🧮 algebra

1. The problem asks to find the equation of a line passing through a given point (which is missing). 2. To determine the equation of a line, we need at least two things: a point on

1. Problema 60: Simplifique a expressão $$\frac{x - x^3}{x^2 + 4x + 4} - \frac{8x}{2x + 4}$$. Primeiro, fatoramos denominadores e numeradores relevantes:

1. The problem states: Rewrite the logarithmic equation $$91 = \log_5 y$$ as an exponential equation. 2. Recall that the logarithmic equation $$\log_b a = c$$ can be rewritten as t

1. Stated problem: Simplify the expression $c^1 \times \sqrt[3]{c^3}$.\n\n2. Break down the expression: $c^1$ is simply $c$. The term $\sqrt[3]{c^3}$ means the cube root of $c^3$.\

1. **State the problem:** Simplify the expression $$rs - 3 ( r - s )^2 + 4s^2$$ and verify the right side $$rs - 3 ( r - s ) ( r - s ) + 4s^2$$. 2. **Expand the squared term:** Sin

1. **State the problem:** We are given a total of 175 teachers to be apportioned among five high schools based on their student populations using Webster's method. 2. **List the po

1. Problem 38: Find which equation is equivalent to $y - 34 = x(x - 12)$. Expand the right side:

1. The problem is to show that the function defined by $f(x) = 12$ has no maximum. 2. Note that $f(x) = 12$ is a constant function, meaning it has the same value for every $x$.

1. We are given the polynomial equation $$6x^6-25x^5+31x^4-31x^2+25x-6=0$$ and asked to solve it using synthetic division. 2. First, try to find rational roots using the Rational R

1. **State the problem:** Given mappings from numbers on the left to numbers on the right, find the unknown output, especially for inputs 9 and 19. 2. **Analyze the first set:** 4

1. The problem presents three circles each with four numbers around and asks to find the missing value in the third circle (J).\n\n2. Let's observe the numbers around each circle a

1. Problem 28: A total of 35000 is invested at 4%, 5%, and 6%. The first year interest is 1780. In the second year, 6% investment earns 7%, others remain same, total interest 1910.

1. The problem is to find the equation of a circle. 2. A circle with center at point $C(h, k)$ and radius $r$ is defined by all points $P(x, y)$ such that the distance between $P$

1. Let's learn about the equation of a line, which helps us describe straight lines on a coordinate plane. 2. The most common form is the slope-intercept form: $$y = mx + b$$.

1. The problem is to simplify the expression $\frac{x^2 - 4}{x+2}$. 2. Recognize that the numerator $x^2 - 4$ is a difference of squares, which factors as $x^2 - 4 = (x-2)(x+2)$.

1. **State the problem:** Simplify the expression $x^2 - 4(x + 2)$. 2. **Apply the distributive property:** Multiply $-4$ by both $x$ and $2$. This gives

1. **State the problem:** David's salary after a 3% pay cut is $3346.50. We need to find his original salary before the pay cut.

1. The problem is to simplify the expression, but no specific expression was provided. 2. To simplify any expression, we typically combine like terms, factor expressions, or apply

1. We are asked to solve the quadratic equation $$x^2 - 3x + 1 = 0$$. 2. To solve this, we use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $$a=1$$, $$b=

1. The problem asks us to calculate the product of $-10$ and $-4$. 2. Multiplication of two negative numbers results in a positive number.

1. **State the problem:** Simplify the expression $$2p^2 + 2(p - 4q)(p - 4q) + 11pq$$. 2. **Expand the square:** The term $$ (p - 4q)(p - 4q) $$ is a binomial squared, so we apply