🧮 algebra

1. Evaluate $3\sqrt{3} \left(2 - \sqrt{12}\right) \left\lfloor \frac{2013}{10} \right\rfloor$. - First, simplify inside the brackets:

1. The problem asks to identify the terms of the expression $$5x^2 + 9x + 6$$ from the given options. 2. Recall that a term in an algebraic expression is a part separated by plus o

1. **Problem:** Given the function $d(s) = s^2 + 0 = d(s) = s = s$, find $d(1)$. Step 1: Simplify the function: $d(s) = s^2$.

1. The problem asks if the given data represents a function. 2. A function assigns exactly one output value for each input value.

1. The problem asks whether the given data represents a function. 2. Recall that a function assigns exactly one output value (y) for each input value (x).

1. **Problem:** Given the function $d(s) = 3s - 5 + s$, and $d(s) = s$, find $(d \, h \, r)(1)$. Step 1: Simplify $d(s)$:

1. **State the problem:** We need to find two consecutive numbers whose sum is 13. 2. **Define variables:** Let the first number be $x$. Since the numbers are consecutive, the next

1. The problem is to verify the equality of the expressions: $$(5 \times 8) \times 2 = 2 \times (20 \times 2)$$ and explore equivalent expressions. 2. Calculate the left side: $$(5

1. The problem asks us to find the number that should replace the gap in the equation $$(26 \times 37) \times 12 = \square$$ given that $$26 \times (37 \times 12) = 11544$$. 2. By

1. The problem asks to evaluate two expressions using the associative property of addition. 2. For part (a), we have $ (3 + 5) + 2 $. First, calculate inside the parentheses:

1. Simplify each expression and state restrictions. **a)** $\frac{1}{3} + \frac{5}{4}$

1. The problem is to find the $r$-th term ($U_r$) of the sequence: 4, 8, 16, ... 2. Identify the type of sequence. The terms are 4, 8, 16, which increase by multiplication, so this

1. The problem asks for the square roots of 1. 2. By definition, a square root of a number $a$ is a number $x$ such that $x^2 = a$.

1. The problem asks for the degree of the polynomial $$ax^5 + bx^3 + cx^2 + d$$. 2. The degree of a polynomial is the highest power of the variable $x$ with a non-zero coefficient.

1. The problem is to solve the equation or expression provided by the user. 2. Since no specific equation or expression was given, please provide the exact problem you want to solv

1. প্রশ্ন 5: A এবং B একটি ব্যবসাতে 3:2 অনুপাতে বিনিয়োগ করেছে। মোট লাভের 5% একটি বিদ্যালয়ে দান করা হয় এবং A মোট লাভের 8550 টাকা পায়। মোট লাভ কত ছিল? 2. প্রথমে, মোট লাভকে $x$ ধরা

1. **State the problem:** Given the equations $5^m = 35^n$ and $7^p = 35^n$, show that $$n = \frac{mp}{m+p}$$ where $m + p \neq 0$. 2. **Rewrite the given equations:**

1. The problem is to write the equation $y + 1 = x$ in terms of $y$. 2. To isolate $y$, subtract 1 from both sides of the equation:

1. The problem asks to express the given answer in the form $y + 1 = $ something. 2. To rewrite an expression in the form $y + 1 = $, isolate $y + 1$ on one side.

1. We are asked to find the equation of a parabola with vertex at $(1,-1)$ and passing through points $(-4,24)$ and $(7,35)$. The vertex form of a parabola is given by: $$y = a(x -

1. The problem asks to express each number in standard form, which means writing it as $a \times 10^n$ where $1 \leq a < 10$ and $n$ is an integer. 2. For $0.00007$, move the decim