🧮 algebra

1. State the problem. The problem is to simplify $(-2)\times(+2)$.

1. The problem is to find the determinant of the 2x2 matrix: $$\begin{bmatrix}-7 & 0 \\ 3 & 1\end{bmatrix}$$

1. The problem is to analyze the function $h = -d^2 + 4$ and understand its graph. 2. This is a quadratic function in terms of $d$, where the coefficient of $d^2$ is negative, indi

1. The problem is to solve the system of equations: $$3x + 2y = -5$$

1. Problem: Simplify the expression $11x-2x+3y+5y$. 2. Strategy: Combine like terms by grouping x-terms together and y-terms together.

1. Problem: Find the H.C.F of $6x$ and $3y$. 2. Factor each monomial into numeric primes and variable factors: $6x = 2\cdot 3\cdot x$ and $3y = 3\cdot y$.

1. **State the problem:** Factor the expression $tw + 10t - 2w - 20$. 2. **Group terms:** Group the terms to factor by grouping:

1. The problem is to simplify the expression $\frac{79}{22}$.\n\n2. Since 79 and 22 have no common factors other than 1, the fraction is already in its simplest form.\n\n3. Therefo

1. Statement of the problem. Solve the equation $4x = 20$.

1. The problem states that Boone County has 858 to spend on new street signs, and each sign costs 26. 2. We need to find how many signs the county can buy with 858.

1. The problem is to simplify the expression $x + 5$. 2. Since $x + 5$ is already in its simplest form, no further simplification is needed.

1. The problem is to solve the equation $4x = 20$ for $x$. 2. To isolate $x$, divide both sides of the equation by 4:

1. **Find** $(2x + 9)^2$. This means we need to square the binomial. 2. Use the formula for squaring a binomial: $$(a + b)^2 = a^2 + 2ab + b^2$$

1. **State the problem:** Solve for $x$ in the equation $$x - 14 = 20$$

1. **State the problem:** Solve for $x$ in the equation $$4x = 20.$$\n\n2. **Isolate the variable:** To solve for $x$, divide both sides of the equation by 4 to get $$x = \frac{20}

1. The problem is to solve for the variable $x$ in the equation: $$x + 13 = 27$$

1. **State the problem:** Solve for $x$ in the equation $$\frac{x}{28} = \frac{9}{7}$$. 2. **Understand the equation:** This is a proportion where two fractions are equal.

Problem: Solve for the variable x in the equation $\frac{x}{28} = \frac{9}{7}$. 1. Multiply both sides by 28 to isolate x.

1. Find the sum of $(4x + 2y - 6z) + (5y - 2z + 7x) + (-9z - 2x - 3y)$. Combine like terms:

1. **Problem a:** Determine if the point $(-3,4)$ lies on the line given by the equation $$y + 3x + 2 = 0.$$ 2. Substitute $x = -3$ and $y = 4$ into the line equation:

1. The problem is to express the number $7.5 \times 10^{-2}$ in decimal form. 2. Recall that $10^{-2}$ means $\frac{1}{10^2} = \frac{1}{100} = 0.01$.