cases} 1 - 2x & \text{if } x < 2 \\ x - 3 & \text{if } x \geq 2 \end{cases}$$

1. **State the problem:** We need to graph the piecewise function $$f(x) = \begin{cases} 1 - 2x & \text{if } x < 2 \\ x - 3 & \text{if } x \geq 2 \end{cases}$$

1. The problem asks how the graph of $g(x) = -|x - 5|$ relates to the graph of $f(x) = |x|$ and to sketch the graph of $g(x)$. 2. Recall the base function $f(x) = |x|$ is a V-shape

1. The problem asks us to find the domain of the function $$g(x) = \sqrt{3 - x}$$. 2. The domain of a function involving a square root requires the expression inside the root to be

1. **State the problem:** Find the domain of the function $$f(x) = \frac{x - 9}{x + 3}$$. 2. **Recall the domain rule for rational functions:** The domain includes all real numbers

1. **Stating the problem:** Undersök hur många procent $P = x \cdot y$ ökar om $x$ ökar med 10 % och $y$ ökar med 20 %.

1. **State the problem:** Find the domain of the function $$f(x) = \frac{x - 9}{x + 5}$$. 2. **Recall the domain rule for rational functions:** The domain includes all real numbers

1. The problem asks to find the value of $y$ for $y = f(1)$ using the graph of the function $f$. 2. From the description, the graph has a local maximum near $y=5$ at $x=0$, a local

1. Problemet handlar om att hitta elpriset per kWh år 2013, givet att priset år 2014 var 27 öre och att detta pris var 40 % lägre än året innan. 2. Formeln för att beräkna ursprung

1. The problem asks to evaluate the permutation expression $6P5$. 2. The formula for permutations is:

1. The problem asks to evaluate the combination $15C2$, which represents the number of ways to choose 2 items from 15 without regard to order. 2. The formula for combinations is:

1. **State the problem:** Find the y-intercept and x-intercepts of the function $$g(x) = -(x+5)^2 + 8$$ and describe the graph shape. 2. **Y-intercept:** The y-intercept occurs whe

1. **State the problem:** We are given the function $$g(x) = -(x + 5)^2 + 8$$ and need to find: (A) Intercepts

1. **State the problem:** Simplify the expression $(-4s + 2t) - (-s + t)$. 2. **Recall the rule:** When subtracting a group, distribute the minus sign to each term inside the paren

1. The problem is to match each quadratic equation with the correct graph among functions f, g, m, and n. 2. The general form of a parabola is $$y = a(x-h)^2 + k$$ where $(h,k)$ is

1. The problem asks how the graph of $g(x) = (x + 6)^2 + 1$ is related to the graph of $f(x) = x^2$. 2. The base function is $f(x) = x^2$, which is a parabola with vertex at $(0,0)