🧮 algebra

1. The problem is to solve the equation $\log 4 + \log p^2 = 2$ for $p$. 2. Use the logarithm property that $\log a + \log b = \log (ab)$ to combine the terms:

1) Problem: Determine the domain and range of the cubic curve with one local maximum and one local minimum crossing the x-axis near the origin. Step 1. A cubic function is generall

1. The problem is to expand and simplify the expression $$(m + 5)(m + 2)$$. 2. Use the distributive property (FOIL method) to expand:

1. **State the problem:** Thuto runs 6 km in 24 minutes at a constant speed. We need to find how long it will take him to run 10 km at the same speed. 2. **Convert time to hours:**

1. Given expression: $2ax + 4bx + 8cx + 6dx$ Method: HCF

1. The problem is to expand and simplify the expression $$(x + 2)(x + 7)$$. 2. Use the distributive property (FOIL method) to expand:

1. Problem 15: Volume of gas tank and cost to fill the tank. The cost to fill the tank is directly proportional to the volume of the gas tank.

1. **State the problem:** Expand and simplify the expression $$(7b - 3)(2b - 1)$$. 2. **Apply the distributive property (FOIL method):**

1. **State the problem:** Thuto runs 6 km in 24 minutes. We want to find how long it will take him to run 10 km at the same constant speed. 2. **Convert time to hours:** 24 minutes

1. **Stating the problem:** Simplify the expression $\sqrt{6} \sqrt{42}$.\n\n2. **Recall the property of square roots:** The product of square roots can be combined as the square r

1. **State the problem:** Expand and simplify the expression $$(5x - 3)(2x - 7)$$ and write the result in the form $$ax^2 - bx + c$$. 2. **Apply the distributive property (FOIL met

1. The problem involves three parallelograms with algebraic expressions for their sides and diagonals. 2. For parallelogram SRUT, the sides are given as $2x + 15$ and $x + 15$. The

1. Diketahui deret geometri: 3 + 6 + 12 + ... + 192. 2. Tentukan rasio deret geometri: $r = \frac{6}{3} = 2$.

1. **State the problem:** Find the area between the ellipse given by $$\frac{x^2}{9} + \frac{y^2}{4} = 1$$ and the line $$x + y = 2$$. 2. **Rewrite the line equation:** Solve for $

1. The problem asks to find the interval on which the function defined by the equation $$2y^3 + 3x = 3x^{10} - x$$ is continuous. 2. First, rewrite the function explicitly if possi

1. **State the problem:** Find the area enclosed by the graphs of the circle $x^2 + y^2 = 4$, the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$, and the line $x + y = 2$. 2. **Analyz

1. **Stating the problem:** We are given a quadratic number pattern: -5, -4, -1, 4, ... We need to find the two consecutive terms in the first differences sequence whose product is

1. The problem is to simplify the expression $=$. 2. Since the expression is empty or invalid, there is nothing to simplify or solve.

1. **State the problem:** We have several questions about numbers, inequalities, and ordering on a number line. 2. **Question 1:** Classify the numbers \(-0.3, \frac{1}{5}, 0, -\fr

1. The problem is to find the value of $x$ that satisfies the equation $$\frac{2x+3}{5} = 7.$$\n\n2. Start by eliminating the denominator 5 by multiplying both sides of the equatio

1. **Problem statement:** Fatema's distance from Tomsville after $t$ hours is given by the function $$D(t) = 15.5 - 5t.$$ We are asked to find the inverse function $D^{-1}(x)$ and