🧮 algebra

1. **State the problem:** We need to order the functions $f(x)$, $g(x)$, and $h(x)$ by their maximum values from smallest to largest. 2. **Find the maximum value of $f(x) = (6 - x)

1. **State the problem:** Identify the error in generating an expression equivalent to $$4 + 2x - \frac{1}{2} (10 - 4x)$$ and then correct the error. 2. **Original expression:** $$

1. **State the problem:** We are given that $a - b = b - c = 2$ and need to find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$

1. **Énoncé du problème :** Développer l'expression $4(x + 2)$ en utilisant la distributivité. 2. **Formule utilisée :** La distributivité s'exprime par $a(b + c) = ab + ac$.

1. The problem states that the zero of the linear function is the ordered pair $(2,0)$. This means the function crosses the x-axis at $x=2$. 2. A zero of a function is a point wher

1. The problem is to graph a line using the zero point (0,0) and another point from a given table. 2. To graph a line, you need two points. One point is given as the origin (0,0).

1. **State the problem:** We have a mapping from input values to output values: Input: 7, 8, 10, 14

1. **State the problem:** Solve the inequality $12 \leq 3x - 3 - 2x$. 2. **Simplify the right side:** Combine like terms on the right side.

1. **State the problem:** Solve the inequality $2 + 2x \geq 3x - 1$ for $x$. 2. **Write down the inequality:**

1. **State the problem:** A rectangular lawn measures 8 meters by 4 meters and is surrounded by a flower bed of uniform width $x$ meters. The total area of the lawn plus the flower

1. **State the problem:** Solve the equation $2^x + x = 5$ for $x$. 2. **Understand the equation:** This is a transcendental equation involving both an exponential term $2^x$ and a

1. **State the problem:** You are given the height function of a curved arch support:

1. **State the problem:** Simplify the rational function $$f(x) = \frac{x^3 - x^2 - 12x}{4x^3 - 4x^2 - 8x}$$. 2. **Factor numerator and denominator:**

1. The problem is to classify the given numbers and fractions as integers or non-integers. 2. The numbers given are: 20, 5, \frac{1}{5}, 15%, -10, and 15.

1. **State the problem:** We need to order the temperatures 0°F, 12°F, -15°F, and -8°F from coldest to warmest. 2. **Understand the concept:** On the temperature scale, smaller num

1. **State the problem:** Solve the cubic equation $$ (3x - 4)^3 = 8 $$ 2. **Recall the formula:** To solve an equation of the form $$ (a)^3 = b $$, take the cube root of both side

1. **State the problem:** Solve the equation $ (x+1)(x+3)(x+5)(x+7) = 9 $. 2. **Rewrite the equation:** Notice the terms are symmetric around the middle. Group them as $[(x+1)(x+7)

1. **State the problem:** Multiply the expressions $3x^2$ and $6xy$. 2. **Recall the multiplication rule for algebraic terms:** When multiplying terms with the same base, add their

1. Let's solve the equation $-4 - \frac{2y}{5} = -12$ step-by-step. 2. First, we want to get rid of the $-4$ on the left side to isolate the term with $y$. We do this by adding $4$

1. The problem is to isolate $y$ in the expression $\frac{2y}{5} + 16$. 2. To isolate $y$, we want to get $y$ alone on one side of the equation.

1. **State the problem:** Evaluate the expressions: 1) $\left(\sqrt[3]{64}\right)^2$