🧮 algebra

1. The problem is to find the linear equation for the sequence with term numbers 0 to 4 and term values -27, -19, -11, -3, 5. 2. The formula for a linear sequence is $y = mx + b$,

1. **State the problem:** We need to find the composition of functions $f$ and $g$, denoted as $(f \circ g)(x)$, which means $f(g(x))$. 2. **Recall the functions:**

1. The problem asks to find the composition of functions $(h \circ g)(x)$, which means $h(g(x))$. 2. Given functions are:

1. The problem is to simplify the fraction $\frac{1}{4}$. 2. The fraction $\frac{1}{4}$ means one part out of four equal parts.

1. The problem is to determine the algebraic equation for the given number pattern and decide if it is linear. 2. The table shows term numbers $t = 1, 2, 3, 4$ and term values $v =

1. Problem: The number of bacteria increased by 280 percent overnight. If there were 30,000 bacteria yesterday, how many bacteria were present this morning? Formula: New amount = O

1. **State the problem:** Simplify the expression $\left(j^4 k^{-1} m^8\right)^{-1}$ using exponent rules. 2. **Recall the rule for negative exponents:** For any base $a$ and expon

1. **State the problem:** We need to predict the population of a city after 50 years given the current population and an annual decrease rate. 2. **Given data:**

1. **Problem statement:** Predict the population of a city in 50 years given the current population is 954,000 and it is decreasing at an annual rate of 0.1%.

1. **Problem statement:** We have a medicine whose amount decreases exponentially in the body with a half-life $T_{1/2} = 7$ hours. Initially, at $x=0$, the amount is $b=50$ mg.

1. **State the problem:** Simplify the expression $(-5^5)^2$. 2. **Recall the order of operations:** Exponents are evaluated before applying the negative sign if the negative is no

1. Problem: Simplify $6^4 \cdot 6^4$. 2. Use the rule for multiplying powers with the same base: $a^m \cdot a^n = a^{m+n}$.

1. The problem states that the graph of the quadratic function $$y = 9x^2 + 9x - 4$$ is stretched horizontally by a factor of 5. 2. A horizontal stretch by a factor of 5 means ever

1. **State the problem:** Factor the expression $$16y^2z^2 - 16y^2z - 12y^2$$ completely. 2. **Identify common factors:** Notice that each term contains a factor of $$4y^2$$.

1. **State the problem:** We are given two functions $f(x)$ and $h(x)$ with their values at $x = -2, -1, 0, 1, 2$. We want to express $h(x)$ as a transformation of $f(x)$. 2. **Lis

1. The problem asks to find the degree of a monomial. 2. The degree of a monomial is the sum of the exponents of all variables in the monomial.

1. **Problemstellung:** Gegeben ist die Exponentialfunktion $f$ mit $f(x) = 4^x$. **a)** Welcher Punkt liegt auf dem Graphen von $f$?

1. **State the problem:** We are given two angles expressed as $4(x + 1)^0$ and $(7x + 3)^0$ and asked to find the value of $x$. 2. **Interpret the notation:** The notation $( ext{

1. **State the problem:** Evaluate the expression $$-12 - (14 + -15 \div 15) \times -9$$. 2. **Recall order of operations:** Parentheses first, then division and multiplication fro

1. **State the problem:** Find the roots and vertex of the quadratic function $$y = x^2 + 14x - 72$$. 2. **Formula for roots:** Use the quadratic formula $$x = \frac{-b \pm \sqrt{b

1. **Problem Statement:** Simplify the expression by combining like terms and using the distributive property. 2. **Key Concepts:**