🧮 algebra

1. The problem asks to identify which function corresponds to the given graph. 2. The graph shows symmetry about the y-axis, two peaks at $x=\pm 1$ with value 1, and a minimum at $

1. **State the problem:** Solve the quadratic equation $2x^2 + 3x - 2 = 0$ using the discriminant formula $D = b^2 - 4ac$. 2. **Identify coefficients:** Here, $a = 2$, $b = 3$, and

1. **State the problem:** Simplify the expression $$S = \left(\left(-a^{3}\right)^{-\frac{2}{3}} - \left(\frac{\left(a^{-1}\right)^{3}a}{3} \middle/ \left(2a+1\right)^{\frac{5}{3}}

1. **State the problem:** A human and a turtle compete in a 1 km race. The turtle moves at a constant speed of 0.2 km/h and receives a 980 m head start. The human runs at a speed 1

1. Change the following fractions to 8ths. **a)** Convert $\frac{1}{2}$ to eighths:

1. **State the problem:** Solve the quadratic equation $2x^2 - 3x + 4 = 0$ using the discriminant formula. 2. **Recall the quadratic formula and discriminant:** The quadratic formu

1. **State the problem:** Find the prime factors of 13. 2. **Recall the definition:** A prime number is a number greater than 1 that has no positive divisors other than 1 and itsel

1. **State the problem:** We need to find the ratio of the speeds of a bus and a train given their distances traveled and times taken. 2. **Formula for speed:** Speed is calculated

1. **Stating the problem:** We are given six different graphs with points labeled on their axes and curves. The task is to analyze the first graph, which is a cubic function with p

1. Express $8^{-1}$ using positive indices. 2. Express $c^{-5}$ using positive indices.

1. The problem is to simplify the expression $(Kk)^3$. 2. The rule for exponents states that when raising a product to a power, you raise each factor to that power: $ (ab)^n = a^n

1. **Problem statement:** We are given a geometric progression (G.P.) where the third term is 10 and the sixth term is 80. We need to find the common ratio $r$. 2. **Formula for th

1. Énonçons le problème : Calculer la valeur de $B = \frac{3^{-6} \times 5^5}{(5^2)^3 \times 3^{-5}}$. 2. Rappelons les règles des puissances importantes :

1. **State the problem:** Simplify the expression $4x - 2c + 4x$. 2. **Identify like terms:** Terms with $x$ are like terms and can be combined. The term with $c$ is different and

1. The problem asks for the equation of the line passing through points (0,7) and (7,0) in slope-intercept form $y=mx+b$. 2. The slope-intercept form is $y=mx+b$, where $m$ is the

1. **State the problem:** Reduce the expression $$3x^2y(x^3y - y^2x^2) - 5x^3y^2x^2 - 2xyx^4y + 5xy^2x^4y^2 - 4x^3yxy^2$$ to a standard polynomial. 2. **Expand the terms:**

1. The problem asks to classify the polynomial expressions given. 2. For the first expression $x - 8$:

1. **State the problem:** Solve the equation $$3 (8)^{2t - 1} = 3^{3x}$$ for $t$ and $x$. 2. **Rewrite the bases:** Note that $8 = 2^3$, so rewrite the equation as $$3 (2^3)^{2t -

1. Let's clarify the problem: You want to understand what formula was used in a certain math problem. 2. Typically, formulas depend on the context, such as algebraic equations, geo

1. **State the problem:** Simplify the expression $$3x^2y(x^3y - y^2x^2) - 5x^3y^2x^2 - 2xyx^4y + 5xy^2x^4y^2 - 4x^3uyy^2.$$ 2. **Rewrite and clarify terms:** Note that $x^3y$ mean

1. **State the problem:** We need to find two numbers where the difference between them is 26 and one number is three times the other. 2. **Define variables:** Let the two numbers