🧮 algebra

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

1. The problem is to simplify and factor the quadratic expression given: $2x^2-24x+72$. 2. First, note the expression is a quadratic trinomial.

1. **State the problem:** Find the equivalent expression with rational exponents for $\left(\sqrt{2xy}\right)^3$. 2. **Rewrite the square root as a rational exponent:** The square

1. We are given the expression $3x^2 - 4x + 1$. 2. To analyze or simplify this quadratic expression, we can factor it if possible.

1. Stated problem: Simplify the quadratic expression $2x^2 + 15x + 28$. 2. Factor the quadratic expression by finding two numbers that multiply to $2 \times 28 = 56$ and add to $15

1. The problem demonstrates how a function maps elements from a domain to a range. 2. From Figure 1.2, the function $f$ takes an input $x$ from the domain and produces an output $f

1. Problem: Given $a = b + c$ with $b = 7.13$ (correct to 2 decimal places) and $c = 8900$ (correct to 2 significant figures), find the upper bound of $a$. 2. Find upper bounds:

1. Problem: An object thrown vertically upward has height given by $$h = -16t^2 + 96t$$. Find when the height is 144 feet.

1. The problem is to understand the expression $x = 10t + 4f$. 2. Here, $x$ is expressed in terms of two variables, $t$ and $f$, where the coefficient of $t$ is 10 and the coeffici

1. Stating the problem: Solve for the variables in the equation $$2x(5t+2f)=10$$. 2. Expand the left-hand side: Multiply 2x with each term inside the parentheses.

1. The interval notation provided is $[-3, \infty)$. 2. This means all numbers starting from $-3$ including $-3$ itself, and extending to positive infinity.

1. Solve the equation $$\frac{1}{x} = \frac{2}{3x - 1}$$ First, cross multiply to get rid of the fractions: