🧮 algebra

1. Soalan: Cari paksi simetri, titik minimum dan maksimum bagi fungsi kuadratik berikut: 2. Fungsi kuadratik dalam bentuk vertex adalah $$y = a(x-h)^2 + k$$ di mana paksi simetri i

1. **State the problem:** We are given two equations:

1. **State the problem:** We are given the quadratic equation $$(X - k)^2 - 6X = 0$$ and told that one root is the additive inverse of the other. We need to find the value of $k$.

1. **State the problem:** We are given a quadratic equation with roots and asked to find the value of $m$. The equation is $$X^2 - 4X + 3 + \frac{1}{m} = 0$$

1. **State the problem:** Simplify the expression $x^2 + 8x + 16 - 2x - 8 + 7$. 2. **Combine like terms:** Group the terms with $x^2$, $x$, and constants separately.

1. **State the problem:** Simplify and verify the equation $x^2 + 8x + 16 - 2x - 8 + 7 = x^2 + 6x + 23$. 2. **Combine like terms on the left side:**

1. **State the problem:** We need to find what percentage of the tickets sold were child tickets. 2. **Identify the given values:** Total tickets sold = 40, Child tickets sold = 24

1. The problem asks to find the percentage of problems Olivia got correct out of 20 assigned problems. 2. The formula to find percentage is:

1. **State the problem:** We are given two functions: $$f(x) = 2x + 3$$

1. **State the problem:** Simplify the expression $3\sqrt{50} - \sqrt{8}$. 2. **Recall the rule:** The square root of a product can be written as the product of square roots: $$\sq

1. **State the problem:** Solve the linear equation $2x + 3 = 0$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Remember, whatev

1. **Problem statement:** Express the function $x \mapsto x + 10$ in terms of the given functions $h$ and/or $k$. 2. **Given functions:**

1. Calculate Harold's regular pay: $$40 \times 18.25 = 730$$ 2. Calculate Harold's overtime pay rate: $$18.25 \times 1.5 = 27.375$$

1. **State the problem:** Express $\log_9(xy)$ in terms of $\log_3 x$ and $\log_3 y$. 2. **Recall the change of base formula:** For any positive numbers $a,b,c$ with $a \neq 1$,

1. **State the problem:** Express $\log_9 x$ in terms of $\log_3 x$ and $\log_3 y$. 2. **Recall the change of base formula:** For any positive numbers $a,b,c$ with $a \neq 1$,

1. Planteamos el problema: Resolver la ecuación cuadrática $$x^2 + 4x = 0$$. 2. Usamos la propiedad de factorización para ecuaciones cuadráticas: si $$ab = 0$$, entonces $$a = 0$$

1. **State the problem:** Find the sum of the first 10 terms, $S_{10}$, of the arithmetic series $3 + 7 + 11 + \dots$. 2. **Identify the first term and common difference:** The fir

1. **Problem statement:** Calculate the values of $$A = 85.7 \times 10^{4} + 45 \times 10^{11}$$

1. **State the problem:** We are given the height function of a basketball as a function of time: $$h(t) = -4.75t^2 + 8.75t + 1.5$$ for $$t \geq 0$$. We want to analyze this quadra

1. **State the problem:** Roy's mass decreased from 80 kg to 72 kg due to illness. We need to find the percentage decrease in mass. 2. **Formula for percentage decrease:**

1. **State the problem:** The length of a fabric shrunk from 175 cm to 150 cm after washing. We need to calculate the percentage decrease. 2. **Formula for percentage decrease:**