🧮 algebra

1. We are given the identity $$(x + 5)(x + 2)(x + a) \equiv x^3 + bx^2 + cx - 30$$ and asked to find integers $a$, $b$, and $c$. 2. First, expand the left side step-by-step.

1. The problem is to simplify the expression $|-3.14|$. 2. The absolute value function $|x|$ returns the distance of $x$ from 0 on the number line, which means it always outputs a

1. The problem is to find the value of $|-5|$. 2. The absolute value of a number is its distance from zero on the number line, regardless of direction.

1. **Problem 11:** Find the domain of $$f(x) = \sqrt[3]{\frac{x}{\sqrt{x}}}$$. - Step 1: Simplify the expression inside the cube root.

1. The problem is to evaluate the absolute value of the expression $|7|$. 2. The absolute value of a number is its distance from zero on the number line, regardless of direction.

1. **Problem 1: Finding (f o f o f)(1) given the curve y = f(x).** The graph shows the function $f(x)$ with key points: $f(1) = 2$ (from the given approximate coordinates near x=1)

1. **Problem statement**: Find the domain of $ (f+g)(x) $ where $ f(x)=\sqrt{x-1} $ and $ g(x)=\sqrt{1-x} $.

1. **State the problem:** We are given a function $$f(x) = \frac{2x}{5} - 1$$ and asked to find the value of $$f^{-1}(3) + f(-0.5)$$. 2. **Find $$f^{-1}(3)$$:**

1. Stating the problem for question 4: Find the domain of the function $$f(x) = \sqrt{\frac{3 - x}{5 - x}}$$. 2. To find the domain of $$f(x)$$, ensure the expression inside the sq

1. Stating the problem: Calculate the value of the expression $444 \times 6 + (40 \times 2) - 700 \times \left(4 \div 2\right)$.\n\n2. First, evaluate each multiplication and divis

1. **Problem 1:** Find the domain of the function $f(x) = \sqrt{x-1} + \sqrt{x+2}$. 2. To find the domain, ensure the expressions under the square roots are non-negative:

1. State the problem: Simplify the expression $$444 \times 6 + (40 \times 2) - 700 \times (4 + 2)$$. 2. Calculate each multiplication:

1. The problem is to solve the quadratic equation $3x^2 - x - 17 = 0$ for $x$. 2. Identify coefficients: $a=3$, $b=-1$, $c=-17$.

1. Stating the problem: Solve the equation $$\sqrt{x+8} + \sqrt{x+1} = 7$$. 2. Isolate one square root: Let’s isolate $$\sqrt{x+8}$$.

1. **State the problem:** Beth drives a total of 200 miles in 4 hours. She drives the first 18 miles at 36 mph. We need to find her average speed for the remaining part of the jour

1. Let's state the problem: evaluate the expression $160\div 4 - (3+7)\times 14 + (120-59) - 1 \times 7 \div (1+1) + (166 \div 166) \times 5$. 2. Calculate each part inside parenth

1. The problem is to factorize algebraic expressions. 2. To factorize means to write a given expression as a product of its factors.

1. Let's solve a new algebra problem step-by-step. 2. Consider the quadratic equation $$2x^2 - 4x - 6 = 0$$.

1. Let's first understand the structure of your question request. 2. If you want to attempt a problem similar to one you've seen before, I will create a sample question involving a

1. The problem is to express the expression $$49x^{3/2}$$ in indices (exponential) form. 2. We note that $$49$$ is a perfect square and can be written as $$7^2$$.

1. **State the problem:** Simplify the expression $5b + 6n - 2t + 3 + 3b - 4n - 5t$. 2. **Group like terms:** Group terms with $b$, $n$, $t$ and constant terms separately.