🧮 algebra

1. The problem asks us to find all values of $k$ such that the graph of the quadratic function $$y = x^2 + 20x + k$$ does not intersect the x-axis. 2. The graph intersects the x-ax

1. The problem asks us to find all values of $k$ such that the graph of the quadratic equation $$y = x^2 + 6x + k$$ intersects the x-axis at two distinct points. 2. To find where t

1. The problem asks us to find all values of $k$ such that the quadratic equation $3x^2 - 18x + k = 0$ has real, unequal roots. 2. Recall that for a quadratic equation $ax^2 + bx +

1. **Problem 1:** Calculate $4^7 - 4^6$ and express $2^7 + 2^6$ as $a^b$ where $a,b$ are natural numbers. - Calculate $4^7 - 4^6$:

1. The problem asks us to find all values of $k$ such that the quadratic equation $kx^2 + 16x - 64 = 0$ has equal roots. 2. Recall that a quadratic equation $ax^2 + bx + c = 0$ has

1. **Problem statement:** A shopkeeper raises the price of a product by 50% on the cost price. We need to find the discount percentage on the marked price so that the shopkeeper st

1. **State the problem:** We need to find a two-digit number such that when we add 18 to the number formed by interchanging its digits, the sum of the digits of the original number

1. **State the problem:** We need to find how much more money is needed for Phase 3 to match the total cost of Phases 1 and 2 combined. 2. **Convert Phase 1 cost from base 4 to dec

1. **State the problem:** We need to find how much more money is needed for Phase 3 to match the total cost of Phases 1 and 2 combined. 2. **Convert Phase 1 cost from base 4 to dec

1. **State the problem:** Find values of $l$ and $m$ such that the polynomial $$x^4 + 4x^3 + 16x^2 + lx + m$$ is a perfect square. 2. **Assume the polynomial is a perfect square of

1. Stating the problem: Solve the equation $ (x-2)(x+3) = 0 $ for $ x $. 2. Use the zero product property: If the product of two factors is zero, then at least one of the factors m

1. **State the problem:** Find the truth set of the equation $$3x + 5x - 2 = 0$$. 2. **Combine like terms:** Add the terms with $x$ together:

Problem: Solve the quadratic equation $2x^2 - 3x - 5 = 0$. 1. Level 1 — Identify coefficients and apply the quadratic formula.

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Identify coefficients:** The quadratic is in the form $ax^2 + bx + c$ where $a=1$, $b=5$, and $c=6$.

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 25$. 2. **Identify coefficients:** Here, $a=1$, $b=5$, and $c=25$.

1. **Classer dans l’ordre croissant les nombres** $\sqrt{2}$, $\sqrt[3]{4}$, $\sqrt[6]{5}$.\n - Calculons les valeurs approchées :\n

1. State the problem: Multiply the numbers $0.05$ and $1.38$. 2. Write the multiplication expression: $$0.05 \times 1.38$$

1. The problem is to multiply the two numbers: $0.05$ and $1.38$. 2. Multiply the numbers directly: $$0.05 \times 1.38 = 0.069$$

1. **State the problem:** We need to evaluate the expression $6.8 \times 1.3 \times 204 + 68$ and check why the answer 2.72 is incorrect. 2. **Calculate the multiplication part:**

1. **Stating the problem:** We want to understand the laws of indices (exponents) and how they relate to repeated multiplication, which can be seen as a form of repeated addition i

1. The problem asks to find the solution set of the inequality $$|x - 2| \leq -4$$ in the real numbers $\mathbb{R}$. 2. Recall that the absolute value $|x - 2|$ represents the dist