🧮 algebra

1. The problem asks if all parabolas follow the 1-4-9 rule. 2. The 1-4-9 rule is a property related to the distances of points on a parabola from the vertex along the axis of symme

1. The problem asks about the 1-4-9 rule for graphing quadratic functions and how it makes sense. 2. The 1-4-9 rule is a helpful guideline for plotting points around the vertex of

1. **State the problem:** We are given a table showing the number of songs (x) and the total cost (y) of a subscription. We need to find the slope $m$ of the line relating these va

1. **State the problem:** We are given the exponential function $$y = 1100(1.48)^{-7x}$$ and need to determine if it represents growth or decay, and find the percentage rate of inc

1. **State the problem:** We are given the exponential function $$y = 300 \left(\frac{1}{2}\right)^{-\frac{x}{68}}$$ and need to determine if it represents exponential growth or de

1. **Restate the problem:** You want to understand step 3 where we rewrite the function $y = 300 \left(\frac{1}{2}\right)^{-\frac{x}{68}}$. 2. **Recall the exponent rule:** For any

1. **State the problem:** We are given the exponential function $$y = 300 \left(\frac{1}{2}\right)^{-\frac{x}{68}}$$ and need to understand its behavior. 2. **Formula and explanati

1. The problem is to understand and represent numbers on a number line. 2. A number line is a straight line where each point corresponds to a real number.

1. **State the problem:** Solve the inequality $2x - 16 > -26$. 2. **Add 16 to both sides to isolate the term with $x$:**

1. Staðfesta vandamálið: Við erum með annars stigs margliðu $$f(x) = 2x^2 - 8x + 6$$ og viljum finna topppunktaformið $$f(x) = a(x - h)^2 + k$$. 2. Formúla fyrir að færa margliðu y

1. The problem asks if the fraction $\frac{3}{4}$ equals the division expression $4 \div 3$. 2. Recall that a fraction $\frac{a}{b}$ means $a$ divided by $b$, or $a \div b$.

1. **State the problem:** We have a circle given by the equation $$x^2 + y^2 + 6x - 2y - 26 = 0$$ and a line $$y = kx - 5$$. We want to find the values of the constant $k$ such tha

1. **State the problem:** We have a curve given by $$y = x^2 + 2cx + 4$$ and a line given by $$y = 4x + c$$, where $$c$$ is a constant. We want to find the values of $$c$$ for whic

1. **Problem statement:** (i) Show that two distinct lines $y = ax + c$ and $y = a'x + c'$ have a common point unless $a = a'$. Also show this when one line has infinite slope.

1. **Planteamiento del problema:** Calcular el dominio de la función $$f(x) = e^{\frac{3x}{x^2 - 1}} + \frac{2x}{x^2 + 9}$$.

1. **Problem:** Solve for $x$ in the equation $x - 5 = -8$ and then evaluate $(x^2 - 5)(x^3 - x)$. 2. **Step 1: Solve for $x$.**

1. **State the problem:** Given the equation $$R_G T_G + R_B T_B = 120$$ with $$R_G = 4$$, $$R_B = 10$$, and the relation $$T_G = T_B + 2$$, find the values of $$T_G$$ and $$T_B$$.

1. **State the problem:** Determine the domain of the function represented by a V-shaped graph centered at the origin (0,0). 2. **Understand the graph:** The graph is a V-shape wit

1. **State the problem:** We need to find the domain of the exponential function shown in the graph. 2. **Recall the domain of exponential functions:** The domain of any exponentia

1. The problem states that a 14-inch pepperoni pizza is sliced into 8 equal pieces, and one slice contains 352 calories. 2. We want to find the total calories $c$ in the whole pizz

1. **State the problem:** Calculate the value of $1.005^{96}$. 2. **Formula used:** The expression is an exponentiation where the base is $1.005$ and the exponent is $96$.