🧮 algebra

1. **State the problem:** Calculate the value of $-1.75 - \frac{22}{20}$.\n\n2. **Convert decimals and fractions:** Note that $-1.75$ is a decimal and $\frac{22}{20}$ is a fraction

1. **State the problem:** We have two drones at points C and D on the ground. The drone at C follows the path $f(x) = -x^2 + 2x + q$, and the drone at D follows $g(x) = mx + 5$. We

1. **State the problem:** We need to find scalars $a$, $b$, and $c$ such that every point $(x,y)$ on the line $ax + by = c$ is equidistant from the points $(2,-1)$ and $(3,2)$. 2.

1. Problem: Simplify the expression $$\frac{2}{5} + \frac{1}{3} + \frac{1}{12} - \frac{2}{180}$$. 2. Find the least common denominator (LCD) of 5, 3, 12, and 180.

1. **State the problem:** Calculate the value of $-1.2 - \frac{29}{20}$.\n\n2. **Convert decimals and fractions to a common form:** Convert $-1.2$ to a fraction. Since $1.2 = \frac

1. The problem is to find the domain of the function $$f(x) = \frac{x - 1}{x^2 + 1}$$. 2. The domain of a function is the set of all real numbers for which the function is defined.

1. The problem is to verify the identity for the square of a sum, which states that $$(a+b)^2 = a^2 + 2ab + b^2.$$\n\n2. Start with the left-hand side (LHS): $$(a+b)^2.$$\n\n3. Exp

1. The problem is to understand the concept of an identity in algebra. 2. An identity is an equation that is true for all values of the variable involved.

1. The property used in expansion is the **distributive property** of multiplication over addition. 2. This property states that for any numbers $a$, $b$, and $c$, we have $$a(b+c)

1. נניח שהאיבר הראשון בסדרה החשבונית הוא $a_1 = a$ והפרש הסדרה הוא $d$. 2. מספר האיברים בסדרה הוא $3n$.

1. The problem is to understand the transformation from the base function $y=x^2$ to the transformed function $y=(x-2)^2$. 2. The base function $y=x^2$ is a parabola with its verte

1. Stating the problem: Solve the equation $$3(x + 1)^2 + 2(x - 3)^2 = (5x - 2)(x - 1) + 30$$ for $x$. 2. Expand each term:

1. The problem is to simplify the expression $\frac{5}{5_{base3}}$. 2. First, convert the base 3 number $5_{base3}$ to base 10.

1. **State the problem:** We have a function representing the cost $C$ in k10 for internet browsing based on the number of hours $h$ used. The cost function is $C(h) = 10h$. 2. **D

1. The problem is to simplify the expression $\frac{1}{3} - 5_{base\ 2} + \frac{1}{3} + 5_{base\ 2}$.\n\n2. First, recognize that $5_{base\ 2}$ is a number in base 2. However, the

1. The problem involves simplifying the expression: $\frac{1}{3} - 5 \times 2 + \frac{1}{3} + 5 \times 2$. 2. First, calculate the multiplication parts: $5 \times 2 = 10$.

1. **State the problem:** Wendy and Anna together have 136 plums. Wendy has 14 more plums than Anna. We need to find how many plums Anna has. 2. **Define variables:** Let $A$ be th

1. The problem states that the terms in the sequence increase by the same number each time, meaning it is an arithmetic sequence. 2. We are given Term 1 = 3 and Term 5 = 19.

1. The problem asks us to find which two recurring decimals among $0.3\dot{5}$, $0.35\dot{3}$, $0.35\dot{3}$, and $0.3\dot{5}$ are equivalent. 2. Let's write each recurring decimal

1. Let's analyze the behavior of the function as $x$ approaches negative infinity. 2. Suppose the function is $y = a^x$ where $a > 0$ and $a \neq 1$.

1. **State the problem:** We need to sketch a polynomial $P(x)$ with zeros at $-5$, $1$, and $4$, and with end behavior such that as $x \to \infty$, $P(x) \to -\infty$, and as $x \