🧮 algebra

1. **State the problem:** Evaluate the expression $4 (7 - 3)^2$. 2. **Recall the order of operations:** Parentheses first, then exponents, then multiplication.

1. **State the problem:** Evaluate the expression $$56 \div (16 - 2^3)$$ using the order of operations. 2. **Recall the order of operations:**

1. **State the problem:** Evaluate the expression $$18 \div 3^2 \cdot 3$$ using the order of operations. 2. **Recall the order of operations:** The order is Parentheses, Exponents,

1. **State the problem:** We are given a function rule $y = 6x - 1$ and a table with values of $x$. We need to find the corresponding $y$ values using the function. 2. **Formula:**

1. সমস্যাটি হলো: $a^2 + 1 = 3a$ যেখানে $a > 0$। 2. প্রথমে সমীকরণটি থেকে $a^2 - 3a + 1 = 0$ পাওয়া যায়।

1. The problem asks us to find the equation of the axis of symmetry for the function $$f(x) = -4 |x + 1| - 1$$. 2. The axis of symmetry for an absolute value function of the form $

1. **State the problem:** We need to graph the region determined by the system of inequalities: $$y \leq 4x + 6$$

1. **State the problem:** Simplify the expression $\sqrt{4} - \sqrt{16}$.\n\n2. **Recall the square root rule:** The square root of a number $a$ is a value $b$ such that $b^2 = a$.

1. **State the problem:** We are given the function $y = 3|x - 3| + 2$ and want to understand its graph and key features. 2. **Formula and explanation:** The function involves an a

1. **State the problem:** We are given the function $$y = -|x + 4| - 3$$ and asked to analyze its graph and key features. 2. **Recall the absolute value function:** The basic absol

1. The problem asks to express $7^8 + 7^5$ in index form. 2. Recall the index laws: when adding powers with the same base, you cannot combine the exponents directly. You can only f

1. The problem is to express a number or expression in index form, which means writing it as a power of a base. 2. The general formula for index form is $a^n$, where $a$ is the bas

1. **State the problem:** Calculate $7^8 + 7^5$. 2. **Recall the formula and rules:** When adding powers with the same base but different exponents, you cannot combine the exponent

1. The problem asks to find the equation of the line shown in the graph. 2. The graph is a straight line passing through the origin (0,0) and the point (10,100).

1. The problem is to calculate the value of $7^4 + 7^5$. 2. Recall the properties of exponents: $a^m \times a^n = a^{m+n}$ and $a^m + a^n$ cannot be simplified by exponent rules un

1. The problem asks to describe the transformation from the function $f(x) = x^2 + 6$ to $g(x) = 4x^2 + 6$. 2. Recall that the general form of a vertical stretch or compression of

1. **State the problem:** Write the equation $y + 7 = \frac{9}{10}(x + 3)$ in standard form. 2. **Recall the standard form of a linear equation:** The standard form is $$Ax + By =

1. **State the problem:** Simplify the expression $$(m + 5n)(m - 2n) + 6n^2$$. 2. **Use the distributive property (FOIL) to expand:**

1. **Problem Statement:** Write an equation in standard form with an x-intercept of 4 and a y-intercept of 5. 2. **Recall the intercepts:**

1. **State the problem:** Write the equation in standard form for the line passing through points $(-1, 19)$ and $(3, 35)$.\n\n2. **Find the slope $m$ using the formula:** $$m = \f

1. **Stating the problem:** We are given the function in the form $a[b(x - h)] + k$ and asked to evaluate and solve for specific values. 2. **Given function:** $f(x) = -15[5(x - 15