🧮 algebra

1. State the problem: Solve the inequality $ (t + 5)(t + 7) \leq -1$. 2. Move all terms to one side to compare with zero:

1. The problem is to solve the inequality $f(x) \geq 0$ given that the solution to $f(x) < 0$ is $(1, 5)$. 2. From the given solution for $f(x) < 0$, the function is negative betwe

1. Given the graph of the parabola $y = f(x)$, we want to solve the inequalities $f(x) \leq 0$ and $f(x) > 0$. 2. From the graph, observe that the parabola opens upwards with verte

1. The problem asks to solve the inequality $f(x) < 0$ for the given parabola $y = f(x)$. 2. Identify where the parabola is below the x-axis (where $f(x)$ is negative).

1. **Problem Statement:** Sketch the graph with the given asymptotes and points. 2. **Given information:**

1. The problem asks to find the domain of the function given by $$y = -x + 5 + 3$$

1. The function given is $$y = -x + 7$$ with domain options specifying inequalities on $$x$$. 2. To find the domain, we analyze each option:

1. We are given the equation $234x \times 434 = 223$ and need to find the value of $x$. 2. First, calculate the constant product $234 \times 434$:

1. Let's identify the context first: the expression was simplified to 2x in step 4. 2. Usually, this comes from combining like terms or simplifying a multiplication or division.

1. Stated problem: Solve the equation $$4(2^{2x}) - 25 = 0$$ for $x$. 2. Add 25 to both sides to isolate the exponential term:

1. The problem asks to expand the expression $-4x^2 + 24x - 4$. 2. This expression is already expanded as a quadratic polynomial with three terms: one quadratic term $-4x^2$, one l

1. The problem is to expand the expression "it". However, "it" is not a mathematical expression that can be expanded. 2. If you have a specific algebraic expression, polynomial, or

1. The problem is to analyze and simplify the quadratic expression $$-4x^2 + 24x - 4$$. 2. First, factor out the greatest common factor from all terms, which is $$-4$$.

1. **Question 9:** A line $y=mx+c$ is perpendicular to a line $y=px+q$ if the gradients satisfy $p=-\frac{1}{m}$. So from the options, none exactly matches this, but usually it is

1. **Find the gradient of the line through points R(4, 0) and S(-2, 1).** Gradient formula is $$m=\frac{y_2 - y_1}{x_2 - x_1}$$.

1. Solve the equation $\frac{3x - 4}{3} = \frac{3x^2 + 5x - 12}{2}$ for $x$. Multiply both sides by 6 to clear denominators:

1. The problem states that Isaac and Victoria share money in the ratio $2:5$ and Victoria receives 6.60. 2. Let the total number of parts be $2 + 5 = 7$ parts.

1. We are given the formula $$R=\frac{x^2}{y}$$ and values $$x=2.9 \times 10^5$$ and $$y=6.2 \times 10^4$$. 2. Substitute the given values into the formula:

1. Stating the problem: We need to find the equation of a circle with center at the origin $(0,0)$ and radius $3$. 2. Recall the equation of a circle centered at the origin: $$x^2

1. **Problem:** Factor $x^2 + 5x + 6$. 2. **Strategy:** Look for two numbers that multiply to $6$ and add to $5$.

1. **Stating the problem**: We have a sequence starting at 3. Each term is generated from the previous as follows: - If the term is even, next term = term \div 2