🧮 algebra

1. **State the problem:** Diana initially has 12 birds, 8 of which are green. She buys 9 more green birds. We need to find the fraction of green birds out of the total birds now. 2

1. **State the problem:** We need to compare the fractions $\frac{2}{3}$ and $\frac{4}{7}$ to determine which is larger. 2. **Compare the fractions:** To compare fractions, we find

1. **State the problem:** Solve the equation $f(x) = 5$ where $f(x) = |3x - 4|$. 2. **Recall the definition of absolute value:** For any real number $a$, $|a| = b$ means $a = b$ or

1. **State the problem:** Solve the simultaneous equations: $$-x + 3y = 7$$

1. **State the problem:** Solve the quadratic equation $$ax^2 + bx + c = 0$$ for $$x$$. 2. **Rewrite the equation by dividing all terms by $$a$$ (assuming $$a \neq 0$$):

1. **State the problem:** We want to simplify the expression $1 - a$. 2. **Understand the expression:** This is a simple algebraic expression where 1 is a constant and $a$ is a var

1. The problem states that a number $k$ rounded to the nearest integer is 38. 2. When rounding to the nearest integer, the number $k$ must lie within the interval where any value r

1. **State the problem:** We need to find the price per cup of laundry detergent given that a 2-pint container costs 3.08. 2. **Recall the conversion:** 1 pint = 2 cups. Therefore,

1. **State the problem:** Simplify the expression $$6 \div 2(1+2)$$. 2. **Apply the order of operations (PEMDAS/BODMAS):**

1. The problem is to solve the equation given in the 3rd photo (since the photo is not provided, I will assume a typical algebraic problem for demonstration). 2. Suppose the equati

1. **State the problem:** We need to find the population of a town after 5 years, given an initial population of 12,000 and an annual growth rate of 5%. 2. **Formula used:** The po

1. **Problem:** Calculate $$(4.2 \times 10^4) \times (2 \times 10^3)$$ and write the answer in standard form. 2. **Formula:** When multiplying numbers in scientific notation, multi

1. El problema es encontrar un par ordenado $(x,y)$ que satisfaga la ecuación $5x + y = 2$. 2. La fórmula dada es una ecuación lineal en dos variables. Para encontrar una solución,

1. **State the problem:** Find the domain of the rational expression $$\frac{4-x}{3x+21}$$. 2. **Recall the domain rule for rational expressions:** The denominator cannot be zero b

1. **State the problem:** We are given the equation for the area of a rectangular garden as $$x(x - 4) = 140$$ where $x$ is the length in feet, and the width is 4 feet less than th

1. **State the problem:** Simplify the expression $$[-4+9(-4)]:(-3+11)-7\cdot(5-14)$$. 2. **Recall the order of operations:** Parentheses first, then multiplication and division fr

1. **State the problem:** Calculate the value of the expression $-37 + 30 + 13$. 2. **Use the formula:** Addition and subtraction of integers follow the rule of combining positive

1. **Problema:** Resolver la ecuación cuadrática $x^2 - x - 30 = 0$ por factorización. 2. **Fórmula y reglas:** Para factorizar una ecuación cuadrática $ax^2 + bx + c = 0$, buscamo

1. **State the problem:** We want to find how many jumps an athlete who is 5 feet 9 inches tall would need to jump one mile if the athlete jumps at the same ratio as a 2-inch grass

1. The problem is to find the value of $\sqrt{93614.4}$.\n\n2. The square root function $\sqrt{x}$ gives a number which, when multiplied by itself, equals $x$.\n\n3. To find $\sqrt

1. The problem is to graph the function $g(x) = 2 + x$ over the domain $-2 < x < 2$. 2. The function $g(x) = 2 + x$ is a linear function with slope 1 and y-intercept 2.