🧮 algebra

1. **State the problem:** We are given the formula for simple interest: $$I = Prt$$ where $I$ is the interest earned, $P$ is the principal, $r$ is the interest rate, and $t$ is the

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 4x + 1}{2x^4 - 6x^2 - 5x + 7}$$. 2. **Factor numerator and denominator if possible:**

1. **State the problem:** We are given the expression $0.2y^2 + 0.32y + 0.96$ and want to rewrite it in the form $a(5y^2 + 8y + 24)$, where $a$ is a constant. 2. **Identify the for

1. **State the problem:** Supriya uses 12 oz of dough to make one batch of papadums. She has 60 oz of dough in total and wants to find out how many batches ($b$) she can make. 2. *

1. **State the problem:** Supriya uses 12 oz of dough to make one batch of papadums. She has 60 oz of dough in total and wants to find out how many batches she can make. 2. **Write

1. The problem is to understand the shape and behavior of the function $f(x) = a^x$ where $a > 0$ and $a \neq 1$. 2. The formula for an exponential function is $f(x) = a^x$, where

1. We are asked to compare pairs of exponential expressions involving powers of 2 and powers of \( \frac{1}{2} \). The goal is to determine the inequality symbol (\( <, >, = \)) th

1. Problema: Rasti apytikslius lygties $$-x^2 - 3 = 4^{x-1}$$ sprendinius intervale $$x \in [-4,4]$$ remiantis grafiku. 2. Formulė: Lygtis lygina dvi funkcijas: parabolę $$y = -x^2

1. The problem is to find approximate solutions to the equation $$4^{x+2} + 2 = \frac{1}{3}x + 2$$ for $$x \in [-4,4]$$. 2. First, simplify the equation by subtracting 2 from both

1. Išspręskime nelygybę $-12x - 2 \geq -3^{x+1} + 1$.\n\n2. Pirmiausia perkelkime visas išraiškas į vieną pusę, kad būtų lengviau analizuoti: \n$$-12x - 2 + 3^{x+1} - 1 \geq 0$$\n\

1. **State the problem:** Factorize the expression $$3a^2 - 5ab + 2b^2 - a - b - 10$$ by arranging it first in powers of $a$ and then in powers of $b$. 2. **Arrange in powers of $a

1. **State the problem:** Solve the system of linear equations by graphing and find the number of solutions. Given system:

1. **State the problem:** We know that 10 students represent 4% of the seventh grade. We need to find the total number of students in the seventh grade. 2. **Set up the proportion:

1. **State the problem:** Latanya misses 20% of her free throws and missed 48 shots. We need to find the total number of free throws she attempted. 2. **Formula used:** Percentage

1. **State the problem:** Simplify the expression $R = 2 - 5 + r_1 r_2 r_6$. 2. **Apply arithmetic operations:** First, simplify the constant terms $2 - 5$.

1. **State the problem:** Solve for $s$ in the equation $$5s + 2s + 4s - 5s = 6$$. 2. **Combine like terms:** Add and subtract the coefficients of $s$ on the left side.

1. **State the problem:** Solve the equation $-14w + 13w = -11$ for $w$. 2. **Combine like terms:** On the left side, combine $-14w$ and $13w$:

1. **State the problem:** We are given the function $$y = -2^{-\frac{1}{2}x+1} + 5$$ and need to find its domain, range, x-intercept, y-intercept, and asymptotes. 2. **Rewrite the

1. El problema es analizar la función $$f(k) = \frac{2}{k - e^{-1}}$$. 2. Esta función es una función racional, donde el numerador es constante 2 y el denominador es $$k - e^{-1}$$

1. **State the problem:** Solve the compound inequality $$0 \leq 3x - 5 \leq 7$$. 2. **Understand the compound inequality:** This means both inequalities must be true simultaneousl

1. The problem is to write the inequality $x < -9$ or $x > -6$ in interval notation. 2. Recall that interval notation expresses sets of numbers as intervals between two endpoints.