🧮 algebra

1. **State the problem:** Kavitha saved money over three months to buy a laptop. She saved \(\frac{1}{3}\) of the laptop's cost in the first month, \(125\) less than that amount in

1. The problem is to simplify the expression $-2x^{-\frac{1}{2}}$. 2. Recall that a negative exponent means the reciprocal: $x^{-\frac{1}{2}} = \frac{1}{x^{\frac{1}{2}}}$.

1. **State the problem:** We are given the linear equation $$0 = 5y + 4x - 8$$ and need to analyze it. 2. **Rewrite the equation to solve for y:**

1. The problem asks to find the resulting function after applying a series of transformations to the graph of $y=f(x)$.\n\n2. Step 1: Translate the graph 4 units to the left.\nThis

1. Muammo: $f(x) = x^2 + 3$, $g(x) = x - 4$, va $h(x) = x - 5$ berilgan. $f(g(h(x))) = h(g(f(x)))$ tenglik o‘rinli bo‘ladigan $x$ ni toping. 2. Chap tomon: $f(g(h(x)))$ ni hisoblay

1. Muammo: Funksiyaning qiymatlar toʻplamini aniqlash, yaʼni $y=\sqrt{x+5}-4$ funksiyasi uchun $y$ ning mumkin boʻlgan barcha qiymatlarini topish. 2. Dastlab, ildiz ichidagi ifodan

1. The first function is $y = 5x + 4$. This is a linear function with slope 5. 2. A function is decreasing if its slope is negative. Here, the slope is 5, which is positive.

1. **State the problem:** Expand and simplify the expression $$(2 - x)^5$$. 2. **Use the binomial theorem:** The binomial theorem states that $$(a - b)^n = \sum_{k=0}^n \binom{n}{k

1. Muammo: Funksiyaning qiymatlar to'plamini aniqlash: $$y = \sqrt{x + 5} - 4$$. 2. Dastlab, ildiz ichidagi ifodaning manfiy bo'lmasligi kerak, ya'ni:

1. **Problem statement:** A tea dealer mixes two brands of tea, X and Y, to obtain 42 kg of a mixture worth 68 per kg. Brand X costs 74 per kg and brand Y costs 59 per kg. 2. **(a)

1. The problem is to simplify the expression $\frac{2}{x^{1/2}}$. 2. Recall that $x^{1/2}$ is the same as $\sqrt{x}$.

1. **State the problem:** Simplify the expression $\frac{5x^{2}}{x^{\frac{1}{2}}}$. 2. **Apply the law of exponents:** When dividing powers with the same base, subtract the exponen

1. **Problem statement:** Find the domain and range of the given relations. 2. **Part (a): Relation with points (-3, 2.8) and (1.3, -2.1) and a wavy curve passing through (-5,0), (

1. The problem asks for the capacity of one bottle. 2. To find the capacity of one bottle, we need the total capacity and the number of bottles.

1. Simplify each of the following expressions: (a) Simplify $\frac{4x^4}{12x^5}$:

1. **State the problem:** Solve the quadratic equation $$x^2 + x - 2 = 0$$. 2. **Identify coefficients:** Here, $$a = 1$$, $$b = 1$$, and $$c = -2$$.

1. **State the problem:** Simplify the expression $$\frac{3}{2} + \frac{4}{5} - \frac{2}{3} \times \frac{3}{4} + \frac{5}{6} \div \frac{5}{2} - \frac{1}{2} + \frac{3}{6} \times \fr

1. **Problem (a):** Find the rates for a quarter for a house with an assessed annual value of 65000 and an annual rates percentage of 8%. Step 1: Calculate the annual rates.

1. **State the problem:** Factorise the polynomial expression $$3x^4 - 48$$ fully. 2. **Factor out the greatest common factor (GCF):**

1. The problem asks to find how many games City FC lost using the data from the table. 2. From the table, the total games lost by all teams combined is 35.

1. **Problem statement:** We have a group of people who participated to get a vehicle licence.