🧮 algebra

1. **State the problem:** Find the equation of the exponential function passing through points $(-1,1)$ and $(0,3)$. 2. **Recall the general form:** An exponential function can be

1. The problem asks for the prime factorization of 112. 2. Prime factorization means expressing a number as a product of prime numbers only.

1. **State the problem:** We need to find the equation of the exponential function graphed, given points (0,1), (1,4), and (2,16). 2. **Recall the general form of an exponential fu

1. **State the problem:** We are given a table of values for $x$ and $y$ and need to find the exponential function $y = a \cdot b^x$ that fits the data. 2. **Recall the general for

1. **State the problem:** Solve the equation $3\log(x+4) = 6$ for $x$. 2. **Recall the logarithm property:** If $a\log_b(c) = d$, then $\log_b(c) = \frac{d}{a}$.

1. The problem is to simplify the expression $3$. 2. Since $3$ is already a simplified number, there are no operations to perform.

1. **State the problem:** Factor the polynomial $$100x^2 + 180x + 81$$. 2. **Recall the formula for factoring a perfect square trinomial:**

1. The problem asks for the perimeter of a triangle with side lengths given as expressions: $3k + 5m$, $4n - k$, and $9n + m$ centimeters. 2. The perimeter of a triangle is the sum

1. Problem: Factor each algebraic expression. 2. Formula and rules: Factoring involves finding common factors or patterns like difference of squares, grouping, or special products.

1. The problem asks us to find an expression equivalent to $7d + 9d - d$. 2. We use the rule of combining like terms: terms with the same variable can be added or subtracted by add

1. **State the problem:** Factor the expression $$\frac{7}{2}a + 6$$ using $$\frac{1}{2}$$ as the common factor. 2. **Recall the factoring rule:** To factor out a common factor $$c

1. **State the problem:** Solve the equation $$x^8 - 10x^4 + 9 = 0$$ for $x$ in the set of complex numbers. 2. **Rewrite the equation using substitution:** Let $$y = x^4$$. Then th

1. **State the problem:** Tamika pays 5.50 to send 110 text messages. We want to find the cost to send 52 text messages. 2. **Identify the formula:** Since cost is proportional to

1. **State the problem:** Factor the expression $15k - 18$ using 3 as the common factor. 2. **Recall the factoring formula:** When factoring out a common factor $a$ from terms $ax

1. **State the problem:** Find the horizontal asymptote of the function $$y = \frac{9x - 36}{3x + 3}$$. 2. **Recall the rule for horizontal asymptotes:** For a rational function $$

1. The problem is to find the y-intercept of the function $$y = \frac{9x - 36}{3x + 3}$$. 2. The y-intercept occurs where $$x = 0$$. To find it, substitute $$x = 0$$ into the funct

1. **State the problem:** Find what percent 8 is of 128. 2. **Formula:** Percent = $\frac{A}{B} \times 100$

1. **State the problem:** Find what percent 8 is of 128. 2. **Formula:** To find what percent a number $A$ is of another number $B$, use the formula:

1. **State the problem:** Find the value of $$\frac{3}{4} - 0.25 \cdot 11$$. 2. **Recall the order of operations:** Multiplication comes before subtraction.

1. The problem asks: What number is 62.5% of 195? 2. To find a percentage of a number, use the formula:

1. **State the problem:** Find what percent of 72 is 64.8. 2. **Formula:** To find what percent $x$ is of $y$, use the formula: