🧮 algebra

1. **Stating the problem:** We are given the equation $$2 \times 5 = g \times 20$$ and need to solve for $$g$$. 2. **Write the equation:**

1. **State the problem:** Solve for $q$ in the equation $$\frac{39}{26} = \frac{42}{q}$$. 2. **Use the cross multiplication rule:** For two fractions equal to each other, $$\frac{a

1. **State the problem:** We want to write the sum $45 + 90$ as a product using the Greatest Common Factor (GCF) and the distributive property. 2. **Find the GCF of $45$ and $90$:*

1. **State the problem:** We need to find the equation of a line given its graph. 2. **Identify key points:** The line crosses the y-axis at $3$, so the y-intercept $b=3$.

1. **Problem 1: Identify invariant points under $g(x) = -2f(x)$ given $y = f(x)$ and invariant point $(-1,0)$.** - An invariant point $(a,b)$ satisfies $g(a) = b$. Here, $g(x) = -2

1. **Estimate** $$\frac{8.7 \times 20.3}{(8.898 - 6.01)^2}$$ - Calculate numerator: $$8.7 \times 20.3 = 176.61$$

1. **State the problem:** We want to find the factored form of the expression $$2 x \left( 4 x + 3 \right) - \left( 4 x + 3 \right).$$ 2. **Identify common factors:** Notice that b

1. Solve |x| = 9 - The absolute value equation |x| = 9 means x can be 9 or -9.

1. **Problem:** Factor the expression $$5x - 20x^2$$. 2. **Formula and rules:** To factor expressions, look for the greatest common factor (GCF) of all terms.

1. **Problem:** Find the formula for $F(x)$ when $f(x)=20x+14$ is shifted right by 9 units. **Rule:** Shifting right by $h$ units means replacing $x$ by $x - h$.

1. **State the problem:** Find the domain and range of the function $$y = \sqrt{-x - 2} + 8$$ and describe its graph. 2. **Recall the domain rule for square root functions:** The e

1. **State the problem:** Simplify the expression $$\frac{14c^2+91c+44}{c+6}$$. 2. **Formula and rules:** To simplify a rational expression, factor the numerator and denominator if

1. **State the problem:** We have two functions:

1. **State the problem:** Find the range of the exponential function $$y = -3 \cdot 4^x$$. 2. **Recall the properties of exponential functions:**

1. **State the problem:** Find the range of the exponential function $$y = -3 \cdot 4^x$$. 2. **Recall the properties of exponential functions:**

1. **State the problem:** We need to find the range of the function $$y = |x|$$. 2. **Recall the definition:** The absolute value function $$|x|$$ outputs the distance of $$x$$ fro

1. **State the problem:** We need to find the domain of the function $$y = \sqrt{x}$$. 2. **Recall the domain rule for square roots:** The expression inside the square root must be

1. **State the problem:** We need to find the domain of the exponential function $$y = 2^x$$. 2. **Recall the domain rule for exponential functions:** The domain of an exponential

1. **State the problem:** We need to find the range of the function $$y = \sqrt{x}$$. 2. **Recall the domain and range of the square root function:** The square root function $$\sq

1. The problem asks for the domain of the logarithmic function defined by the set $$\{ x \mid x > -4 \}$$. 2. Recall that the domain of a logarithmic function $$\log_b(x - h)$$ is

1. **Problem:** Calculate $\frac{4}{5} \cdot \frac{25}{12}$. **Step 1:** Multiply numerators and denominators: