🧮 algebra

1. The problem is to analyze the four tables of (x, y) pairs and determine the nature of the relationships they represent. 2. We will check if each table represents a function, and

1. **State the problem:** We are given the population of Elmdale in 2010 and 2018 and need to find the continuous growth rate $r$ using the formula for continuous population growth

1. **State the problem:** We need to find the value of $x$ such that $f(x) = 4$ where $f(x) = 2x + 2$. 2. **Write the equation:** Set the function equal to 4:

1. **State the problem:** We are given a table of values for an exponential function and Tegan's proposed equation $y=5(0.25)^x$. We need to verify if this equation correctly repre

1. **State the problem:** We are given points from an exponential function and Saraid's proposed equation $y=125(1.25)^x$. We need to check if this equation correctly represents th

1. **State the problem:** Solve the quadratic equation given in factored form: $$y = 10x(6x - 7)$$ for $x$. 2. **Set the equation equal to zero:** To find the roots, set $$y = 0$$:

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 $$