🧮 algebra

1. The problem asks to find the values of $y$ in the relation $y = 2(x + 2)$ for given $x$ values and then draw the graph of this relation. 2. The relation is given by the function

1. The problem involves analyzing the relations and graphs of the functions given by: $$y = 5e^{-2x}$$

1. **Problem statement:** Find the sums of the given arithmetic series using the provided formulas and verify the answers. 2. **Part (a): Sum of 1 + 2 + 3 + ... + 999**

1. **State the problem:** Simplify and analyze the expression $x^2 - y^2 + 2y - 1$. 2. **Group terms involving $y$:** Rewrite the expression as $x^2 - (y^2 - 2y) - 1$.

1. Escreva sob a forma de potência: 1.a) Temos a expressão $\left(\frac{3}{5}\right)^{\frac{2}{3}} \times \left(\frac{2}{5}\right)^{\frac{2}{3}} \times \left(\frac{5}{25}\right)^{\

1. **Statement of the problem:** Solve the given one-step linear equations and verify the solutions where required. 2. **Question 1:** Solve and verify:

1. Problem: Factorise $w^2 - 5w$. Step 1: Identify the common factor in both terms, which is $w$.

1. نبدأ بكتابة المعادلة المعطاة: $$ هـ - \frac{1}{2} ( ج - 6 ) = 4 $$

1. **Simplify expression a:** Given: $5x^2 - 6x - 3x^2 + 7 - x^2 + 6x$

1. **Problem 1: Vertical and Horizontal Translations** We apply vertical shifts and horizontal translations to 5 functions from the list.

1. Stated problem: Evaluate the expression $$2\sqrt{3} (\sqrt{3} + x) - 4x(x^2 - 3\sqrt{3})$$ for $$x = -\sqrt{3}$$. 2. Substitute $$x = -\sqrt{3}$$ into the expression:

1. The problem asks us to determine whether each expression is odd or even, given that $k$ is an even number. 2. Recall the definitions:

1. **State the problem:** Simplify the expression $9x + 2y - 4x + 11 - 6y + 5$. 2. **Group like terms:** Combine the terms with $x$, the terms with $y$, and the constant terms sepa

1. **Problem (a): Compare $\frac{2}{3}$ of $\frac{3}{4}$ and $\frac{3}{4}$ of $\frac{2}{3}$.** 2. "Of" means multiplication, so calculate each:

1. **State the problem:** Simplify the expression $$\frac{5x^{3}(3x^{4}y^{2})^{3}}{27(x^{5}y^{2})^{2}x^{3}y}$$ given $x=2$ and $y=444$. 2. **Simplify the numerator:**

1. The problem involves finding the values of terms A, B, and C given the sums of terms involving f. 2. From the first graph example, we see that adding 9x, 5x, and 3x gives 14x, a

1. **State the problem:** Simplify the expression $5np + 7n + 5 + 3np + n + p$. 2. **Group like terms:** Group terms with $np$, terms with $n$, terms with $p$, and constants separa

1. Stating the problem: Solve the quadratic equation $u^2 + 9u + 14 = 0$. 2. Factor the quadratic: We look for two numbers that multiply to 14 and add to 9. These numbers are 7 and

1. **State the problem:** Simplify the expression $8a + 7d - 3a + 2v - 5d + 4v$. 2. **Group like terms:** Combine terms with the same variable.

1. **State the problem:** Factor the expression $x^3 - 27$. 2. Recognize that $x^3 - 27$ is a difference of cubes since $27 = 3^3$.

1. The problem is to simplify the expression $$-6m + 8m$$. 2. Both terms have the variable $m$, so we can combine them by adding their coefficients.