🧮 algebra

1. **Énoncé du problème** : Construire un polynôme d'interpolation $P(x)$ de degré 4 passant par les cinq points expérimentaux $(x_i, y_i)$ donnés par :

1. The problem asks to solve the given equations. However, no specific equations were provided in the prompt. 2. Please provide the equations you want solved so I can assist you st

1. પ્રથમ, ચાલો બેગોની કિંમતને $x$ અને પેનોની કિંમતને $y$ માનીએ. 2. આપેલ છે: 2 બેગો અને 6 પેનોની કુલ કિંમત $588$ છે, એટલે કે

1. Simplify the expressions and solve the equations given: a. Simplify $n^2 + 4n + 15n + 60$.

1. **Problem statement:** Given the system of equations:

1. The problem is to find the determinant of the given 3x3 matrix: $$\begin{vmatrix} 1 & 1 & 0 \\ 7z & 2x & 0 \\ x & y & 2 \end{vmatrix}$$

1. Problem 1: Given sum of first 10 terms $S_{10} = 240$ and the 8th term $a_8 = 34$ of an arithmetic progression (A.P), find: 1.a Common difference $d$

1. **State the problem:** We have the parabola $y = x^2 - 6x + 8$ and a horizontal line $PQ$ where $P$ lies on the $y$-axis and both $P$ and $Q$ lie on the parabola. We need to fin

1. **State the problem:** We need to calculate $\sqrt{90} \div \sqrt{2}$ and express the answer as a surd in its simplest form. 2. **Use the property of square roots:** $\sqrt{a} \

1. The problem asks us to find the value of $d$ in the equality $$\frac{\sqrt{10} \times \sqrt{42}}{\sqrt{2}} = \sqrt{d}$$. 2. Start by simplifying the numerator. Using the propert

1. The problem is to rationalise the denominator of the expression $\frac{1}{\sqrt{11}}$. 2. To remove the square root from the denominator, multiply both the numerator and denomin

1. Problem 28: A total of Rs 35000 is invested at three interest rates: 4%, 5%, and 6%. Interest for the first year was Rs 1780. Second year, the amount invested at 6% earned 7% in

1. **State the problem:** We want to write the fraction $\frac{1}{20\sqrt{20}}$ in the form $\sqrt{\frac{5}{n}}$, where $n$ is a positive integer. 2. **Rationalise the denominator:

1. **State the problem:** Simplify the expression $4\sqrt{75} + \sqrt{45} + 3\sqrt{20}$. 2. **Simplify each square root:**

1. The problem asks us to rewrite the quadratic expression $x^2 + 10x + 19$ in the form $(x + a)^2 + b$. 2. This process is called completing the square.

1. সমস্যাটি হলো একটি আয়তাকার মাঠের দৈর্ঘ্য প্রস্থের 3 গুণ এবং প্রতি বর্গমিটারে 7.5 টাকার হার দিয়ে মোট 1822.50 টাকা খরচ করে ঘাস লাগানো হয়েছে। প্রস্থ $x$ মিটার ধরে ক্ষেত্রফল নির্বাচন

1. The problem states that the parabola has the form $$y = (x + a)^2 + b$$ and the vertex is at the point $(-3, -5)$. 2. Recall that for a parabola in vertex form $$y = (x + a)^2 +

1. সমস্যাটি হল একটি আয়তাকার মাঠের দৈর্ঘ্য প্রস্থের 3 গুণ এবং প্রতি বর্গমিটারে 7.5 টাকা দরে মোট 1822.50 টাকা খরচ হয়েছে ঘাস লাগাতে। আমাদের প্রতিটি পরিমাপ নির্ণয় করতে হবে। 2. ধরে নিই

1. The problem is to find the equation of the line in the form $y=mx+b$ where $m$ is the slope and $b$ is the y-intercept. 2. From the description, the line passes through the poin

1. Stating the problem: We need to find the square root of 576. 2. Recall that the square root of a number $x$ is a number $y$ such that $y^2 = x$.

1. The problem is to estimate the value of $\sqrt{74}$ without a calculator and determine between which two numbers it lies. 2. We know that $8^2 = 64$ and $9^2 = 81$. Since $74$ i