🧮 algebra

1. Evaluate without using a calculator: (a) Given $f(x) = 4^x$, find $f(0.5)$, $f(\sqrt{2})$, $f(\pi)$, $f(-\frac{1}{3})$.

1. Let's clarify the problem: You want to move a point or a graph 3 units to the right and 4 units down. 2. The general rule for moving a graph or point horizontally and vertically

1. The problem asks us to transform the graph of the function $y=f(x)$ (dashed curve) to the graph of $y=f(-x+3)-4$ (solid curve). 2. The transformation involves two steps inside t

1. The problem asks us to transform the graph of $y=f(x)$ (dashed curve) to the graph of $y=-f(x-4)-2$ (solid curve). 2. The transformation involves three steps based on the functi

1. **State the problem:** We are given the manufacturer's suggested retail price (MSRP) of a car as 24880 and its expected value after 4 years as 13924. We need to find a linear de

1. **State the problem:** We need to find a linear depreciation function $f(x)$ for a car whose value decreases from 25280 to 11765 over 5 years. 2. **Formula and rules:** A linear

1. Let's clarify the problem: we are solving a quadratic equation that yields the solutions -0.8 and 4.8. 2. The general form of a quadratic equation is $$ax^2 + bx + c = 0$$.

1. **Problem (a):** Given the equations $$4 \cdot 36 = 100\alpha$$

1. **State the problem:** We need to solve the simultaneous equations graphically: $$y = x^2 - x - 6$$

1. **Problem statement:** (a) Given the expressions involving infinite decimals and ratios, simplify and find the value of $x$ in the equation:

1. **State the problem:** We need to find the value of $x$ such that the ratio $\frac{x - 6}{2x}$ is equivalent to the ratio $\frac{1}{3}$. 2. **Write the equation from the ratio:*

1. Problem 200: Prove that $$A = \sqrt[3]{(a - 3b) \sqrt{a^2 - 9b^2}} \cdot \sqrt[3]{(a + 3b) \sqrt{a^2 - 9b^2}} = 1$$

1. **State the problem:** Solve the quadratic equation $$5y^2 + 4y + 17 = 0$$ using the quadratic formula. 2. **Recall the quadratic formula:** For an equation $$ay^2 + by + c = 0$

1. **State the problem:** We have data for mass $y$ (grams) at time $t$ (minutes) and want to check if $y = at^n$ fits the data. 2. **Show the formula and transform it:** Starting

1. **State the problem:** Hana thinks of a fraction equivalent to $\frac{5}{9}$ where the numerator is greater than 18 and the denominator is less than 40. 2. **Recall the rule for

1. **Problem Statement:** Order each set of numbers from least to greatest and fill in the blanks with the correct terms. 2. **Ordering Numbers:** To order numbers, convert all to

1. **مشكلة:** تحديد عدد جذور المعادلة التربيعية من خلال تمثيلها البياني. 2. **معلومات أساسية:** عدد جذور المعادلة التربيعية يساوي عدد نقاط تقاطع منحنى الدالة التربيعية مع محور السي

1. **State the problem:** Solve the equation $c t + ||x - y|| = 2 3 klx - lout$ for the variable of interest. 2. **Understand the notation:** Here, $||x - y||$ denotes the norm (or

1. **State the problem:** Solve the equation $$(x + y)^{10} = y + x$$ given the constraint $$0 \leq x + y \leq 10$$.

1. **State the problem:** Use the distributive property to remove the parentheses in the expression $9(3 + v)$. 2. **Recall the distributive property formula:** For any numbers $a$

1. **Stating the problem:** We are given a quadratic function $$y=2.5(x-5)^2+0.5$$ and a linear equation $$\frac{5}{22}x + \frac{1}{33}y = 1$$. We also have a right triangle EFB wi