🧮 algebra

1. The problem is to evaluate $-100^0$. 2. Recall the rule: any nonzero number raised to the power of 0 is 1.

1. **State the problem:** Rita and Fred share sweets in the ratio 2 : 3. We have two scenarios: - Scenario 1: Altogether they have 90 sweets.

1. The problem states that Archie, Evie, and William share chocolate coins in the ratio 2 : 5 : 3, and altogether they have 90 coins. 2. To find how many coins Evie gets, we use th

1. **State the problem:** Solve the equation $1 - \frac{3x}{2} = \frac{5}{4}$ for $x$. 2. **Isolate the term with $x$:** Subtract 1 from both sides:

1. **State the problem:** We need to find the composite function $f(g(h(x)))$ given the functions: $$f(x) = x^4 + 7, \quad g(x) = x - 9, \quad h(x) = \sqrt{x}$$

1. The problem is to find the sum of the integers from 4 to 9 inclusive, which is written as $$\sum_{i=4}^{9} i$$. 2. The formula for the sum of an arithmetic series is $$S = \frac

1. **State the problem:** Simplify the expression $$A = (5x+3)^2 - (5x-3)(2x+1)$$. 2. **Use formulas:** Recall the formulas for expansion:

1. **State the problem:** Calculate $(-3:2)^2$. Here, the colon ":" is interpreted as division, so the expression is $\left(\frac{-3}{2}\right)^2$. 2. **Formula used:** The square

1. **State the problem:** We have the equation $$6x^2(3x - 16)(3x - u) = 0$$ and the sum of all solutions (roots) is 13. We need to find the value of $u$. 2. **Understand the roots

1. The problem is to evaluate $\log 0.00012$.\n\n2. Recall that logarithms convert multiplication and division into addition and subtraction, and that $\log a^b = b \log a$.\n\n3.

1. Masalani tushuntirish: Ikki xonali sonlar juftligi deganda, farqi 50 ga teng bo'lgan ikkita ikki xonali sonlar nazarda tutilmoqda. 2. Formulani yozamiz: Farq $50$ ga teng bo'lsa

1. **State the problem:** We need to graph the circle given by the equation $$(x + 5)^2 + (y + 2)^2 = 4$$.

1. The problem is to explain what a conic section is and its types. 2. A conic section is the curve obtained by intersecting a plane with a double-napped cone. The shape of the cur

1. Soal nomor 5 meminta kita menghitung nilai dari $$\sum_{i=1}^9 (x_i - 1)$$ dengan nilai-nilai $$x_i$$ yang diberikan hanya sampai $$x_5$$, yaitu $$x_1=1, x_2=2, x_3=3, x_4=5, x_

1. **Stating the problem:** We have a table of Distance (Km) and Time values:

1. **State the problem:** Find the equation of a line perpendicular to the line $y=\frac{3}{2}x - 1$ that passes through the point $(2, -3)$. 2. **Recall the slope of the given lin

1. **Problem:** Factorize the expression $5x^2 - 13x - 6$ completely. 2. **Formula and rules:** To factorize a quadratic expression $ax^2 + bx + c$, find two numbers that multiply

1. **State the problem:** Simplify the expression $2a + 4b - ax - 2bx$. 2. **Group like terms:** Group terms involving $a$ and $b$ separately:

1. **State the problem:** Simplify the expression $\frac{x}{3} + \frac{x-1}{2}$. 2. **Find a common denominator:** The denominators are 3 and 2. The least common denominator (LCD)

1. The problem is to understand and solve transformations as presented in the assignment. 2. Transformations in algebra typically involve shifting, reflecting, stretching, or compr

1. **Problem Statement:** Graph the greatest integer function $f(x) = \lfloor x \rfloor$, which outputs the greatest integer less than or equal to $x$. 2. **Understanding the Funct