🧮 algebra

1. The problem asks to construct tables of ordered pairs for four exponential functions and sketch their graphs. 2. For each function, calculate $y$ at several values of $x$ (e.g.,

1. The problem is to rewrite the quadratic function $f(x)=-2x^2+6x-1$ in the form $a(x+h)^2+k$ where $a$, $h$, and $k$ are constants. 2. Start by factoring out the coefficient of $

1. **State the problem:** Solve the system of equations graphically and verify the solution. Given:

1. Let's start by stating the problem: Calculate $\frac{1}{4}$ divided by 2. 2. Division by a number is equivalent to multiplication by its reciprocal. The reciprocal of 2 is $\fra

1. **Problem:** Solve the system of linear equations using Gauss Elimination and find expressions for $x$, $y$, and $z$. Given system:

1. The problem states that the salvage value $S(t)$ of the company jet after $t$ years is given by: $$S(t) = 700,000 \times (0.8)^t$$

1. Let's start by writing the expression given: $$x^2 + 3y + 3x - y^2$$. 2. Group the terms to see if we can simplify or rearrange: $$x^2 + 3x + 3y - y^2$$.

1. The problem is to understand the expression $X^2 + b^2$ and explore its components. 2. This expression is a sum of squares, where $X$ and $b$ are variables or constants.

1. **Stating the problem:** We are given the salvage value function $$S(t) = 700000(0.8)^t$$ which represents the value of the jet after $$t$$ years. 2. **Find the rate of deprecia

1. The problem involves converting various linear equations into slope-intercept form and finding intercepts or verifying points on lines. 2. For equation $7x + 3y = 21$:

1. Stating the problem: Simplify the expression 2(x + 3). 2. Apply the distributive property which states that $a(b + c) = ab + ac$.

1. The problem asks for the rate of depreciation in dollars per year after 10 years. 2. To find the rate of depreciation, we need a function or formula that models the value of the

1. Solve |x - 1| = 4 This means the expression inside the absolute value can be 4 or -4.

1. Problem: Find the rate of depreciation after 1 year for the salvage value of a company jet given by the formula $$S(t) = 500000(0.9)^t$$ where $S(t)$ is the salvage value in dol

1. State the problem: Solve the inequality $$\sqrt{5 - x} \geq x - 3$$. 2. Consider the domain: The expression inside the square root must be non-negative:

**Exercise A: Express in exponential form** 1. The expression is ³√64².

1. Express the following in exponential form. 1. $\sqrt[3]{64^2}$ is $64^{\frac{2}{3}}$.

1. Stating the problem: Factorise completely the expression $$4x^{2} + 8xy - xy - 2y^{2}$$. 2. Group terms for easier factoring: $$ (4x^{2} + 8xy) - (xy + 2y^{2}) $$.

1. Stating the problem: Evaluate the expression $\left(\frac{1}{3} + 2, 5\right) \times 40\% - 1 \div 6$. 2. First, clarify the expression. Assuming the comma separates two express

1. **Evaluate** $\log_3 1$\nRecall that $\log_b a$ answers the question: "To what power must we raise $b$ to get $a$?"\nSince $3^0 = 1$, we have $\log_3 1 = 0$.\n\n2. **Evaluate**

1. The problem asks to factorise completely the quadratic expression $$9x^2 - 4$$. 2. Notice this is a difference of squares, which has the general formula $$a^2 - b^2 = (a-b)(a+b)