🧮 algebra

1. The problem is to create a math quiz with multiple questions. 2. Let's design a quiz with three algebra problems involving solving equations and simplifying expressions.

1. **State the problem:** Multiply and simplify the expression $$(a + 4b)(3a - 8b)$$. 2. **Apply the distributive property (FOIL method):**

1. **State the problem:** We have a linear function graphed passing through points (0, -4) and (5, 10). We need to find its equation, the inverse function, sketch the inverse, crea

1. Muammo: Arifmetik progressiyaning 3-hadi $a_3=6$, 5-hadi $a_5=9$. Dastlabki 8 ta hadi yig'indisini toping. Formulalar: $a_n = a_1 + (n-1)d$, $S_n = \frac{n}{2}(2a_1 + (n-1)d)$.

1. The problem is to find the number that completes the expression $u^2 - 10u + \square$ so that it becomes a perfect square trinomial. 2. Recall that a perfect square trinomial ha

1. We are given the quadratic equation $x^2 + 3x - 4 = 0$ and need to solve for $x$. 2. To solve, we can use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where

1. The problem is to solve the equation $$2x + 3 = 7$$ for $x$. 2. Start by isolating the variable term on one side. Subtract 3 from both sides:

1. **State the problem:** Solve the equation $$\cos(20) + x \sin(20) = 1$$ for $x$. 2. **Isolate $x$:** Subtract $\cos(20)$ from both sides:

1. **Problem 46:** A garden has 200 trees, all are red. After planting some new trees, the percentage of red trees decreases to 20%. Find the total number of trees after planting.

1. The problem is to graph the function $f(x) = x^4$. 2. This is a polynomial function where the variable $x$ is raised to the fourth power.

1. Problem a: Graph the function $f(x) = 5x^4 - 13$ on the window $[-2, 2] \times [-16, 16]$ and find its domain and range. 2. The function is a polynomial, so its domain is all re

1. The problem asks to explain how a function relates one variable to another using the terms domain, range, independent variable, and dependent variable. 2. A function is a rule t

1. Solve the inequality \( \frac{x^2 - 9x + 20}{x - 6} \leq 0 \). Step 1: Factor the numerator:

1. **State the problem:** Solve the system of linear equations: $$3x - y = -1$$

1. **State the problem:** Solve the equation $3x - 7 = -1$ for $x$. 2. **Add 7 to both sides:**

1. The problem is to express the equation $3x - y = -1$ in a more useful form, such as solving for $y$. 2. Start with the given equation:

1. **State the problem:** Solve the simultaneous equations using the elimination method: $$\text{(1) } x + 2y = 10$$

1. The problem states that the internet cafe charges an initial fee of 4 plus 0.40 for every minute used. 2. We want to create a table of values for the total cost $C$ based on the

1. **State the problem:** We have a table showing the number of minutes $t$ a computer is used and the total cost $C$ to use it. The values for $t$ are 0, 1, 2, and 3 minutes, but

1. **State the problem:** We need to find the total cost $C$ of producing $p$ phones in a day, given that each phone costs 50 dollars to produce and there is a fixed daily cost of

1. **State the problem:** Amber is x years old and her brother is y years old.