🧮 algebra

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

1. The problem is to solve for number 15 (assuming the problem is solving the number 15 or an equation involving 15). 2. Since the problem statement isn't explicit, if we treat it

1. Solve the equation $3|2t-1|-4=16$ for $t$. Start by isolating the absolute value: