🧮 algebra

1. The degree of the expression $2x - 4xy^2 + 5x^2y^3$ is the highest sum of exponents in any term. - Term $2x$ has degree $1$.

1. The problem is to find the equation of a parabola given its vertex and x-intercepts. 2. The parabola opens downward with vertex at (0, 6) and x-intercepts at -2 and 1.

1. The degree of the expression $2x - 4xy^2 + 5x^2y^3$ is the highest sum of exponents in any term. - For $2x$, degree is $1$.

1. **Problem:** Find the degree of the expression $2x - 4xy^2 + 5x^2y^3$. The degree of a term is the sum of the exponents of the variables in that term.

1. The degree of the expression $2x - 4xy^2 + 5x^2y^3$ is the highest sum of exponents in any term. - Term $2x$ has degree $1$.

1. The problem involves finding the roots $x_2$, $x_3$, and $x_4$ of a polynomial or equation where you already have $x_2 = 1.348$. 2. To find $x_3$ and $x_4$, you typically use me

1. The problem asks to find the $x$-coordinate where the curve $y=x^3 - x$ crosses the horizontal line $y=1$. 2. Set the curve equal to 1: $$x^3 - x = 1$$

1. **Task 1: Representing and solving the toy cost problem** (i) Let the costs of the three toys be $x$, $y$, and $z$.

1. **State the problem:** We are given that 25% of a number is 80, and we need to find the number. 2. **Translate the problem into an equation:** 25% means 25 per 100, or \frac{25}

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