🧮 algebra

1. **State the problem:** We need to determine the slope of the line segment that passes through the points approximately $(-5, 7)$ and $(6, -6)$. 2. **Recall the slope formula:**

1. **State the problem:** We need to determine the slope of the line passing through the points $(-7, -7)$ and $(7, 7)$. 2. **Recall the slope formula:** The slope $m$ of a line pa

1. **State the problem:** Find the slope of the line passing through the points (0, -4) and (1, -6). 2. **Recall the slope formula:** The slope $m$ between two points $(x_1, y_1)$

1. The problem states that Hulu produces 20% of its own original shows and there are 500 shows available in total. 2. To find the number of original shows, we calculate 20% of 500.

1. The problem is to find the lowest common denominator (LCD) of the fractions $\frac{9}{20}$ and $\frac{8}{15}$.\n\n2. The denominators are 20 and 15. We need to find the least co

1. The problem asks us to find the value of the fraction $$\frac{59049}{729}$$ using the given table of powers of 9. 2. From the table, we see that $$59049 = 9^5$$ and $$729 = 9^3$

1. State the problem: Calculate $\left(9.3 \times 10^{-4}\right) \div \left(3 \times 10^{2}\right) + \left(5.2 \times 10^{-7}\right)$ and express the answer in standard form. 2. Di

1. **State the problem:** Calculate $\left(6 \times 10^4\right)^2 - \left(4 \times 10^8\right)$ and express the answer in standard form. 2. **Square the first term:**

1. The problem states that the input 6 first goes through an addition operation "+ 8" and then the result is divided by 2. 2. Start by adding 8 to the input 6:

1. The problem states that an input number goes through two operations: first, 3 is added to it, then the result is multiplied by 4, and the final output is 20. 2. Let the input be

1. The problem is to rearrange the equation $m = r + z$ to make $r$ the subject and then to make $z$ the subject. 2. To make $r$ the subject, subtract $z$ from both sides:

1. We start with the equation given: $$n = \frac{p - 2t}{15}$$ 2. Our goal is to make $p$ the subject, which means we want to express $p$ in terms of $n$ and $t$.

1. The problem describes a function machine that takes three inputs: $n$, $c$, and $a$. 2. Each input is transformed by the function machine into outputs: $8n$, $8c$, and $8a$ resp

1. Problem 11(a): Find an equation for the quadratic curve modeling the mouse hole entrance. - The entrance is symmetrical and 6 cm wide at the top, so the curve passes through poi

1. The problem gives input-output pairs: inputs 1, 2, 5, and A correspond to outputs 2, 4, 10, and 18 respectively. 2. We need to find the value of A such that the output is 18.

1. The problem states that a function machine takes an input $k$ and first adds 6, then subtracts 2, producing an output. 2. We start with the input: $k$.

1. The problem asks us to find the input value of a function machine that produces an output of 42 after passing through an intermediate value of -34. 2. We start by understanding

1. The problem states that an unknown input goes through two operations: division by 5, then subtraction by 1, resulting in an output of 3. 2. Let the unknown input be $x$.

1. The problem shows a function machine where the input is 6 and the operation is \( \times u \), meaning multiply by some unknown number \( u \). 2. To find the output, we multipl

1. **State the problem:** We have a function machine that takes an input number and applies three operations in sequence: add 3, multiply by 4, then subtract 3. We need to find the

1. The problem asks us to find the input value to a function machine that produces an output of 43 after an intermediate step of -22. 2. We interpret the function machine as having