🧮 algebra

1. **State the problem:** Solve the equation $$4(x + 4) = x + 1$$. 2. **Apply the distributive property:** Multiply 4 by each term inside the parentheses.

1. **Problem:** We have groups arriving with the first group having 1 person, the second group 3 people, and each subsequent group having 2 more people than the previous group. Fin

1. **Problem Statement:** We are running a fund-raising concert. The first group has 1 person, the second group has 3 people, and each subsequent group has 2 more people than the p

1. The problem is to find the determinant of the matrix \(\begin{bmatrix} 8 & 5 \\ -4 & -13 \end{bmatrix}\). 2. The formula for the determinant of a 2x2 matrix \(\begin{bmatrix} a

1. The problem is to find the determinant of the 2x2 matrix $$\begin{pmatrix} 85 & -4 \\ -3 & ? \end{pmatrix}$$. However, the matrix is incomplete as the bottom right element is mi

1. **State the problem:** Expand the cubic polynomial $$f(x) = 2x^3 + 7x^2 + x - 6$$ in powers of $$(x-2)$$. 2. **Recall the binomial expansion formula:** To expand a function arou

1. **Problem:** Find the zeros of the polynomial function $f(x) = 2x^3 - 3x^2 - 8x + 12$ using the Rational Root Theorem. 2. **Rational Root Theorem:** Possible rational roots are

1. **Problem statement:** An article originally priced at $700 is discounted by 20%. We need to find (a) the amount of the discount, (b) the final cost after the discount, and (c)

1. **State the problem:** Calculate the sales tax and total price for a refrigerator priced at 682 with a 7% sales tax.

1. **State the problem:** Solve for $t$ in the equation $$-12 \sqrt{-57t + 64} + 64 + 21 = -75.$$\n\n2. **Simplify the constants on the left side:** $$64 + 21 = 85,$$ so the equati

1. **State the problem:** Solve for $f$ in the equation $$6 = 5 + \sqrt{64} + f$$. 2. **Recall the formula and rules:** The square root of a number $x$ is a value that, when multip

1. **State the problem:** Solve for $d$ in the equation $$-55 + 48\sqrt{d} = 89.$$\n\n2. **Isolate the square root term:** Add 55 to both sides to get $$48\sqrt{d} = 89 + 55.$$\n\n

1. **State the problem:** Solve the system of linear equations: $$2x + 3y = 7$$

1. **State the problem:** Solve the equation $$4(-\frac{1}{4}x + 3) = 6.5$$. 2. **Apply the distributive property:** Multiply 4 by each term inside the parentheses:

1. **Evaluate the expression** $8 + 8 \div 8 + 8$. - According to order of operations (PEMDAS), division comes before addition.

1. Evaluate $18 - 3^2 \cdot 2$. First, calculate the exponent: $3^2 = 9$.

1. The problem asks to evaluate four expressions and find the corresponding letter for each answer. 2. Evaluate expression 1: $8 + 4^2 \div 2$

1. **State the problem:** We need to evaluate each of the four expressions and find their values. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplicat

1. **Evaluate** $3 \cdot (7 - 2) - 5$. Start by solving inside the parentheses:

1. **State the problem:** Simplify the expression $$\frac{1B^3}{-3a^3c^3} \cdot \frac{a^2B}{-4B^2}$$. 2. **Write the expression as a single fraction:**

1. **State the problem:** Simplify the expression $$\frac{3x^7 \cdot x^2}{x^9}$$ with no negative exponents. 2. **Use the laws of exponents:** When multiplying powers with the same