🧮 algebra

1. **Problem Statement:** (a) What is true about the equations for parallel lines?

1. **State the problem:** We need to find an angle whose complement measures 20 degrees less than one-third of its supplement. 2. **Recall definitions:**

1. **State the problem:** Simplify the expression $$(2x^6)^{-2}$$. 2. **Recall the power of a product rule:** When raising a product to a power, apply the exponent to each factor i

1. **Problem statement:** Find the equation of the line using the point-slope formula and write the final equation in slope-intercept form for each part. 2. **Formula:** The point-

1. **Problem Statement:** We need to sketch the cost of renting snowshoes for the first five hours, where the cost is $7 for the first hour or less, and $4 for each additional hour

1. The problem is to determine which graph is correct based on the given function or data. 2. To decide which graph is right, we need the function or data points that the graph rep

1. **State the problem:** Solve the equation $$\sqrt{\frac{x}{8}} + \sqrt{\frac{x}{2}} = 6$$ for $x$. 2. **Rewrite the equation:** Let us express the square roots with a common bas

1. The problem describes four step functions with given intervals and values for $y$ over $x$ intervals. 2. Step functions are piecewise constant functions that jump at interval bo

1. The problem asks to evaluate $f(3)$ for the given step function. 2. A step function is constant on intervals and changes value at specific points. The value at a point depends o

1. The problem asks to determine the y-value of a step function when $x=4$. 2. The function is a step function defined piecewise with constant values on intervals:

1. The problem asks to convert the number 100000 to its negative standard form. 2. Negative standard form means expressing the number as a negative number in scientific notation.

1. **Problem:** Expand and simplify the expression $$(2x - 3)^2$$. 2. **Formula:** Use the square of a binomial formula: $$(a - b)^2 = a^2 - 2ab + b^2$$.

1. **State the problem:** Simplify the expression $1 + (x \times 15\%)$. 2. **Understand the percentage:** 15% means 15 per 100, or $0.15$ in decimal form.

1. **Problem statement:** Find two positive numbers $x$ and $y$ such that their product is 250, i.e., $$xy=250,$$ and the sum $$S = x + 4y$$ is minimized. 2. **Formula and approach

1. We are given two systems of linear equations to solve and graph. 2. For system (a):

1. Problem a: Solve the system using substitution: $$\frac{x}{3} + \frac{y}{5} = 2$$

1. **State the problem:** Solve or analyze the equation $$\frac{x}{3} + \frac{y}{5} = 2$$. 2. **Understand the equation:** This is a linear equation in two variables $x$ and $y$. I

1. **Problem Statement:** (a) Find the values of $h$ and $k$.

1. **Stating the problem:** Calculate the value of the expression $$\frac{4.6^3}{31.4} \times (9.3 \times \sqrt{89})$$, then evaluate $$\frac{\sqrt{61.2}}{13.001 - 0.045}$$, and fi

1. **State the problem:** Evaluate the expression $3x - 5y + 2x$ for $x = -2$ and $y = -4$. 2. **Combine like terms:** The expression has terms with $x$ and $y$. Combine the $x$ te

1. **Stating the problem:** We want to find the 10th term ($a_{10}$) of an arithmetic sequence where the first term ($a_1$) is 11 and the common difference ($d$) is 4. 2. **Formula