🧮 algebra

1. **State the problem:** We need to find the cost of 5 tulips and 6 roses given two purchases: 7 tulips and 9 roses cost 25.90, and 4 tulips and 8 roses cost 19.80. 2. **Define va

1. **Problem statement:** Find the sum of the first 40 terms of an arithmetic series given that the sum of the first 12 terms is 186 and the 20th term is 83.

1. **State the problem:** Solve the equation $3x - 4 = 5x + 2$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the inequality $$3m + 5 > 2(m - 7)$$. 2. **Apply the distributive property:** Expand the right side:

1. The problem asks for the average rate of change in bounce height as the drop height changes from 20 inches to 60 inches. 2. The average rate of change formula is:

1. **State the problem:** We need to find the value of $f(-2)$ for the function $y = f(x)$, which is a parabola with vertex at $(-5, -9)$ and passes through $(-2, -4)$. 2. **Recall

1. The problem asks to find the value of $f(-4)$ for the function $y = f(x)$, which is a parabola with vertex at approximately $(-2, -6)$ and passing through $(-4, -2)$. 2. The ver

1. **Problem:** Graph the function $y=4^x$ and identify at least two points on the graph. 2. **Formula and rules:** The general form of an exponential function is $y=a^x$ where $a>

1. **State the problem:** We are given five expressions: $$A = x(x+2) + 2x(x+1)$$

1. **State the problem:** Graph the exponential function $y=4^x$ by hand and include at least two points on the graph. 2. **Recall the formula:** The general form of an exponential

1. **State the problem:** Determine if the expression $\frac{2\cos x}{1} \times \frac{1}{\cos x}$ equals 2. 2. **Write the expression:**

1. **State the problem:** We are given multiple expressions: $A=6x+3$

1. **Problem statement:** There are 4 housekeepers working on each floor. Each room requires one housekeeper. If the housekeepers try to distribute the work equally, how many house

1. The problem is to solve a system of equations using the substitution method. 2. The substitution method involves solving one equation for one variable and then substituting that

1. **State the problem:** Solve for $x$ in the equation $$x = \frac{-9}{-9}$$ and verify the value of $x$. 2. **Recall the rule:** Dividing two negative numbers results in a positi

1. **State the problem:** Graph the function $$f(x) = \frac{4}{x-5}$$ and identify its transformations and asymptotes. 2. **Recall the general form and asymptotes:** The parent fun

1. **State the problem:** Find the domain and simplify the multiplication of the expressions:

1. **State the problem:** Find the domain and simplify the multiplication of the rational expressions

1. **State the problem:** Simplify the expression $\left(x^{-\frac{1}{3}} \cdot y^{-\frac{1}{2}}\right)^9 \cdot \sqrt{y}$.\n\n2. **Recall the rules:** When raising a product to a p

1. **Stating the problem:** We have the function $$y = |2(x - 4)^2 + 8|$$ defined for $$x < 5$$, and we want to adjust it so that the graph passes through the five yellow star poin

1. **State the problem:** Simplify the algebraic expressions given: - $20m + 500$