🧮 algebra

1. **State the problem:** Compute the sum $$\sum_{k=2}^5 (2k+1)$$. 2. **Formula and explanation:** The summation $$\sum_{k=a}^b f(k)$$ means adding the values of the function $$f(k

1. **State the problem:** We are given a piecewise function $$h(x)$$ defined as: $$h(x) = \begin{cases} -1 & \text{if } x < 0 \\ -2 & \text{if } x = 0 \\ 2 & \text{if } x > 0 \end{

1. **Problem statement:** Given the function $f(x) = 2 - x^2$, evaluate (a) $f(x+1)$ and (b) $f(x) + f(1)$. 2. **Recall the function:** $f(x) = 2 - x^2$.

1. **State the problem:** Find the slope $m$ of the line passing through the points $(-5,3)$ and $(x+1, x-2)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1

1. **Problem Statement:** Given the function $g(t) = t + 5t - 1$, evaluate (a) $g(5)$ and (b) $g(2s - 5)$. 2. **Simplify the function:** Combine like terms in $g(t)$. Since $t + 5t

1. **Masalah:** Diberikan bilangan bulat $a=2$, $b=3$, dan $c=4$ (berbeda dari contoh Anda). Gambarlah fungsi $$y = ax^2 + bx + c = 2x^2 + 3x + 4$$ dan jelaskan cara memperolehnya.

1. **Menentukan nilai a, b, dan c** Misalkan kita pilih a=2, b=-3, dan c=1 sebagai contoh berbeda.

1. **Problem:** Determine which statements about inequalities are true. - A. $3 < -3$

1. **State the problem:** Find the sum of the mixed numbers $-3 \frac{1}{3}$ and $1 \frac{1}{3}$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Find the sum of $-3 \frac{3}{4} + (-\frac{3}{4})$. 2. **Convert mixed number to improper fraction:**

1. Énonçons le problème : Calculer le déterminant de la matrice $$A = \begin{pmatrix} 2 & 4 & 1 & -1 \\ 0 & -1 & -1 & 1 \\ -4 & -8 & -2 & -1 \\ -7 & 0 & -1 & 2 \end{pmatrix}$$

1. **Problem Statement:** Order the following expressions from least to greatest: $$e^2, 2!, \infty, \log_4(7), \frac{5}{6}, \sqrt{5}, \sum_{i=1}^6 i, \frac{2\pi}{6}, \int_3^8 x\,

1. The problem is to order a set of numbers or expressions from least to greatest. 2. To order numbers from least to greatest, compare their values and arrange them starting with t

1. **State the problem:** We need to select all the squares containing perfect squares and order them from least to greatest. 2. **Recall what a perfect square is:** A perfect squa

1. **State the problem:** Find the slope of the line passing through the points $(-9,7)$ and $(-6,-3)$.\n\n2. **Formula for slope:** The slope $m$ between two points $(x_1,y_1)$ an

1. **State the problem:** Simplify the expression $$f_3(x) - g_3(x) = (0.90x - 372) - (0.95x - 447)$$. 2. **Recall the rule for subtraction of expressions:** When subtracting, dist

1. **State the problem:** Solve the equation $15 + 7y = -25 + 2y$ for $y$. 2. **Write down the equation:**

1. **State the problem:** Calculate the value of $x$ given by the expression $x = \frac{39}{0.02}$.\n\n2. **Formula and rules:** Division of a number by a decimal can be simplified

1. **State the problem:** Solve the quadratic equation $-3x = x^2 + 5x - 7$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero:

1. **State the problem:** Simplify the expression $f_2(x) - g_2(x) = (0.68x - 108) - (0.70x - 147)$. 2. **Recall the rule:** When subtracting expressions, distribute the minus sign

1. **State the problem:** Simplify the expression $$f_2(x) - g_2(x) = (0.68x - 108) - (0.70x - 147)$$. 2. **Apply the subtraction:** Distribute the minus sign to the second parenth