🧮 algebra

1. **Problem:** A cell phone company charges a monthly fee of $30 for the first 1000 text messages and 10 cents for each additional text message. Miriam’s bill for June is $35.70.

1. **State the problem:** We need to find the least amount of money Josue earned in a single week based on the given line graph points. 2. **Identify the data points:** The earning

1. **State the problem:** We are given the function $$y = -3x$$ and need to fill in the table of values for $$x = -3, -2, -1, 0, 1, 2, 3$$ and then use these values to graph the fu

1. **State the problem:** Solve the equation $$3 - \frac{9}{2} = \frac{2x - 5}{18}$$ for $x$. 2. **Rewrite the left side:** Convert $3$ to a fraction with denominator $2$ to combin

1. **State the problem:** Solve the linear equation with fractions: $$\frac{x + 8}{5} - \frac{x - 5}{3} = 5$$

1. **State the problem:** Simplify or analyze the expression $$ (3 - x^2) \sqrt{(5x + 4)^3} $$. 2. **Recall the properties of radicals and exponents:**

1. **State the problem:** Ben and Steven have some sweets. We want to find how many sweets Ben has initially.

1. **State the problem:** Ben and Steven have some sweets. We want to find how many sweets Ben has initially.

1. **State the problem:** We need to find the value of $$10\ 000^{3/4}$$. 2. **Recall the exponent rule:** For any positive number $a$ and rational exponent $m/n$, $$a^{m/n} = \sqr

1. **State the problem:** We need to find the value of $81^{3/2}$. 2. **Recall the exponent rule:** For any positive number $a$ and rational exponent $m/n$, we have $$a^{m/n} = \le

1. Let's start by understanding the role of $a$ in transformations of functions. 2. When we write a function transformation like $y = f(ax)$, the parameter $a$ affects the $x$-axis

1. **State the problem:** Factor the trinomial $$ (5x + 3)^2 + 8(5x + 3) + 15 $$ and verify if it equals $$ 25x^2 + 40x + 48 $$. 2. **Rewrite the expression:** Let $$ u = 5x + 3 $$

1. **State the problem:** Factor the expression $$12x^5y^4 - 9xy^5 + 27x^2y^8$$ by factoring out the greatest common factor (GCF). 2. **Find the GCF of the coefficients:** The coef

1. **State the problem:** Solve for $n$ in the equation $$2^7 = 2^n$$. 2. **Recall the rule:** When the bases are the same and nonzero, if $$a^x = a^y$$ then $$x = y$$.

1. **State the problem:** We are given a linear function $f(x)$ with values at $x=-5, 1, 4$ and corresponding $f(x)$ values $-12, -4, 0$. We need to find $f(10)$. 2. **Recall the f

1. **State the problem:** We are given a graph of the function $g(x)$, which is a downward-opening parabola with vertex approximately at $(-1, 2)$ and crossing the y-axis at about

1. **Problem Statement:** We have a bacteria culture growing with a constant relative growth rate. Given bacteria counts at two times, find the growth rate, initial size, expressio

1. प्रश्न समजून घेऊया: A एका कामाला 32 दिवसांत पूर्ण करतो. B हा A पेक्षा 160% अधिक कार्यक्षम आहे. आपल्याला B किती दिवसांत तेच काम पूर्ण करेल हे शोधायचे आहे. 2. सूत्र वापरूया: कार्य

1. **State the problem:** Solve the equation $$\frac{x+4}{6} - \frac{3x}{2} = 5$$ by clearing denominators. 2. **Identify the denominators:** The denominators are $6$ and $2$.

1. **State the problem:** Solve the inequality $$4v - 3 \geq 6v - 5$$ for $v$. 2. **Write down the inequality:** $$4v - 3 \geq 6v - 5$$

1. **State the problem:** We need to find which values of $m$ satisfy the inequality $$m > 7$$. 2. **Understand the inequality:** The inequality $m > 7$ means $m$ must be strictly