🧮 algebra

1. The problem states the function is $y = x\x^2$ with a "+4" on top of $x$. 2. Interpreting the notation: Assuming the problem means $y = \frac{4+x}{x^2}$, which means "4 plus $x$

1. Let's start by understanding the given function. You mentioned it's $y=4x^2$ but with a $+x$ on top of the $4$. This suggests the function is $y=\frac{x+4}{x^2}$. 2. Rewrite the

1. **State the problem:** We need to find two consecutive even integers such that five times the smaller integer is less than four times the greater integer. 2. **Define variables:

1. **State the problem:** Given the function $y=\frac{4}{x^2+x}$ and the corresponding table of $x$ and $y$ values:

1. **State the problem:** Kevin wants to buy pencils at P4.50 each and has no more than P55.00 to spend. 2. **Define variables:** Let $x$ be the number of pencils Kevin can buy.

1. **State the problem:** Two planes are 3600 miles apart and fly toward each other. Their rates differ by 90 miles per hour. We need to find each plane's speed if they meet in 5 h

1. **State the problem:** We need to find how many kilograms of pili nuts priced at 75 pesos per kg should be mixed with 30 kg of cashew nuts priced at 100 pesos per kg to get a mi

1. Let's define the variables: Let $x$ be the number of hours Kerby spends running.

1. Stating the problem: We need to divide the polynomial $$6x^4 - 4x^3 + 8x^2 - 2x + 1$$ by the binomial $$3x + 1$$. 2. Set up the long division: We are dividing $$6x^4 - 4x^3 + 8x

1. The problem is to convert ?2,900 to US dollars given the exchange rate 1 USD = ?58.00. 2. To find how many US dollars correspond to ?2,900, we divide the amount in the local cur

1. We are given the equation $$\sqrt[4]{8} \cdot 625 \cdot 81 \cdot \Box = \Box \cdot 5 \cdot 2$$ where \Box represents unknown values that are the same on both sides. 2. To solve

1. We start with the expression: $$4y(3x-1)+(3x-1)^2$$ 2. Notice that both terms contain the factor $(3x-1)$.

1. The problem asks whether the expression $(q^2-2)x^2(-9x^6y^7+11)$ can be written as $x^2[(q^2-2)(-9x^6y^7+11)]$. 2. Start by distributing $x^2$ inside the parentheses in the sec

1. Stating the problem: We need to verify if the expression $(q^2-2)x^2(-9x^6y^7+11)$ can be rewritten as $x^2[(q^2-2)x^2(-9x^6y^7+11)]$. 2. Start with the original expression:

1. **State the problem:** Factorise the expression $$-9x^8 y^7 (q^2 - 2) + 11 x^2 (q^2 - 2)$$. 2. **Identify common factors:** Notice that the binomial $$q^2 - 2$$ appears in both

1. **State the problem:** Solve the inequality $$x^3 - 2x^2 + 5x + 20 \geq 2x^2 + 14x - 16$$ and analyze the sign of $$(x - 4)(x - 3)(x + 3) \geq 0$$.

1. The problem gives a 4x4 matrix: $$\begin{pmatrix} 6 & -5 & 1 & -3 \\ 2 & -4 & 8 & 3 \\ 4 & -7 & -6 & 5 \\ -2 & 9 & 7 & -1 \end{pmatrix}$$

1. Solve each inequality and express the solution in interval notation. (a) Solve $$-4[x + 2(3 - x)] \leq 5(2 - 4x) + 6$$

1. The problem is to draw the feasible regions for the systems of linear inequalities given in parts a, b, and c. These regions are bounded by lines and axes. 2. Part (a): 2x + y \

1. **State the problem:** We are asked to graph the solution regions of three systems of linear inequalities. 2. **Part a:** The inequalities are:

1. Let's start by understanding the logarithm (log). The logarithm answers the question: "To what power must we raise a certain base to get a number?" 2. The logarithm with base $b