🧮 algebra

1. **State the problem:** We need to graph a parabola with x-intercepts at $x = -3$ and $x = 5$, and a minimum value of $y = -4$. 2. **Formula and important rules:** A parabola wit

1. **State the problem:** Order the pairs for Graph C and Graph D based on their given functions and points.

1. **State the problem:** Find integer values for $a$ and $c$ such that the quadratic equation $ax^2 - 5x + c = 0$ has two imaginary solutions.

1. **State the problem:** Solve for $y$ in the equation $2x + 4 = -y$. 2. **Rewrite the equation:** The goal is to isolate $y$ on one side. Starting with:

1. **State the problem:** Simplify the expression $$(p+q)(p-q)+3(p+2q)$$. 2. **Use the distributive property and difference of squares formula:**

1. **State the problem:** Simplify the expression $$(4m-1)^2 - 3m(y+x)^2$$. 2. **Recall formulas:**

1. The problem is to rewrite the expression $\left(\frac{5}{8}\right)^{-2}$ without an exponent. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$.

1. The problem is to rewrite the expression $4^{-4}$ without using an exponent. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$ and $n$ is a po

1. **State the problem:** Solve the proportion $$\frac{3}{36} - \frac{4}{27} = \frac{3}{x}$$ for $x$. 2. **Rewrite the equation:**

1. **State the problem:** We have the function $f(x) = \log_{\frac{1}{9}} x$ and need to determine which of the given statements about $f(x)$ is true. 2. **Recall properties of log

1. **State the problem:** Simplify the expression $ (a - b)^2 - 3b(2b - a) $. 2. **Recall formulas and rules:**

1. Stating the problem: Simplify the square root expressions and products for questions 35 to 49. 2. Recall the rule: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ and $\sqrt{a}

1. **State the problem:** Simplify the expression $$\frac{\sqrt{32}}{\sqrt{25}}$$. 2. **Recall the quotient property of square roots:** $$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}

1. The problem is to solve the equation or expression given previously (not specified here, so assuming a generic algebraic problem). 2. We start by stating the problem clearly: So

1. **State the problem:** Simplify the expressions $5 \cdot 4^{-1}$ and $9 \cdot 8^{-3}$ using factor form. 2. **Recall the rule for negative exponents:** For any nonzero number $a

1. **State the problem:** Solve for $x$ in the equation $5(-3 + x) = 35$. 2. **Use the distributive property:** Multiply 5 by each term inside the parentheses.

1. **State the problem:** Solve the inequation $$(2e^x - 1)(e^x - 3) \geq 0.$$\n\n2. **Understand the problem:** We want to find all values of $x$ such that the product of the two

1. **State the problem:** A boy thinks of a number $x$. He squares it and subtracts the original number from the square, resulting in 42. We need to find the number $x$. 2. **Write

1. **State the problem:** We are given two equations based on the cost of apples and berries: - Cost of 3 apples and 1 berry is 22

1. **Problem:** Given the function $c(x) = \frac{120 + 4x}{x}$ representing the average cost per book when printing $x$ copies, answer the following: 2. **Step 1: Calculate cost pe

1. **State the problem:** We need to find the approximate sum of the first 50 terms of two geometric sequences. 2. **Recall the formula for the sum of the first $n$ terms of a geom