🧮 algebra

1. **State the problem:** Joan owes 440 for food and lodging and earns 1.25 for every 10 trees she plants. We need to find how many trees she must plant to break even, meaning her

1. Let's clarify how to get the fraction $\frac{3}{2}$. 2. Suppose you have an equation or expression where you need to solve for a variable or simplify a fraction.

1. The problem asks to write the root expression $7\sqrt{7}$ in index (exponent) form. 2. Recall that the square root of a number $a$ can be written as $a^{\frac{1}{2}}$.

1. **Problem statement:** We want to find a cubic function $f(x) = ax^3 + bx^2 + cx + d$ that passes through the points $P_1(0, -1)$, $P_2(1, 1)$, $P_3(-1, -7)$, and $P_4(\frac{1}{

1. **State the problem:** We need to find the range of house values in the village. The range is the difference between the highest and lowest valuations. 2. **List the valuations:

1. **State the problem:** Solve the expression $$3 \times (-8) \times (-4)$$. 2. **Recall the multiplication rules for negative numbers:**

1. **State the problem:** Mr. Chain has apples where 3 out of 4 are red and the rest are green. He sold half of the total apples. Of the apples sold, 5 out of 6 were red. After sel

1. **State the problem:** Ricky initially had 3 times as much money as Lina. After both spent 180, Ricky had 5 times as much money as Lina. We need to find how much money each had

1. **State the problem:** Simplify the expression $50 + 50 - 25 \times 0 + 2 + 2$. 2. **Recall the order of operations:** Multiplication must be done before addition and subtractio

1. The problem asks to name the fraction shown by the arrow on the number line between 0 and 1, closer to 0. 2. The number line is divided into 4 equal parts between 0 and 1, so ea

1. **State the problem:** Solve the inequality $$-3x + 10 \leq 19$$ for $$x$$. 2. **Isolate the variable term:** Subtract 10 from both sides:

1. **State the problem:** Solve the inequality $$\frac{x}{4} - 1 < 9$$ for $$x$$. 2. **Add 1 to both sides:**

1. **State the problem:** We are given the profit function of a small business:

1. **State the problem:** There are 56 sheep in total, each either white or black. The number of white sheep is 6 times the number of black sheep. We need to find how many black sh

1. **State the problem:** Simplify the expression $$\left( \frac{3\sqrt{8}}{2\sqrt{7}} \right)^2$$. 2. **Recall the formula:** When squaring a fraction, square the numerator and th

1. **State the problem:** Convert the decimal number 10.08 into a fraction. 2. **Understand the decimal:** The number 10.08 has two digits after the decimal point.

1. Problemet er at finde den afledte funktion $f'(x)$ for en given funktion $f(x)$.\n\n2. Den generelle regel for differentiation er, at hvis $f(x) = x^n$, så er $f'(x) = nx^{n-1}$

1. **Problem (a):** Tom's car has lost 18% of its value and is now worth 18450. 2. **Formula:** If the original value is $V$, then after losing 18%, the value is $V \times (1 - 0.1

1. The problem is to simplify the expression $\frac{ab - bc}{b}$. 2. We start by factoring the numerator:

1. **Problem statement:** Estimate powers of 2 using the approximation $2^{10} \approx 1000$. 2. **Recall the rule:** $2^{a+b} = 2^a \times 2^b$ and $2^{ka} = (2^a)^k$.

1. **Stating the problem:** We need to identify which dot pattern corresponds to blank 1 and blank 2 from the given options, then find the number sequence that matches the dot coun