🧮 algebra

1. The problem is to solve the system of non-linear equations given by the points: $(-1, 2), (1, -2), (1, 1), (3, -1)$

1. The problem asks to represent the relation shown in the arrow diagram as a set of ordered pairs. 2. The arrow diagram shows arrows from numbers to houses: 3 to House Q, 4 to Hou

1. El problema es calcular la expresión $$\log_{\sqrt{7}} \sqrt[7]{343} + \log_{3\sqrt{4}} \sqrt[3]{16} + \log_{4\sqrt{3}} \sqrt[4]{27}$$. 2. Recordemos que $$\log_a b = \frac{\log

1. **State the problem:** Factor the polynomial $4x^3 + 6x^2 - 18x$ completely. 2. **Identify the greatest common factor (GCF):** Look at the coefficients 4, 6, and -18. The GCF of

1. **State the problem:** Simplify the expression $2m^4 \times 5m^2$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying terms with the same base, a

1. The problem is to understand how to find specific features or points on a graph. 2. To find points on a graph, you need to know the function equation, for example, $y=f(x)$.

1. **State the problem:** Solve the equation $$\frac{1}{x+y} + \frac{1}{x-y} = 0$$ for $x$ and $y$. 2. **Use a common denominator:** The denominators are $x+y$ and $x-y$. The commo

1. **Stating the problem:** Solve the linear equation $8x + 9 = 4x + 12$ for $x$. 2. **Formula and rules:** To solve linear equations, we isolate the variable $x$ by performing the

1. **State the problem:** Simplify the expression $$\frac{8 - 5}{x - 12} = 51 = 5$$. 2. **Analyze the expression:** The expression as given is ambiguous because it shows $$\frac{8

1. The problem is to analyze the function $f(x) = x^2 - 2x + 1$. 2. This is a quadratic function in standard form. We can rewrite it to identify its properties.

1. The problem states: Start with 2 blue circles and 1 red square, then add 4 red squares each time. 2. We want to find the pattern rule for the number of red squares in each step.

1. The problem is to create a graph of a parabola similar to the one described, which opens upwards with a vertex near (1.5, 0). 2. The general form of a parabola is given by the q

1. **State the problem:** Solve the equation $$-22.5 = 3(3x - 4.5)$$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses:

1. **State the problem:** Solve the equation $$10.5 = 4x - 4.5 - 3x$$ for $x$. 2. **Rewrite the equation:** Combine like terms on the right side.

1. **Stating the problem:** We are given vectors along a path and two diagonal vectors converging to a point, with a final vertical vector labeled 5. We want to analyze the vector

1. **Énoncé du problème :** Résoudre l'équation irrationnelle $$\sqrt{3x^2 + 2x + 4} = 2 - x$$. 2. **Formule et règles importantes :** Pour résoudre une équation avec une racine ca

1. **State the problem:** We are given the ratio of ages of Rahul and his sister as 4:3 currently, and 8 years ago, the ratio was 6:5. We need to find Rahul's current age. 2. **Set

1. The problem is to simplify the expression $-\left(\frac{-7}{-9}\right)$.\n\n2. Recall that a negative divided by a negative is positive, so $\frac{-7}{-9} = \frac{7}{9}$.\n\n3.

1. **State the problem:** Simplify the expression $-\left(-\frac{7}{9}\right) - \sqrt{\frac{49}{100}}$. 2. **Recall the rules:**

1. **Problemos uždavinys:** Arnas užrašė dviženklį skaičių, o Meinardas užrašė tą patį skaičių, bet sukeistais skaitmenimis. Meinardo skaičius yra 9 vienetais didesnis už Arno, o A

1. The problem asks if the function $y=\frac{1}{3}x^2 - 3$ is the same in standard form and vertex form. 2. The standard form of a quadratic function is generally written as $y = a