🧮 algebra

1. The problem asks to factor the quadratic expression $y = t^2 + 2t - 48$. 2. To factor, we look for two numbers that multiply to the constant term $-48$ and add to the coefficien

1. The problem is to find the percentage discount from 550,000. 2. To find a percentage discount, we need to know the discount amount or the new price after the discount.

1. Problem: Find the original price if the discount is 8% and the discount amount is 55.60. Step 1: Let the original price be $x$.

1. **State the problem:** We are given the graph of function $f(x)$, which forms a "V" shape centered at the origin $(0,0)$. We want to compare $f(x)$ to the function $$g(x) = -2|x

1. Stating the problem: Solve the equation $$e^{x+y} - 3xy - 2 = y$$ for the relationship between $$x$$ and $$y$$. 2. Rearrange the equation to isolate terms:

1. The problem involves the term $-3xy$ as part of an equation or expression. 2. If you provide the full equation, I can help solve or simplify it involving the term $-3xy$.

1. The original function is given as $f(x) = -x^2$. 2. We apply a vertical stretch to $f(x)$ by a factor of 8. A vertical stretch multiplies the $y$-values by the stretch factor.

1. The original function given is $f(x) = |x|$. 2. The transformed function is $g(x) = |x - 5|$.

1. The problem is to find the value of $2000 \times 80000$ in standard form. 2. First, express the numbers in scientific notation:

1. **Problem:** Solve the equation $\frac{5-x}{2x} - \frac{3-2x}{x} = 1$ using the quadratic formula. 2. **Rewrite the equation:** Find a common denominator $2x$:

1. **State the problem:** Two acid solutions with concentrations 25% and 55% are mixed in ratio $m:n$ to form mixture $M$.

1. **Problem statement:** Find the number of ordered integer pairs $(x,y)$ satisfying the equation $$\frac{5}{x} + \frac{1}{y} = \frac{1}{18}.$$\n\n2. **Rewrite the equation:** Mul

1. **State the problem:** We are given two conditions involving $a$ and $b$ (both greater than 1): $$a^{\frac{1}{a}} = b^{\frac{1}{b}}$$

1. Solve the inequality: 2(x - 3) < 4 Distribute 2: 2x - 6 < 4

1. The problem is to solve an algebraic equation or expression without using subtraction. 2. Instead of subtraction, we can rewrite expressions using addition and multiplication by

1. **Problem 1:** Simplify and factor $ (4x^2 - 16x + 7)(4x^2 - 16x + 15) + 16$. - Let $y = 4x^2 - 16x$. Rewrite expression as $(y + 7)(y + 15) + 16$

1. **Problem:** Simplify and expand the expressions given. 2. For the first expression:

1. Stating the problem: You asked to factorize an expression using factorization type IV, which typically is the method of factoring using grouping or a specific advanced technique

1. The problem is to factorize $q^3 - 4^3$. 2. Recognize that this is a difference of cubes, which has the formula $$a^3 - b^3 = (a-b)(a^2 + ab + b^2).$$

1. We start with the expression $(4x^2 - 16x + 7)(4x^2 - 16x + 15) + 16$. 2. Multiply the two quadratics:

1. **Write the polynomial in standard form.** The standard form orders terms from highest degree to lowest: $$f(x) = 3x^5 + x^3 + 2x + 4$$