🧮 algebra

1. **State the problem:** We need to find the equation of the trend line passing through points (1, 1) and (6, 8) in slope-intercept form: $$y = mx + b$$.

1. لنوضح ما هو مطلوب في المسألة: حل المعادلة $2^n = 8$ لإيجاد قيمة $n$. 2. نعلم أن $8$ يمكن كتابته كـ قوة أساسية للعدد $2$: $$8 = 2^3.$$

1. **State the problem:** Simplify the expression $x - 3 + 2$. 2. **Combine like terms:** The terms $-3$ and $+2$ are constants and can be combined.

1. Stating the problem: We need to find the reciprocal of the mixed number $3 \frac{3}{4}$.\n\n2. Converting the mixed number to an improper fraction: \n$3 \frac{3}{4} = \frac{3 \t

1. Stating the problem: Solve the equation $16 + 37x = -11$ for $x$ and express $x$ as a fraction in simplest form. 2. Subtract 16 from both sides to isolate the term with $x$:

1. Problem: Solve for $t$ in the equation $\frac{13^t}{13^{20}} = 13^5$. 2. Use the property of exponents that $\frac{a^m}{a^n} = a^{m-n}$. So we rewrite the left-hand side as $13^

1. State the problem: Solve the equation $$\frac{r^2}{9} - 4 = 0$$ for $r$. 2. Isolate the term with $r^2$ by adding 4 to both sides:

1. **State the problem:** Find the value of $w$ such that $$(8^3 \times 8^4)^5 = 8^w.$$\n\n2. **Use the property of exponents for multiplication:** When multiplying powers with the

1. **State the problem:** We need to find the two possible values of $w$ from the equation

1. The problem asks to evaluate $$\frac{7.4 \times 10^5 + 1.3 \times 10^4}{5.5 \times 10^{-4}}$$ and express the answer in standard form with 2 significant figures. 2. First, simpl

1. Given the equation $ (90 - x)(x + 10) = 475 $. 2. Expand the left side by distributing:

1. We are given the equation $(n + 90)(n - 10) = 475$ and asked to solve for $n$. 2. First, expand the left side using the distributive property:

1. **State the problem:** We need to find the equation of the trend line passing through the two yellow points on the scatter plot, which are approximately at coordinates $(4,8)$ a

1. **State the problem:** We are given two points on a line: (4, 6) and (6, 0).

1. The problem asks for the equation of the trend line passing through the two orange points (0, 9) and (8, 3) in gradient-intercept form (\(y = mx + b\)). 2. First, we calculate t

1. The problem asks for the equation of the trend line passing through the two orange points on the scatter plot: $(4,0)$ and $(8,7)$. 2. To find the equation of a line in slope-in

1. Multiply each expression step-by-step: 1.a. Multiply $(6a^2) \times (-4ab)$:

1. The problem asks for the equation of the trend line passing through two given points \((0,8)\) and \((8,4)\).\n\n2. To write the equation in gradient-intercept form \(y = mx + b

1. Stated problem: Solve the equation $ (x+2)^2 = 4x + 4 $.\n\n2. Expand the left side: $ (x+2)^2 = x^2 + 4x + 4 $.\n\n3. Substitute expanded form back into equation: $ x^2 + 4x +

1. Problem: Perform synthetic division on the polynomial using the divisor represented by the root (position_hint: bottom-right), assuming divisor is $x - r$ with root $r$. The coe

1. **State the problem:** We need to find which values among: 61 × 10⁻⁵, 0.61 × 10⁻⁵, 0.000 061, 0.000 61, 0.61 × 10⁻³, and 61 × 10⁻³ are equivalent to 6.1 × 10⁻⁴. 2. **Convert the