🧮 algebra

1. **State the problem:** Given $a = -2$ and $b = 3$, find the value of $a^2 - b^3$. 2. **Calculate $a^2$:**

1. Stating the problem: We need to find the ratios of different ingredients Sara has for baking a cake. 2. Count the ingredients:

1. The problem states that a component costs 0.05 each and the manufacturer needs 2,000 components per month. 2. First, calculate the monthly cost by multiplying the cost per compo

1. **State the problem:** Simplify the expression $$(2p^2)^3(3q)^2$$. 2. **Apply the power to each factor inside the parentheses:**

1. **State the problem:** Maria and Marc both travel approximately 50 miles but at different speeds and conditions. Maria drives at 50 mph on a highway, while Marc drives at 40 mph

1. **Stating the problem:** We want to find a combination of the given numbers whose sum is exactly $1656.29$. 2. **List of numbers:** $219.25, 483.16, 163.09, 252.13, 128.67, 903.

1. **State the problem:** Simplify the expression $$3x^2 - 5x + 3 - 4 + 2x^2 - 6x$$. 2. **Group like terms:** Combine the terms with $$x^2$$, the terms with $$x$$, and the constant

1. **State the problem:** Maria and Marc both travel 50 miles to work. Maria drives at 50 mph without stopping. Marc drives at 40 mph but stops for 10 minutes to get coffee. We nee

1. State the problem: Find the value of $(-2) + (-4)(2)$. 2. Evaluate the multiplication part first: $(-4)(2) = -8$.

1. **State the problem:** We need to analyze the function $$y = (x^2 + 2)^2 (x^4 + 4)^4$$ and understand its behavior. 2. **Rewrite the function:** The function is a product of two

1. The problem is to simplify the expression: $$2 + 2(5 \times 9) - 8$$. 2. First, calculate the multiplication inside the parentheses: $$5 \times 9 = 45$$.

1. **Masalah 7:** Diberi jarak perjalanan ETS dari Butterworth ke Kuala Lumpur ialah 390 km dan tempoh perjalanan ialah 4 jam 15 minit. 2. Tukar tempoh perjalanan ke dalam jam saha

1. The problem is to evaluate the expression $3^4 \times 6^4$. 2. First, calculate each power separately:

1. **Problem:** Find $x$ if $\log_2(x^2 - 6x + 40) = 5$. 2. Rewrite the logarithmic equation in exponential form:

1. **State the problem:** Simplify the expression $$(\sqrt{5} - \sqrt{1})^2$$. 2. **Recall the formula:** The square of a difference is given by $$(a - b)^2 = a^2 - 2ab + b^2$$.

1. **Problem 3:** Simplify the expression $$\frac{2\sqrt{14} + \sqrt{6}}{\sqrt{14} + \sqrt{6}} - \frac{\sqrt{14}}{\sqrt{14} - \sqrt{6}} = \sqrt{2} \sqrt{7}$$. 2. First, note that $

1. The problem is to evaluate the expression $$(3^1 + 4^1 + 5^1)^0$$. 2. First, simplify the terms inside the parentheses:

1. The problem is to solve a quadratic equation using the squaring method. 2. Suppose the quadratic equation is $ax^2 + bx + c = 0$.

1. The problem is to solve an equation using the squaring method. 2. The squaring method involves isolating the square root term and then squaring both sides of the equation to eli

1. **State the problem:** Solve the quadratic equation $$x^2 + 4x - 5 = 0$$. 2. **Identify coefficients:** Here, $$a = 1$$, $$b = 4$$, and $$c = -5$$.

1. **State the problem:** Solve for $t$ in the equation $$\ln \frac{500000}{250000} = \ln \left(1 + \frac{0.3}{4}\right)^{4t}.$$\n\n2. **Simplify the left side:** \nCalculate the f