🧮 algebra

1. **State the problem:** We have a rectangular patio with dimensions length $8x - 10$ ft and width $2x$ ft.

1. **State the problem:** Simplify the expression $4(x-5)$. 2. **Formula used:** Use the distributive property of multiplication over subtraction:

1. Problem 10a: Complete the table assuming linear growth. Given points: $t=0$, $s(0)=24$ and $t=1$, $s(1)=186$.

1. **Problem 6a:** A 400 mg dose of Ibuprofen is taken. The half-life is 3 hours, so every 3 hours the amount halves. Find the amount remaining after 12 hours. 2. **Formula:** The

1. **State the problem:** Find the values of $a$ and $b$ for the exponential function $y = ab^x$ passing through points $(3, 20)$ and $(5, 4.05)$.

1. **Problem Statement:** Explain what the numbers 2.5 and 1 represent in the equation $$h = 2.5t + 1$$ where $$h$$ is height in feet and $$t$$ is time in seconds.

1. The problem: Learn the supposition method, a technique used to solve equations by assuming a value for a variable and then verifying or adjusting it. 2. The supposition method i

1. **State the problem:** Find the least common multiple (LCM) of the expressions $12w^4 y^7$ and $10w^6 y^2 x^8$. 2. **Recall the formula and rules:**

1. **State the problem:** We are given the line $y = -2x + 8$ and a point $(7, -3)$. We need to find: - The equation of the line perpendicular to $y = -2x + 8$ passing through $(7,

1. **Problem statement:** Place one arithmetic operation (+, -, ×, ÷) between each pair of digits from 1 to 9 (digits can be rearranged and brackets used) to create an expression w

1. **State the problem:** We have four equations involving flower values:

1. **State the problem:** We have the following equations with flower symbols representing variables:

1. **State the problem:** Calculate $ (8 \times 10^2) \times (4 \times 10^6) $ and express the answer in standard form. 2. **Recall the rule for multiplying numbers in scientific n

1. The problem is to find the value of $\left(8^{\frac{1}{2}}\right)^4$. 2. Use the power of a power rule: $\left(a^m\right)^n = a^{m \times n}$.

1. The problem is to solve problem 9. Since the user did not specify the exact problem statement, I will assume it is a typical algebraic problem labeled as number 9. 2. To proceed

1. **State the problem:** We have a rectangular pool where the length is 2 meters shorter than twice its width. We need to write an expression for the perimeter and then find the p

1. **Problem Statement:** We are given the function $y = (3 - 2x)(2 + x)$ and a linear equation $3y - 5x + 6 = 0$. We need to analyze these graphs and solve related questions.

1. **Problem Statement:** We are given data points $(x_i, y_i)$ and want to fit a quadratic model $$y = b_0 + b_1 x + b_2 x^2$$ using the least squares method.

1. **State the problem:** We are given data points for the value of an investment $x$ and the number of years $y$ it took to reach that value. We want to find the logarithmic regre

1. **Exercice N°1** **Problème :** Calculer les termes et la raison d'une suite arithmétique donnée.

1. **State the problem:** Solve the linear equation $2y + x = 6$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we need to get $y$ alone on one side of the equa