🧮 algebra

1. **State the problem:** We want to find the intersection points and area between two parabolic curves. The father's birth month is June (6) and last two digits of birth year unkn

1. **State the problem:** We are given the polynomial $$4x^3 - 6x + ax + 3$$ and told that when it is divided by $$2x - 1$$, the remainder is 7. 2. **Understand the divisor:** Firs

1. The problem is to simplify the sum of mixed numbers: $3 \frac{1}{2} + 4 \frac{1}{3} + 5 \frac{1}{4}$.\n\n2. Convert each mixed number to an improper fraction:\n- $3 \frac{1}{2}

1. The problem states that when the polynomial $$4x^3 - 6x + ax + 3$$ is divided by $$2x - 1$$, the remainder is 7. 2. By the Remainder Theorem, the remainder of a polynomial $$f(x

1. Diketahui fungsi $f(x) = x + 3$ dan $g(x) = 2x^2 - 1$. Tentukan $(f + g)(x)$. $(f + g)(x) = f(x) + g(x) = (x + 3) + (2x^2 - 1) = 2x^2 + x + 2$.

1. **State the problem:** We have three functions: - $f(x)=\frac{4x+5}{1-2x}$

1. **Stating the problem:** Simplify each expression involving mixed numbers by converting to improper fractions, performing operations, and simplifying results. 2. **Convert mixed

1. The problem asks which of the given expressions is NOT a factor of the polynomial $f(x) = x^3 - 13x - 12$. 2. Recall that if $(x - r)$ is a factor of $f(x)$, then $f(r) = 0$. We

1. Problem: Simplify the following expressions: a) $3 \frac{1}{2} + 4 \frac{1}{3} + 5 \frac{1}{4}$

1. The problem is to add the two fractions $\frac{4}{9}$ and $\frac{7}{9}$. 2. Since the denominators are the same (9), we can add the numerators directly.

1. **State the problem:** We are given two parabolas based on family birthdates. Given:

1. State the problem: Solve for $x$ in the equation $$\frac{5}{8} - \frac{3}{5} = \frac{x}{10}.$$\n\n2. Find the least common denominator (LCD) of the fractions on the left side. T

1. We are given a quadratic function $f(x)$ and are asked to find its vertex coordinates, maximum or minimum value, axis of symmetry, and y-intercept. 2. The general form of a quad

1. The problem is to find the sum of the first 19 terms of an arithmetic sequence. 2. The sum of the first $n$ terms of an arithmetic sequence is given by the formula $$S_n = \frac

1. The problem asks for the sum of the first 19 terms of a sequence, but the sequence type was not specified. Assuming it is an arithmetic sequence. 2. The formula for the sum of t

1. The problem presents the sequence: 1, 6, 13, 22, 33, ? and asks to find the next number. 2. Observe the differences between consecutive terms:

1. The term "Matrixe" seems to refer to matrices, which are rectangular arrays of numbers arranged in rows and columns. 2. A matrix is typically written as $$\begin{bmatrix} a_{11}

1. The problem asks to rewrite the quadratic function $f(x) = -2x^2 + 6x - 1$ in the vertex form $a(x+h)^2 + k$, where $a$, $h$, and $k$ are constants. 2. Start with the given func

1. Problem: Simplify the following expressions: a) $3 \frac{1}{2} + 4 \frac{1}{3} + 5 \frac{1}{4}$

1. The problem requires us to first equate $f(x)$ and $g(x)$, then solve the equation $f(x) + g(x) = 0$ for problem #2. 2. Step 1: Equate $f(x) = g(x)$.

1. The problem states we have a quadratic function $f(x) = 3x^2 + 4x - 5$ and a straight line passing through the point $(1,-1)$ with gradient $m$. The line is described by the equ