🧮 algebra

1. The problem asks for the number of distinct zeros of the polynomial function $$h(t) = (t - 8)^1 (t - 4)^2 (t - 2)^3 (t - 1)^4$$. 2. Recall that the zeros of a polynomial are the

1. **State the problem:** We need to find five consecutive terms of an arithmetic sequence whose sum is 40 and the product of the first, middle, and last terms is 224. 2. **Define

1. Tehtävässä pyydetään piirtämään samaan koordinaatistoon kaksi suoraa: $y=-2x+4$ ja $y=4$. 2. Suora $y=-2x+4$ on lineaarinen funktio, jossa kulmakerroin on $-2$ ja vakiotermi $4$

1. **State the problem:** Myka starts hiking at a temperature of 68°F. The temperature drops by 5.4°F for every 1,000 feet she hikes up. We need to find the temperature after she h

1. **Problem 1: Temperature drop during hike** Myka's temperature drops 5.4°F for every 1,000 feet she hikes up.

1. **State the problem:** Tori bought 7 pumpkins and paid with a 20-dollar bill. She received 5.37 dollars in change. We need to find the cost of each pumpkin. 2. **Set up the equa

1. **State the problem:** Find the first two terms of an arithmetic sequence given that the sixth term is 21 and the sum of the first seventeen terms is 0. 2. **Recall formulas for

1. **Problem statement:** Schreibe die folgenden Ausdrücke mit positiven Exponenten und kürze, wenn möglich. 2. **Wichtige Regeln:**

1. The problem asks which expression is equivalent to $$\frac{36y^2 - 8x - 1}{12x - 2y^2 + 11}$$ for all values of $x$, $y$, and $z$, where defined. 2. To find an equivalent expres

1. **State the problem:** Graph the piecewise function:

1. **Énoncé du problème** : Étudier la fonction rationnelle $$f(x) = \frac{-8}{x+4} + 4$$ et répondre aux questions a) à d). 2. **Identification des paramètres** : La fonction est

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

1. **Problem statement:** Bestimme die Steigung und den y-Achsenabschnitt der linearen Funktion $f$, deren Graph durch die Punkte $P(1|2)$ und $Q(-2|11)$ verläuft.

1. **Stating the problem:** Vi har ekvationen $$3x + 4 = 10$$ och ska beräkna vänstra ledet (VL) när $$x = 2$$. 2. **Formel och regler:** Vänstra ledet är uttrycket $$3x + 4$$. För

1. **Problem statement:** Find the sum of the arithmetic series $3 + 7 + 11 + 15 + \ldots$ to 20 terms. 2. **Formula used:** The sum of an arithmetic series is given by

1. Das Problem lautet: Löse die Gleichung $$2x + 3 = 7$$ nach $$x$$ auf. 2. Die verwendete Formel ist die lineare Gleichung in der Form $$ax + b = c$$, wobei $$a$$, $$b$$ und $$c$$

1. The problem is to find the missing numbers in the sequence: 10 → 7 → [blank] → 1 → [blank] → -5. 2. First, observe the pattern in the given numbers: 10, 7, 1, -5.

1. **State the problem:** We have the sequence 11 → 8 → ? → 2 → ? → -4 and need to find the missing terms. 2. **Identify the pattern:** Look at the differences between known terms.

1. **Stel het probleem vast:** We moeten de uitdrukkingen uit oefening 17 uitrekenen. 2. **Formules en regels:** Bij het vermenigvuldigen van breuken vermenigvuldig je de tellers m

1. Problem: Find three consecutive integers where 5 times the sum of the first two is 7 more than the opposite of the third. Let the integers be $x$, $x+1$, $x+2$.

1. **State the problem:** We are given a projectile's altitude function $h(t)$ with points $(0,5)$, $(12,19.4)$, and $(25.93,0)$, and asked which statement about the projectile's m