🧮 algebra

1. **State the problem:** Solve the system of linear equations by graphing: $$4x - 2y = 8$$

1. **Problem Statement:** Find the sums of the given arithmetic progressions (APs) in Q4, Q5, Q6, Q7, Q9, Q10, and Q12. ---

1. The problem is to rewrite the equation $$-3y = 15 - 4x$$ in slope-intercept form, identify the y-intercept and slope, and determine which line corresponds to this equation. 2. T

1. **State the problem:** We need to find the y-intercept and slope of the line given by the equation $$-3y = 15 - 4x$$ and identify which line (A, B, C, or D) represents this equa

1. **State the problem:** Solve the equation $6x + 2x = 8$ for $x$. 2. **Combine like terms:** $6x + 2x = (6 + 2)x = 8x$

1. The problem asks which line represents the linear equation $$-3y = 15 - 4x$$ and to rewrite it in slope-intercept form. 2. Start by rewriting the equation in slope-intercept for

1. **Stating the problem:** Simplify and solve the expression $179 - 78 - 35$ and verify the value of $F$ given $F.F = 36$. 2. **Calculate the expression:**

1. **Find the common difference $d$ for each arithmetic progression (AP).** The common difference formula is:

1. **State the problem:** We are given two functions, $f(x)$ and $g(x) = 9(x - 8)^2 - 6$, and we want to compare their minimum values. 2. **Recall the vertex form of a parabola:**

1. **State the problem:** We want to find the profit function $P(x)$ where $x$ is the additional amount charged per seat above $5$ dollars.

1. **Problem statement:** Simplify each expression without using a calculator. 2. **Recall exponent rules:**

1. The problem is to interpret the linear equation $y = 1772 + 334x$ in the context of eagle breeding pairs over time. 2. The equation is in the form $y = mx + b$, where $m$ is the

1. Given the function $f(x) = \frac{2}{3} \cdot 3^{3x + 12}$, evaluate it at $x = -1$. 2. Substitute $x = -1$ into the exponent: $3(-1) + 12 = -3 + 12 = 9$.

1. **State the problem:** We are given the function $$f(x) = \frac{2}{3} \cdot 3^{3x + 12}$$ and want to understand its behavior and graph. 2. **Recall the exponential function for

1. The problem is to subtract the fractions $\frac{2}{3}$ and $\frac{1}{2}$. 2. To subtract fractions, we need a common denominator. The denominators are 3 and 2. The least common

1. The problem involves simplifying an algebraic expression or equation, specifically step 2 from a previous explanation. 2. Step 2 usually involves dividing both sides of an equat

1. **Problem statement:** Determine between which two consecutive integers the number $\sqrt{7}$ lies without using a calculator. 2. **Recall the concept:** The square root of a nu

1. The problem is to find the square root of 789. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. The problem is to find the square root of 784. 2. The square root of a number $x$ is a value $y$ such that $$y^2 = x$$.

1. **State the problem:** Solve the system of linear equations by elimination for the first box labeled "THE": $$\begin{cases} 5x - 2y = -6 \\ x + y = -6 \end{cases}$$

1. **State the problem:** Simplify the expressions: (i) $5 + 3(2 - 7x) + 4x$