🧮 algebra

1. Problem 41: We analyze the depreciation of values over time given the drop every 6 years. - For each item, the value drop rate per year is calculated by dividing the drop amount

1. **State the problem:** We are given the number pattern 698, 683, 670, 659, 650 and need to find the next two numbers. 2. **Identify the pattern:** Look at the differences betwee

1. **Problem Statement:** Verify the correctness of matrix operations and determinant calculations given in the problem. 2. **Matrix B calculation:** Given matrices

1. Problem 41: Find the rate of change for the resale value of a refrigerator given the data points from (0, 600) to (15, 0). Step 1: Identify two points on the line: $(0,600)$ and

1. Problem 38: Compare the rate of change of profits of companies A and B. - The rate of change of profit is the slope of the profit vs. year graph.

1. The problem is to solve the quadratic equation $$2x^2 + 5x - 18 = 0$$ by completing the square. 2. First, divide the entire equation by 2 to make the coefficient of $x^2$ equal

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

1. **State the problem:** We have a sequence of tile patterns where the number of tiles increases by the same amount each time. We want to find an expression for the number of tile

1. **State the problem:** We have a sequence of patterns made from tiles. Each pattern adds the same number of tiles as the previous one. We want to find an expression for the numb

1. The problem is to solve the equation $$2x + 3 = 7$$ for $x$. 2. Start by isolating the variable term on one side. Subtract 3 from both sides:

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

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