🧮 algebra

1. **State the problem:** Find the equation of an ellipse with vertices at $(-5,0)$ and $(5,0)$ and passing through the point $(-3,4)$. 2. **Recall the standard form of an ellipse

1. **State the problem:** We need to find which equation best matches a parabola that opens downward with vertex at approximately $(4,1)$. 2. **Recall the vertex form of a parabola

1. **State the problem:** We are given the area of a parallelogram as $28x^2 + 37x + 12$ square meters and its base as $4x + 3$ meters. We need to find the height. 2. **Formula:**

1. The problem asks to write an algebraic expression for a number divided by 8. 2. Let the number be represented by the variable $x$.

1. **State the problem:** Julia spends time at the gym running and lifting weights in a ratio of 3 minutes running to 5 minutes lifting weights. 2. **Formula and rule:** The ratio

1. **State the problem:** We have $n$ players on a sports team. Each player receives 5 pairs of Sox, but 4 pairs are kept in reserve (not given to the players directly). 2. **Under

1. **State the problem:** Farah packs 4 outfits for every 3 days of vacation. We need to determine which of the given statements about outfits packed for different vacation lengths

1. Let's start by stating the problem: solving a system of equations with 3 variables means finding values for $x$, $y$, and $z$ that satisfy all three equations simultaneously. 2.

1. **State the problem:** Find the slope and y-intercept of the line given by the equation $6x + 2y = 5$. 2. **Rewrite the equation in slope-intercept form $y = mx + b$ where $m$ i

1. **State the problem:** Simplify the expression $$\frac{8x^6}{x^5}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing terms with the same base, subtr

1. **State the problem:** Find the slope and y-intercept for each given linear equation. 2. **Recall the slope-intercept form:** The equation of a line in slope-intercept form is $

1. **State the problem:** Simplify and solve the equation $$4x - 9^2 + 6 = 10$$ for $x$. 2. **Rewrite the equation:** Note that $9^2$ means $9$ squared, which is $81$. So the equat

1. We are asked to simplify the expression $$\frac{1}{4}(4x - 12) - \frac{1}{2}(4 - 10x)$$. 2. First, distribute the fractions over the terms inside the parentheses:

1. **State the problem:** We are given two linear equations representing monthly earnings: $$7.50x + 15y = 750$$

1. **State the problem:** We have two linear equations: $$7.50x + 15y = 750$$

1. **State the problem:** Solve the equation $$-3(2x + 1) = 5(5 - 4x)$$ for $x$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor out

1. **State the problem:** Simplify the expression $$\frac{5c^3d^2}{1.5c^4d^{14}}$$. 2. **Write the formula and rules:** When dividing powers with the same base, subtract the expone

1. **State the problem:** Solve the equation $$3(-9 - 4x) = -5(2x - 1)$$ for $x$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor ou

1. **Stating the problem:** Simplify the expression $$\frac{4b^{2}c}{12bc^{3}}$$ and verify if the simplification is correct. 2. **Formula and rules:** When simplifying fractions w

1. **State the problem:** We need to find an expression for the total cost to purchase and operate 6 snow fans. 2. **Identify given values:**

1. Statement of the problem: Determine which statement about the graph of $y=\frac{1}{3}\left(\frac{2}{3}\right)^x$ is true. 2. Formula and rules: For an exponential function $y=a