🧮 algebra

1. **State the problem:** We are given gallons per minute (gpm) for sections B, C, D, E, F, and G, and several inequalities involving section A's gpm. We need to determine the poss

1. **State the problem:** Multiply the binomials $ (x + 19)(3x + 1) $. 2. **Formula used:** To multiply two binomials, use the distributive property (also known as FOIL method for

1. **State the problem:** Calculate the value of the expression $$VP = 34000 - 28000 \times 100$$. 2. **Formula and rules:** This is a simple arithmetic expression involving subtra

1. **State the problem:** Multiply the polynomials $ (x + 2)(x^3 - 6x + 3) $. 2. **Recall the distributive property:** To multiply two polynomials, multiply each term in the first

1. **State the problem:** Find the vertex of the quadratic function $h(t) = -16t^2 + 40t$. 2. **Formula and rules:** The vertex of a quadratic function $h(t) = at^2 + bt + c$ is gi

1. The problem asks to find the unit rate and the constant of proportionality for calories burned per minute based on the given data points. 2. The data points given are (2, 20), (

1. **State the problem:** We need to find the unit rate of calories burned per minute from the given data points. 2. **Identify the data points:** The points given are approximatel

1. **State the problem:** Solve the inequality $$\frac{40-k}{5} > 0$$. 2. **Formula and rules:** To solve inequalities involving fractions, multiply both sides by the denominator i

1. Het probleem is om te bepalen of een wiskundige uitdrukking of berekening eenvoudiger kan worden gemaakt. 2. Bij het vereenvoudigen van wiskundige uitdrukkingen gebruiken we reg

1. Heidi and Micah have 11 more dimes than nickels. 2. The overall average for all 30 days is 783.17 per day.

1. **Problem:** Heidi and Micah have 51 dimes and nickels. The total value is 4.10. Find how many more dimes than nickels there are. 2. **Define variables:** Let $d$ = number of di

1. **State the problem:** We need to find the value of the function $f(x) = 3x^2 - 5$ at $x = -2$. 2. **Recall the formula:** The function is given by

1. **State the problem:** Find the equation of the line passing through the points $\left(-\frac{3}{2}, 4\right)$ and $\left(\frac{5}{2}, -2\right)$.\n\n2. **Formula used:** The sl

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 3x + 2y = -9 \\ x - 2y = -3 \end{cases}$$

1. **State the problem:** Simplify the expression $$\frac{1}{e^3}$$ and write it in the form $$a^p$$. 2. **Recall the rule for negative exponents:** For any nonzero number $$a$$ an

1. **State the problem:** Determine whether the function $t(x) = 4x^6 + 13$ is even, odd, or neither. 2. **Recall definitions:**

1. The problem asks us to determine if the function $p(x)$ is even, odd, or neither based on its graph. 2. Recall the definitions:

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate the variable $x$ by performing inverse operations. Important rules: addition a

1. **State the problem:** Simplify the expression $$5 \times \frac{4 \times 10^2}{4 \times 10^1}$$. 2. **Write the formula and rules:** When dividing terms with the same base, subt

1. **State the problem:** Find the equation of the line which contains the point $C$ and is perpendicular to the line $2x - 3y + 6 = 0$. 2. **Find point $C$:** From question 10(i),

1. **State the problem:** Solve the equation $$\frac{2x+3}{4} = \frac{x-1}{2}$$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, multiply both sides by th