🧮 algebra

1. The problem describes a parabola with the axis of symmetry $x=2$, vertex at $(2,1)$, minimum value $1$, no maximum, domain all real numbers, and range $y \geq 1$. 2. The general

1. **State the problem:** Simplify the expression $3.6 \times 5 - 4.8 \div 4 + 10.2$. 2. **Recall order of operations:** Multiplication and division are performed before addition a

1. **State the problem:** We are asked to find the result of adding the two equations: $$\begin{aligned}

1. **State the problem:** Solve the system of equations: $$\begin{aligned}&-3y+5x = 26 \\\ &-2y-5x = -16\end{aligned}$$

1. **State the problem:** Simplify the expression $$-6 + \frac{25}{3} - 1$$. 2. **Combine like terms:** First, combine the integer terms $$-6$$ and $$-1$$.

1. **State the problem:** Simplify the expression $$\frac{3}{8}(2^4) + \frac{25}{24}(2^3) - \frac{1}{2}(2)$$. 2. **Recall the powers of 2:**

1. We are asked to solve the system of equations by elimination: $$\begin{cases} y = -3x + 5 \\ y = -8x + 25 \end{cases}$$

1. **State the problem:** Solve for $m$ in the equation $$\frac{4}{5} = \frac{1}{8} m.$$\n\n2. **Write the formula and explain:** We want to isolate $m$ on one side. Since $m$ is m

1. Stating the problem: Solve for $z$ in the equation $$\frac{7}{10} = \frac{2}{5} z$$. 2. To isolate $z$, divide both sides of the equation by $\frac{2}{5}$.

1. **Problem statement:** A rectangular piece of paper has sides of length $a$ cm and $b$ cm. It is cut in half vertically, creating two smaller rectangles each with dimensions $\f

1. **State the problem:** We have a vector $\mathbf{v} = \langle 12, 8 \rangle$ and a scalar $k$ such that $k\mathbf{v} = \langle 9, 6 \rangle$. We need to find the scalar $k$. 2.

1. **State the problem:** Solve the system of equations: $$x = 3y + 11$$

1. **State the problem:** Evaluate the product of two numbers in scientific notation: $$(7.7 \times 10^{-3})(3 \times 10^{-5})$$ 2. **Recall the exponential rule:** When multiplyin

1. **State the problem:** Multiply the numbers in scientific notation: $$(7.7 \times 10^{-3}) (3 \times 10^{-5})$$ 2. **Recall the multiplication rule for scientific notation:** Wh

1. **Stating the problem:** We are given population data over time and need to find an equation modeling this growth. 2. **Observing the data:** The population increases from 35.0

1. **State the problem:** Simplify the expression $$\frac{2x^4 y^3}{-9x^3 y^7}$$ and write the result using positive exponents. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\frac{2ab^{-1}}{2^{-1}a^{-4}b^2}$$ and write the result using positive exponents only. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\frac{5^5 z^{-5}}{5^6 z^{-8}}$$. 2. **Recall the laws of exponents:**

1. **State the problem:** Simplify the expression $$r \cdot r^{-8} \cdot r^{-4}$$ and write the result using positive exponents. 2. **Recall the exponent rule:** When multiplying p

1. **State the problem:** Simplify the expression $$\frac{p^8 p}{p^{-1}}$$ and write the result using positive exponents. 2. **Recall exponent rules:**

1. **State the problem:** Simplify the expression $$-8^0 - 2^0$$. 2. **Recall the rule:** Any nonzero number raised to the power of 0 is 1, i.e., $$a^0 = 1$$ for $$a \neq 0$$.