🧮 algebra

1. (a) (i) Calculate the exact value of \( \frac{1 \frac{4}{5} - \frac{1}{3}}{2 \frac{2}{5}} \). Step 1: Convert mixed numbers to improper fractions.

1. The problem is to solve the quadratic equation using the method shown in the photo, which is likely the quadratic formula. 2. The quadratic formula is given by:

1. **State the problem:** We need to find the equation of an exponential function of the form $$y = a(2)^x + d$$ given that the graph is a vertical reflection and shift of $$y = 2^

1. (a) (i) Calculate the exact value of $1 \frac{4}{5} - 1 \frac{3}{2} \frac{2}{5}$. Step 1: Convert mixed numbers to improper fractions.

1. **Problem Statement:** We are given a graph that represents a transformation of the exponential function $y=2^x$. The graph shows exponential decay, starting near $y=5$ at $x=-5

1. প্রথম প্রশ্ন: $3x^2 + 7x + 8 = 0$ এর মূলের প্রকৃতি নির্ণয় কর। মূলের প্রকৃতি নির্ণয়ের জন্য আমরা ডিটারমিন্যান্ট ব্যবহার করি, যা হলো $$\Delta = b^2 - 4ac$$

1. **State the problem:** Solve the quadratic equation $$4x^2 + 4x - 15 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^2 + bx + c = 0$$ is $$x = \frac{-b \pm \s

1. **State the problem:** We are given two functions, $f(x)$ and $g(x)$, representing distances traveled by two cars at different times $x$. We need to find specific values and com

1. **Problem Statement:** We need to analyze and compare the costs of two cellphone packages: Economy and Gold, based on the number of minutes used.

1. **State the problem:** We have an arithmetic sequence where the terms increase by the same amount each time. The first term is 3, and the fifth term is 19. We need to find the 6

1. **State the problem:** We have a geometric sequence where the first term $a_1=2$ and the second term $a_2=6$. We need to find the fourth term $a_4$. 2. **Recall the formula for

1. **Problem Statement:** We analyze the population growth of Green Leaf Beetles and Red Bark Beetles over time $t$ (in hours). 2. **Given Functions:**

1. **Problem Statement:** We need to analyze and compare the cost functions for two cellphone packages: Economy and Gold.

1. **State the problem:** Solve the quadratic equations by factoring. 2. **Recall the factoring method:** For a quadratic equation $ax^2 + bx + c = 0$, find two numbers that multip

1. **State the problem:** Resolve the expression $$\frac{7x+2}{(2x-3)(x+1)^2}$$ into partial fractions. 2. **Formula and rules:** For a rational function where the denominator fact

1. **State the problem:** Solve for $d$ in the equation $$2(3d + 7) = 4d + 26$$. 2. **Use the distributive property:** Multiply 2 by each term inside the parentheses:

1. **State the problem:** Solve the equation $21 - 2x = 8x + 5$ for $x$. 2. **Write down the equation:**

1. **State the problem:** We need to find the two possible values of $x$ that satisfy the equation $$4(7 + 5x^2) = 348.$$\n\n2. **Write the formula and simplify:** Start by distrib

1. **State the problem:** Resolve the expression $$\frac{7x+2}{(2x-3)(x+1)^2}$$ into partial fractions. 2. **Formula and rules:** For a rational function where the denominator fact

1. **State the problem:** Resolve the given rational function into partial fractions. Since the user did not provide a specific function, let's consider a general example: $$\frac{

1. **State the problem:** Simplify the expression $\frac{4}{5} - \frac{5}{10} + \frac{3}{10}$.\n\n2. **Find a common denominator:** The denominators are 5 and 10. The least common