🧮 algebra

1. **State the problem:** We have the function $f(x) = x^4$ and want to find the formula for $g(x)$, which is the graph of $f(x)$ shifted left by 6 units. 2. **Recall the rule for

1. **State the problem:** Factor the expressions $12 + 30$ and $36 + 63$ by finding their greatest common factors (GCF). 2. **Formula and property used:** Use the distributive prop

1. The problem is to graph the function $y = a^x$ where $a > 0$ and $a \neq 1$. 2. The general form of an exponential function is $y = a^x$.

1. **State the problem:** We have a piecewise function defined as: $$f(x) = \begin{cases} 1 + x^2 & \text{if } x < 1 \\ 9x - 7 & \text{if } x \geq 1 \end{cases}$$

1. The problem is to find the value of $a$ in the quadratic function given in vertex form: $$y = a(x - h)^2 + k$$ where the vertex is $(h, k)$ and the parabola passes through a giv

1. **State the problem:** We are asked to identify which of the three distributed expressions is incorrect and to rewrite it correctly.

1. **State the problem:** Chris has traveled 14 blocks out of a total of 35 blocks to the bus station. We need to find what percent of the total distance he has traveled so far. 2.

1. **State the problem:** We need to expand and simplify the expression $$3(x - 2)(2x + 3)$$ and write it in the form $$Ax^2 + Bx + C$$ to find the values of $$A$$, $$B$$, and $$C$

1. **State the problem:** Find the values of $A$, $B$, and $C$ in the expansion of $(4x - 3y)(x + 2y) = Ax^2 + Bxy + Cy^2$.

1. **State the problem:** Simplify the expression $3(u - 6) - 7u$. 2. **Apply the distributive property:** Multiply 3 by each term inside the parentheses.

1. **Simplify the expression** $-9(1 - 10n) - 2(3n + 9)$. 2. **Distribute** the constants inside the parentheses:

1. The problem is to understand the vertex form of a quadratic function, which is given by the formula: $$y = a(x - h)^2 + k$$

1. **State the problem:** Simplify the expression $5\sqrt{13} - 2\sqrt{13}$. 2. **Identify like terms:** Both terms contain $\sqrt{13}$, so they are like terms and can be combined

1. **State the problem:** Simplify the expression $3\sqrt{7} + 6\sqrt{7}$. 2. **Identify like terms:** Both terms contain $\sqrt{7}$, so they are like terms and can be combined by

1. **State the problem:** Write an equation in slope-intercept form of the line that passes through the points $(-2, 3)$ and $(2, 7)$. 2. **Recall the formula for slope:** The slop

1. The problem is to understand the vertex form of a quadratic function, which is given by the formula: $$y = a(x - h)^2 + k$$

1. **State the problem:** Solve the inequality $$5x + 7 < 26$$ and find the solution set for $$x$$. 2. **Formula and rules:** To solve a two-step inequality, first isolate the vari

1. **State the problem:** Factor completely the expression $$7(3x + 2)^2 (x - 1)^2 + (3x + 2)(x - 1)^3$$ and simplify as much as possible. 2. **Identify common factors:** Both term

1. **State the problem:** Solve the inequality $5 + 7x < 26$ for $x$. 2. **Isolate the variable term:** Subtract 5 from both sides to get the term with $x$ alone.

1. Solve the system of equations by graphing: $$y - \frac{1}{4}x = -1$$

1. **Problem statement:** We have a photograph of dimensions 8 inches by 12 inches inside a frame of width $x$ inches around all sides. We want to find a function $A(x)$ that repre