🧮 algebra

1. The problem asks us to find between which two integers the number $\sqrt{23}$ lies. 2. Recall that $\sqrt{n}$ is the positive number which when squared equals $n$.

1. **State the problem:** Determine which of the numbers 60, 37.555..., 50.674, and \(\sqrt{39}\) are rational numbers. 2. **Recall the definition:** A rational number is any numbe

1. **State the problem:** Find the $x$-value where the two lines $y = 5x + 9$ and $y = -x + 3$ intersect. 2. **Set the equations equal:** Since both expressions equal $y$, set them

1. **State the problem:** Divide $$6 \times 10^{-2}$$ by $$6 \times 10^{-5}$$ and write the answer in scientific notation. 2. **Write the division as a fraction:**

1. The problem asks to find the position of $\sqrt{71}$ on the number line. 2. Recall that $\sqrt{71}$ is the positive number which when squared gives 71.

1. The problem asks to write the number 0.0000089 in scientific notation. 2. Scientific notation expresses a number as $a \times 10^n$ where $1 \leq |a| < 10$ and $n$ is an integer

1. **Stating the problem:** Simplify the expression $(6-\sqrt{7})(6-\sqrt{7})$. 2. **Formula used:** Use the distributive property (FOIL) for binomials: $$(a-b)(a-b) = a^2 - 2ab +

1. **State the problem:** We need to find the simplified expression for the volume of a rectangular prism with dimensions $2x$, $x+2$, and $4x-1$. 2. **Formula for volume of a rect

1. 题目要求求一条直线的方程，该直线垂直于直线 $3x - 4y = 5$，且经过点 $(-2, 1)$。 2. 首先，求已知直线的斜率。将方程 $3x - 4y = 5$ 改写为斜截式：

1. **Stel het probleem vast:** We moeten de oppervlakte van een vloer berekenen die 14 meter lang is en 50 decimeter breed. 2. **Formule voor oppervlakte:** De oppervlakte $A$ van

1. **State the problem:** Solve the equation $$\frac{1}{5} x^3 = 25$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x^3$ first by multiplying both sides

1. The problem is to understand the expression $y = 5.25 + 10544.25$ and simplify it. 2. The formula used here is simple addition of two numbers.

1. To simplify an expression, we look for common factors or terms that can be combined. 2. If the expression is a fraction, we can cancel common factors in the numerator and denomi

1. To simplify an expression, we look for common factors or terms that can be combined. 2. If the expression involves fractions, we try to reduce them by canceling common factors i

1. **Problem 27:** Given the system of equations: $$2a - c = 0$$

1. **State the problem:** Solve the system of equations: $$3x + 2y = 19$$

1. **State the problem:** We are given a rectangle with perimeter 40 cm and a relationship between length $l$ and width $w$: twice the length is five centimeters more than three ti

1. **State the problem:** We want to find the baseball ticket prices in 2009 using the previous equation or model given for ticket prices over the years. 2. **Recall the formula:**

1. **State the problem:** We need to find the equation of the line of fit in slope-intercept form $y=mx+b$ using the points $(2001, 17.60)$ and $(2002, 18.75)$. 2. **Formula for sl

1. Let's solve the quadratic equation $2x^2 - 4x - 6 = 0$ as another example. 2. The general form of a quadratic equation is $ax^2 + bx + c = 0$.

1. Let's solve a fraction problem: Simplify the expression $$\frac{6}{8} + \frac{3}{4}$$. 2. The formula to add fractions is $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ wher