🧮 algebra

1. The problem is to solve the equation $$2x + 3 = 11$$ for $x$. 2. Start by isolating the variable term $2x$ on one side. Subtract 3 from both sides:

1. The problem asks for the axis of symmetry of the curve given by the quadratic equation $$y = 3x^2 - x - 4$$. 2. Recall that the axis of symmetry for a parabola in the form $$y =

1. The problem asks to define the region shown in the sketch. 2. The parabola opens upwards with vertex at approximately $(2,0)$ and intersects the x-axis at $x=-1$ and $x=5$.

1. The problem is to understand algebraic expressions suitable for class 6 IIT foundation level. 2. An algebraic expression is a combination of numbers, variables (like $x$, $y$),

1. The problem states that if $P(x) = Q(x) \cdot (x - a)$, then $a$ is a root (solution) of $P(x)$. We are given $P(x) = 2x^3 - 3x^2 + 5x - 6$ and need to express it in the form $P

1. The question "why we plug in -1" usually arises when solving equations or evaluating functions. 2. Plugging in a value like $-1$ means substituting $x = -1$ into the expression

1. **State the problem:** We are given the polynomial $$x^4 + px^3 - 2x^2 + qx - 3$$ which is exactly divisible by $$(x+1)^2$$. We need to find the values of $p$ and $q$ where $p,q

1. Diberikan fungsi intensitas cahaya lampu taman: $$I(x) = -x^{2} + 10x - 9$$ di mana $x$ adalah jarak horizontal dari tiang lampu dan $I(x)$ adalah intensitas cahaya. 2. Karena k

1. **Menyatakan masalah:** Seorang kontraktor memiliki bahan pagar sepanjang 100 meter untuk memagari taman berbentuk persegi panjang.

1. Soal meminta kita mencocokkan pernyataan dengan jawaban yang benar berdasarkan informasi tentang fungsi kuadrat dengan titik puncak (4, -3) dan memotong sumbu-y di (0, 13). 2. B

1. **Stating the problem:** We are given three points (0, 3), (1, 0), and (3, 0) that define the boundary of a flower planting area. We need to determine which statements about the

1. Soal menyatakan lintasan semprotan air mancur mengikuti fungsi kuadrat $$f(x) = -x^2 + 8x$$. 2. Fungsi kuadrat ini berbentuk parabola yang membuka ke bawah karena koefisien $$x^

1. **State the problem:** We need to graph the region defined by the inequalities: $$y - x < 2$$

1. Soal 1: Diberikan fungsi lintasan air mancur $f(x) = -x^2 + 8x$. Kita diminta untuk menggambar sketsa lintasan dan menentukan ketinggian maksimum. 2. Sketsa lintasan air mancur

1. The problem asks to define the region bounded by the parabola, the vertical lines $x=-1$ and $x=5$, and the $x$-axis. 2. From the description, the parabola opens upwards with ve

1. **State the problem:** We need to define the region bounded by the curve $$y^2 = 4x$$, the line $$y = 4$$, the y-axis $$x=0$$, and the vertical line $$x=4$$. 2. **Analyze the cu

1. **State the problem:** We are given a system of inequalities: $$y - x < 2$$

1. **Problem:** Determine between which two integers the number $\sqrt{3}$ lies. Step 1: Identify perfect squares around 3. The perfect squares near 3 are $1 = 1^2$ and $4 = 2^2$.

1. Problem: Determine if $\sqrt{196}$ is rational or irrational. Step 1: Calculate $\sqrt{196}$. Since $196 = 14^2$, $\sqrt{196} = 14$.

1. Simplify $\sqrt[3]{1}$: Since $1^3 = 1$, $\sqrt[3]{1} = 1$.

1. **State the problem:** We need to analyze and graph the region defined by the system of inequalities: $$y - x < 2$$