🧮 algebra

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: - $(f + g)(x)$

1. **State the problem:** We are given two functions: $$f(x) = 3x - 30$$

1. **State the problem:** We are given the linear equation $5x - 4y = 5$ and asked to express $y$ in terms of $x$, then identify the correct graph based on the slope and y-intercep

1. **State the problem:** We are given two functions $f(x) = x^2 - 8x + 7$ and $g(x) = x - 1$. We need to find the values of $(f + g)(0)$, $(f - g)(1)$, $(f \cdot g)(2)$, and $\lef

1. **State the problem:** We have an exponential model of the form $$y = a \cdot b^x$$ that passes through points $(3,5)$ and $(4,10)$. We need to find which of the given points al

1. **State the problem:** Solve the equation $5x - 4y = 5$ for $y$ and express it in slope-intercept form $y = mx + b$. 2. **Rewrite the equation:** Start with the given equation:

1. **State the problem:** We are given a parabola with vertex at $(-1,-4)$, crossing the y-axis at $(0,3)$, and x-axis at approximately $(-3,0)$ and $(1,0)$. We need to find: (a) $

1. **State the problem:** Solve the equation $$-\frac{1}{2}(y - 3) = \frac{25}{4}$$ for $y$. 2. **Use the distributive property:** Multiply both sides by $-2$ to eliminate the frac

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **State the problem:** Solve the equation $$-\frac{1}{2}(y - 3) = \frac{25}{4}$$ for $y$. 2. **Write down the formula and rules:** To solve for $y$, we need to isolate $y$ on on