🧮 algebra

1. The problem asks for the scaling factor of 180. 2. A scaling factor is a number which scales, or multiplies, some quantity.

1. The problem is to find how to get the numbers 1, 27, 35, 44, and 52 from their sum 172 using a scaling factor. 2. First, calculate the sum of the original numbers: $$1 + 27 + 35

1. **State the problem:** Florence bought a golf bag originally costing 125 including VAT at 23%. She received a 15% discount. We need to find how much VAT she paid after the disco

1. **Problem statement:** John received quotes from two companies for repairing his oil tank. Company A charges a call out fee plus a rate per hour, and Company B does the same wit

1. **State the problem:** Simplify the expression $\frac{7!}{5!} \times 7!$. 2. **Recall the factorial definition:** For any positive integer $n$, $n! = n \times (n-1) \times \cdot

1. **Problem:** Explain the Fibonacci sequence and draw a picture using the sequence. 2. **What the Fibonacci sequence is:**

1. **Problem:** How do you factor something? Here is a detailed example. 2. **Formula/rule to use:** For a quadratic like $ax^2+bx+c$, one common factoring goal is to rewrite it as

1. **Stating the problem:** We want to learn how to factor algebraic expressions. Factoring means rewriting an expression as a product of simpler expressions. 2. **Formula and rule

1. The problem is to use the Factor Theorem to determine if a given binomial is a factor of a polynomial or to factorize the polynomial. 2. The Factor Theorem states that if $f(c)

1. **State the problem:** We want to express the polynomial $$2x^3 - 8x^2 + 3x - 4$$ in the form $$a(x - 1)^3 + b(x - 1)^2 + c(x - 1) + d$$ for all values of $$x$$ and find the con

1. 题目要求我们已知方程 $$k^2 - 3k + 1 = 0$$，求 $$k^4 + \frac{1}{k^4}$$ 的值。 2. 首先，我们需要利用已知方程来找到与 $$k$$ 相关的表达式，进而求出 $$k^4 + \frac{1}{k^4}$$。

1. The problem asks for the domain of the inverse of the function $f(x) = 2 + \sqrt{x - 1}$.\n\n2. First, recall that the domain of the inverse function is the range of the origina

1. **State the problem:** We are given values from Pascal's triangle and variables $a$ and $b$ located at specific positions. We need to find the value of the expression $4b - 3a +

1. **Stating the problem:** We want to find a formula or method to get the numbers 17, 32, 48, 60, and 64 such that their sum is 141. 2. **Understanding the problem:** The sum of t

1. **Stating the problem:** We want to find the formula or method used to get the numbers 17, 32, 48, 60, and 64 from a total of 114. 2. **Understanding the problem:** These number

1. **State the problem:** Solve the quadratic equation $$x^2 - 14 = 5x$$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Solve the quadratic equation $$x^2 + 10x + 13 = 4$$ by factoring. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Solve the quadratic equation $x^2 + 10x + 13 = 4$ by factoring. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero:

1. The problem states: If $m\angle A = m\angle B$ and $m\angle B = m\angle C$, then $m\angle A = m\angle C$. What algebraic property justifies this step? 2. The property used here

1. **State the problem:** We need to find the values of the piecewise function $$g(x)$$ at $$x=1$$ and $$x=2$$. 2. **Recall the piecewise function definition:**

1. **State the problem:** We are given the volume function of a box as $$V(x) = 4x^3 - 130x^2 + 1000x$$ and need to show that when $x=1$, the volume is 874 cm³. 2. **Verify volume