🧮 algebra

1. **State the problem:** We are given two equations: $$3y - 5 = 45$$ and $$y = 3x - 2$$. We need to find an equation equivalent to $$3y - 5 = 45$$ but expressed only in terms of $

1. **State the problem:** Kathryn needs 200 pencils and each box contains 32 pencils. We want to find the number of boxes $x$ needed. 2. **Formula:** The total pencils is the numbe

1. **State the problem:** Simplify the cube root expression $$\sqrt[3]{64x^3}$$.\n\n2. **Recall the formula:** The cube root of a product is the product of the cube roots: $$\sqrt[

1. **State the problem:** We need to find Sarah's planting rate $S$ (flowers per hour) given that David plants 10 more flowers per hour than Sarah, and the times to plant 300 and 2

1. **State the problem:** We need to evaluate the expression $$2(|-3| + |-1|)$$. 2. **Recall the absolute value rule:** The absolute value of a number is its distance from zero on

1. **State the problem:** We are given a sequence of balances over 5 years and need to find the formula for the geometric sequence that models this data. 2. **Recall the formula fo

1. **State the problem:** We need to find the value of the function $f(x) = -2(x - 3)(x + 4)$ when $x = 6$. 2. **Formula used:** The function is given as $f(x) = -2(x - 3)(x + 4)$.

1. **State the problem:** We need to divide the polynomial expression $$2x^3 - 6x^2 + 12x$$ by $$2x$$. 2. **Write the division as a fraction:**

1. **State the problem:** We are given a number line with a closed circle at $-7$ and shading extending left to $-\infty$, and a closed circle at $1$ with shading extending right t

1. **State the problem:** We are given the model $$N = 200\sqrt{t}$$ where $N$ is the number of infected people and $t$ is time in days. 2. **Goal:** Find $t$ when $N = 1400$.

1. **State the problem:** Solve the equation $$2^{3x} = 8^{1 - x}$$ for $x$. 2. **Rewrite the bases:** Note that $8$ can be written as a power of $2$ since $8 = 2^3$. So,

1. **State the problem:** Evaluate $$\log_5(5) + \log_5(25) + \log_5(625)$$ using properties of logarithms. 2. **Recall the properties:** The logarithm of a product is the sum of t

1. **State the problem:** We need to find which equation is equivalent to the given linear equation $$3x - 4y = 8$$. 2. **Rewrite the equation in slope-intercept form:** The slope-

1. **State the problem:** We are given the formula $$y = -22 + 1.4x$$ where $y$ is the wind chill adjusted temperature and $x$ is the actual air temperature. We need to find $x$ wh

1. **State the problem:** Tom has a square plot of land with an area between $3000$ and $3100$ square meters. We want to find the possible range for the side length of the square.

1. **State the problem:** We want to find the number of infections in week 10, given that infections grow exponentially at a rate of 30% per week. 2. **Formula for exponential grow

1. **State the problem:** Todd travels 330 miles over pack ice in 11 hours one way and 330 miles in 15 hours on the return. The pack ice drifts at a constant speed, and Todd's snow

1. **State the problem:** We need to find the proper ordering of the polynomial $2x^3 + 4x^5 + 16x - 7$. 2. **Recall the rule for ordering polynomials:** Polynomials are typically

1. **State the problem:** We need to identify the graph that represents the inequality $$y < -2x^2 + 8x - 4$$. 2. **Understand the quadratic function:** The quadratic function is $

1. **State the problem:** We have an account with a starting balance of $2000$ dollars. 2. **Understand the withdrawals:** Each month, $450$ dollars are withdrawn, so the balance d

1. **State the problem:** We are given a sequence of balances over 5 years and need to find the formula for the geometric sequence that models this data. 2. **Recall the formula fo