🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{5}{h} - 2h^2 - 6h + 15f$$ where $h$ and $f$ are variables. 2. **Understand the terms:** The expression contains a rational

1. **State the problem:** Factor the quadratic expression $x^2 + 16x - 36$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multi

1. The problem asks to find the value of $x$ for which $f(x) = x^2 + x + 1$ equals the given points in the set $\{(-2,8), (-1,0), (1,1), (m,-1)\}$. 2. We use the function $f(x) = x

1. **State the problem:** Simplify the expression $4x - 2x^2 - 2$ or rewrite it in a standard polynomial form. 2. **Rewrite the expression:** The given expression is $4x - 2x^2 - 2

1. **State the problem:** Solve the equation $$\frac{2}{3}x + 5 = 4 - \frac{3}{4}x$$ for $x$. 2. **Write down the equation:** $$\frac{2}{3}x + 5 = 4 - \frac{3}{4}x$$

1. **Stating the problem:** We are given that Emma is $y$ years old, Hanna is 2 years older than Emma, and together their ages sum to 26 years. We need to write an equation for the

1. **State the problem:** Find the difference quotient $$\frac{f(x+h)-f(x)}{h}$$ for the function $$f(x) = x^2 - 3x$$.

1. The problem asks to express each number as a power with exponent $\frac{1}{2}$ and then write the answer as a radical. 2. Recall that raising a number to the power $\frac{1}{2}$

1. **Stating the problem:** Solve the system of equations: First system:

1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} y + 1 = 2x \\ y = 3x + 2 \end{cases}$$

1. The problem is to solve the equation given by the user. However, no specific equation was provided, so I will demonstrate solving a simple algebraic equation as an example: $2x

1. Simplify the polynomial expression $a(4a + 3)$. 2. Use the distributive property: $a(b + c) = ab + ac$.

1. **State the problem:** Simplify the expression for the area of the shaded region, which is the area of the larger rectangle minus the area of the smaller rectangle inside it. 2.

1. **State the problem:** Bill's remaining distance to Philadelphia is a linear function of his driving time. Given two points: after 35 minutes, distance is 45 miles; after 53 min

1. The problem asks to state the degree of each function and classify it as linear or quadratic. 2. Recall the definitions:

1. The problem asks which expression can be factored to $$3xy(2x + 1)(x - 4)$$. 2. To check, we expand the factored form using the distributive property:

1. **State the problem:** Solve the system of equations: $$x^2 + y^2 = 9$$

1. **State the problem:** Subtract the mixed numbers $7 \frac{2}{3} - 3 \frac{5}{12}$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** We are given two equations:

1. **State the problem:** We are given a table of heights $y$ (in feet) at different times $x$ (in seconds) and asked to predict the height after 5 seconds. 2. **Analyze the data:*

1. **State the problem:** We have a table showing the height $y$ of a baseball at different times $x$ seconds after it was hit. We want to predict the height after 5 seconds using