🧮 algebra

1. **State the problem:** Determine which pair of equations could not be used to solve the system: $$4x + 2y = 22$$

1. **State the problem:** We need to find two consecutive integers such that twice the smaller integer plus half the larger integer equals 33. 2. **Define variables:** Let the smal

1. The problem is to simplify the expression $$\sqrt{18x^{4}}$$. 2. Recall the property of square roots: $$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$$ and that $$\sqrt{x^{2}} = |x

1. **State the problem:** Simplify the expression $$\left(\dfrac{x^6 y^3}{z^9}\right)^{\frac{1}{3}}$$ where all variables are positive real numbers. 2. **Recall the power of a quot

1. The problem is to simplify the expression $$\frac{2 \pm \sqrt{(-2)^2 + 4(1)(1)}}{2}$$. 2. First, calculate the value inside the square root (the discriminant): $$(-2)^2 + 4(1)(1

1. **Problem Statement:** We are given four linear functions defined on the domain $-4 \leq x \leq 6$:

1. **State the problem:** We need to show algebraically that the curve $C$ with equation $y = x^2 + 3x - 3$ and the line $L$ with equation $y = 5x - 5$ have exactly one point in co

1. **Problem:** Find the x- and y-intercepts of line "A" which has slope 0 and passes through (-5,12). 2. **Understanding the problem:** A line with slope 0 is horizontal. The equa

1. Problema: Rasti geometrinės progresijos 8-tąjį narį $b_8$, kai žinoma, kad $b_{10} \cdot b_6 = 18$ ir visi nariai yra teigiami. 2. Geometrinės progresijos nariai apibrėžiami for

1. Problema: Turime geometrinės progresijos sumos formulę $$S_n = \frac{8}{5} (1 - 6^n)$$ ir norime rasti vardiklį $r$. 2. Geometrinės progresijos suma yra apskaičiuojama pagal for

1. **Problem:** Find the coordinates of the centre and the radius of the circle given by the equation $$9x^2 + 9y^2 + 6x - 24y + 8 = 0$$. 2. **Step 1: Simplify the equation.** Divi

1. **State the problem:** Solve the system of equations: $$\frac{x+1}{3} - \frac{y-1}{2} = 1$$

1. Diberikan soal: Hitung nilai dari $\log_3 9 + \log_3 8 - \log_3 12$. 2. Kita gunakan sifat logaritma: $\log_b m + \log_b n = \log_b (mn)$ dan $\log_b m - \log_b n = \log_b \left

1. **State the problem:** Calculate the value of the expression $344 + 56(153 - 95)$.\n\n2. **Apply the order of operations:** According to the order of operations (PEMDAS/BODMAS),

1. **State the problem:** Ludek has two payment options for 8 days of work. Option 1 pays a fixed $40 per day. Option 2 pays doubling amounts starting at $2 on day 1, $4 on day 2,

1. **State the problem:** Calculate the value of the expression $$(1239+601)(1521-1481)$$. 2. **Apply the order of operations:** First, solve the expressions inside the parentheses

1. **State the problem:** Solve the system of inequalities: $$|3x - 2| < 7$$

1. **State the problem:** Find the expression for the perimeter of a square table whose area is given by $$9x^4 - 24x^2 + 16$$.

1. **State the problem:** A couple is arranging flowers for a wedding. The bride finishes one arrangement in $x$ minutes, and the groom finishes his arrangement 8 minutes later, i.

1. **State the problem:** A bride and groom are arranging flowers. The bride finishes one arrangement in $x$ minutes, and the groom finishes one arrangement 8 minutes later, i.e.,

1. Find the domain and range of $f(x) = 1 + x^2$. - Domain: Since $x^2$ is defined for all real $x$, domain is all real numbers: $(-\infty, \infty)$.