🧮 algebra

1. The problem is to find the nth term formula for each linear sequence given. 2. The formula for the nth term of a linear sequence is generally $$a_n = dn + c$$ where $d$ is the c

1. **State the problem:** Simplify the expression $$0.5(-6y + 10) + 0.7y$$. 2. **Apply the distributive property:** Multiply 0.5 by each term inside the parentheses:

1. **State the problem:** Simplify the expression $-0.3(2v - 7) + 0.3v$. 2. **Apply the distributive property:** Multiply $-0.3$ by each term inside the parentheses:

1. **State the problem:** Simplify the expression $-5d - 5(-0.8d - 0.7)$. 2. **Apply the distributive property:** Multiply $-5$ by each term inside the parentheses:

1. **State the problem:** Simplify the expression $3u - 10(10u - 10)$. 2. **Apply the distributive property:** Multiply $-10$ by each term inside the parentheses:

1. **State the problem:** Solve the equation $$\sqrt{7 + x} + 2 = \sqrt{3 - x}$$ for $x$. 2. **Isolate one square root:** Subtract 2 from both sides:

1. **State the problem:** Simplify the expression $9(-7t + 4t - 10) - 9t$. 2. **Apply the distributive property:** Multiply 9 by each term inside the parentheses.

1. **State the problem:** Solve the equation $$16x + 16 = x^2 + 2x + 1$$. 2. **Rewrite the equation:** Notice that $$x^2 + 2x + 1 = (x + 1)^2$$, so the equation becomes:

1. **State the problem:** Simplify the expression $8(-6f - 9) + 2(9f + 2)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **State the problem:** Simplify the expression $$-7(-3t + 5) + 4t$$. 2. **Use the distributive property:** Multiply $$-7$$ by each term inside the parentheses.

1. **State the problem:** We want to find the value of $b$ in the exponential function $y = ab^x$ given points $(0,1.5)$ and $(1,3)$. 2. **Recall the formula:** The function is $y

1. **State the problem:** We need to find the exponential function $y = ab^x$ that passes through the points $(-1, 0.75)$, $(0, 1.5)$, and $(1, 3)$. 2. **Recall the general form:**

1. **Problem:** Find the percent change from 70 to 56. 2. **Formula:** Percent change is calculated by

1. **State the problem:** We are given the exponential decay function $$y = 200(0.989)^x + 72$$ which models the temperature of tea over time, where $y$ is the temperature and $x$

1. **Problem:** Zalmon walks 3/4 of a mile in 3/10 of an hour. What is his speed in miles per hour? 2. **Formula:** Speed is calculated as distance divided by time:

1. The problem asks to find the equation of the graphed function, which is an absolute value function. 2. The absolute value function is defined as $$y = |x|$$, which creates a "V"

1. The problem asks to describe the function $g(x)$ in terms of $f(x)$ after applying transformations: a vertical stretch by a factor of 4, a shift to the right by 6 units, and a s

1. **State the problem:** We are given two points A(0,-2) and B(-4,0) and need to find which equation matches the graph passing through these points. 2. **Recall the formula:** A l

1. The problem asks to find the equation of the function $g(x)$ whose graph is a parabola opening downwards with vertex at $(0,3)$. 2. The parent function is $f(x) = x^2$, which is

1. The problem asks to find the equation of a parabola that is a transformation of the function $f(x) = x^2$. 2. The parent function is $f(x) = x^2$, which is a parabola opening up

1. **State the problem:** Given two functions $f(x) = x^2 + 5x + 6$ and $g(x) = x + 3$, find the following combined functions: - $(f + g)(x)$