🧮 algebra

1. Problem: Add the fractions $\frac{1}{8} + \frac{7}{4} + \frac{3}{7}$. 2. To add fractions, find a common denominator. The denominators are 8, 4, and 7.

1. The problem is to calculate $50\sqrt{900500}$ using long division format. 2. First, understand that $\sqrt{900500}$ means the square root of 900,500.

1. **State the problem:** Calculate $50\sqrt{900500}$ using the long division method for square roots. 2. **Recall the long division method:** This method finds the square root by

1. The problem is to simplify the expressions involving fractional exponents. 2. Recall the rule for fractional exponents: $$a^{m/n} = \sqrt[n]{a^m} = \left(\sqrt[n]{a}\right)^m$$

1. **State the problem:** We have two lines given by the equations $y = ax + b$ and $y = -bx$. They intersect at the point $(2,8)$. We need to find the value of $a$. 2. **Use the f

1. **State the problem:** We are given two points on line 1: $(-3,5)$ and $(6,8)$. We need to determine which of the given points also lies on this line. 2. **Find the slope of the

1. **Problem:** Solve for $x$ in the equation $\frac{1}{2}(x+6) - 3 = 4$. 2. **Formula and rules:** To solve linear equations, isolate $x$ by performing inverse operations step-by-

1. The problem asks for the equation of a line parallel to the y-axis and 3 units to the right of the y-axis. 2. Lines parallel to the y-axis are vertical lines, and their equation

1. The problem is to evaluate the expression $2^4$. 2. The formula for exponentiation is $a^b = a \times a \times \cdots \times a$ ($b$ times).

1. **State the problem:** Solve the simultaneous equations: $$y - 4x = 16$$

1. **State the problem:** Simplify the expression $$\left(s^{-\frac{4}{3}}\right)^5$$ assuming all variables are positive. 2. **Recall the exponentiation rule:** When raising a pow

1. **State the problem:** Simplify the expression $$(-c)^{\frac{5}{3}}$$ assuming all variables are positive. 2. **Recall the rules:** For any positive variable $c$, and rational e

1. **State the problem:** Find the value of $A$ such that the slope from point $(5,8)$ to point $(A,4)$ is undefined.

1. **State the problem:** We have a table showing the number of flyers Trey has printed at different times. We want to find how many flyers he had at the start (time 0) and underst

1. The problem asks to rewrite the left side of the equation $2x^3 y^5 = 8x^3 y^5$ by adding parentheses to make a true statement. 2. We start with the original expression on the l

1. **State the problem:** Multiply the polynomials using the box method: $$(5x + 4)(x - 2)$$ 2. **Set up the box:** The box has 2 rows and 2 columns. The top headers are $x$ and $-

1. **State the problem:** We need to expand and simplify the expression $$(4x - 4)(-4x + 6)$$. 2. **Formula used:** To multiply two binomials, use the distributive property (FOIL m

1. We are asked to solve the linear system using substitution: $$2x - 4y = 7$$

1. The problem involves analyzing a parabola centered at the origin with vertex at (0,0) and points (-3,4) and (2,4) on the curve. 2. The general form of a parabola opening upwards

1. The problem involves understanding the given discrete function with domain $D = \{0,4\}$ and range $R = \{-2,2\}$. We are asked to analyze or interpret this function based on th

1. The problem involves understanding the given sets and their relationships on the Cartesian plane. 2. The domain (D) is given as $D = \{0,4\}$, meaning the input values are 0 and