🧮 algebra

1. Stating the problem: Solve the equation $x + 2x = 45$ for $x$. 2. Combine like terms on the left side: $x + 2x = 3x$.

1. **Problem Statement:** Calculate an estimate of the mean time taken by 100 students to solve a puzzle given the grouped frequency distribution:

1. **Problem statement:** Calculate an estimate of the mean time taken by 100 students to solve a puzzle given the grouped frequency distribution:

1. The problem is to plot the graph of the function $$y = 4x^4 + 6$$ and analyze the given points $(-1,10)$, $(1,6)$, $(1,10)$, $(2,70)$, and $(3,330)$. 2. The function is a polyno

1. The problem states that money is shared between Ali, Kat, and Lena in the ratio 5 : 3 : 4, and Lena's share is 76. 2. Let the common ratio factor be $k$. Then Ali's share is $5k

1. The problem asks to write the numbers $7.²$ and $21.2⁴$ in the form $\frac{a}{b}$ where $b \neq 0$. 2. First, interpret the notation: $7.²$ means $7.2$ (7 point 2) and $21.2⁴$ m

1. **Problem:** Find the equation of the line with slope 3 and y-intercept 9 in slope-intercept form. 2. **Formula:** The slope-intercept form of a line is given by $$y = mx + b$$

1. **State the problem:** Multiply and simplify the expression $$(6 + \sqrt{2})(7 + 8\sqrt{2})$$. 2. **Recall the distributive property (FOIL method):** To multiply two binomials,

1. **State the problem:** Multiply and simplify the expression $$(5 - 9\sqrt{3})(4 - 8\sqrt{3})$$. 2. **Formula used:** Use the distributive property (FOIL method) to multiply two

1. **Problem Statement:** Given the function $y = 4x^4 + 6$ with domain $x = \{-1,0,1,2,3\}$, we need to find the range values. 2. **Formula and Explanation:** The function is a po

1. The problem is to simplify the expression $x^{\frac{1}{3}} - 4x$. 2. Recall that $x^{\frac{1}{3}}$ means the cube root of $x$, and $4x$ means $4$ times $x$.

1. נניח שהפונקציה היא $f(x)$, אך לא סופק ביטוי מדויק לפונקציה. 2. כדי למצוא מתי הפונקציה מתקיימת, יש צורך בביטוי המתמטי של הפונקציה או תנאי מסוים (למשל, מתי הפונקציה שווה לאפס, מתי

1. **Stating the problem:** Solve the system of linear equations:

1. **State the problem:** Factorise the expression $2y + 8yz$. 2. **Identify common factors:** Look for the greatest common factor (GCF) in both terms. Here, both terms have a fact

1. **Problem:** Solve and analyze the quadratic equation $x^2 - 25 = 0$. 2. **Formula:** Quadratic equation standard form is $ax^2 + bx + c = 0$.

1. **Problem:** Solve and analyze the quadratic equation $x^2 - 25 = 0$. 2. **Formula:** Quadratic equation standard form is $ax^2 + bx + c = 0$.

1. The problem is to find the axis of symmetry of a quadratic function. 2. The general form of a quadratic function is $y = ax^2 + bx + c$.

1. **State the problem:** Solve the quadratic equation $$x^2 - 25 = 0$$ and sketch its graph. 2. **Formula and rules:** The standard form of a quadratic equation is $$ax^2 + bx + c

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then di

1. The problem is to find the reciprocal (1 divided by each value) of each number in the given list. 2. The formula to find the reciprocal of a number $x$ is:

1. The problem is to find an algebraic expression that represents the pattern 4, 8, 16, 32, 64, ... 2. This is a geometric sequence where each term is obtained by multiplying the p