🧮 algebra

1. **State the problem:** Solve the equation $-3a + b = 15$ for one variable in terms of the other. 2. **Choose a variable to solve for:** Let's solve for $b$.

1. **State the problem:** Ali and Sasha share money in the ratio 1:4. Sasha's share is 60. 2. **Understand the ratio:** The ratio 1:4 means for every 1 part Ali gets, Sasha gets 4

1. **State the problem:** Simplify the expression $$|0 + 3| - 4^2 - (-8)| + 2\sqrt{5^2} - 3^2 + (-5)^2|$$. 2. **Rewrite the expression clearly:**

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: