🧮 algebra

1. The problem is to solve the equation $$(\lg x)^2 - 5 \lg x + 6 = 0.$$\n2. Let us use a substitution to simplify the problem. Set $$y = \lg x.$$ Then the equation becomes $$y^2 -

1. Stating the problem: Solve the equation $x^2 - x^1 = 31$ for $x$. 2. Rewrite the equation: $x^2 - x = 31$.

1. To derive or understand a formula, first clearly state what you want to find or solve for. 2. Identify the known variables and constants relevant to the situation.

1. Stated problem: Solve for $c$ in the equation $$\frac{1 - e^{-470c}}{1 - e^{-1000c}} = 0.5.$$\n\n2. Multiply both sides by the denominator to clear the fraction:\n$$1 - e^{-470c

1. **Problem 1: Find the percentage discount given the original price and the discount price.** The original price is K30 and the discount price is K24.

1. Find the common ratio of the geometric sequence: 3, 6, 12, 24, 48, ... - The common ratio $r$ is found by dividing any term by its previous term.

1. **State the problem:** We are given the equation $$x^2 - 3y = 31$$ and asked to analyze it. 2. **Rewrite the equation to express y in terms of x:**

1. The equation $y = mx + c$ is the equation of a straight line in slope-intercept form. 2. Here, $m$ represents the slope of the line, which indicates how steep the line is.

1. **Problem 32:** Find the equation of the linear relationship between sales $x$ and selling expense $y$ when sales increase from 100 to 400 and expense from 75 to 150. 2. **Calcu

1. **Problem:** Given $f(x) = x^2 + 3x - 7$, find $f(-2)$, $f(0)$, $f(4)$, $f(3x)$, and $f(2y)$. Step 1: Calculate $f(-2)$. Substitute $-2$ into $f(x)$:

1. **State the problem:** Factor the quadratic expression $$12q^2 + 17q + 6$$. 2. **Multiply the coefficient of** $$q^2$$ *and* the constant: $$12 \times 6 = 72$$.

1. Solve $|-x| = 3,4$. Since $|-x| = |x|$, the equation $|x| = 3$ has solutions $x = 3$ and $x = -3$.

1. Stating the problem: Solve the equation $y = 2x + y$. Step 1: Subtract $y$ from both sides to isolate terms.

1. Diberikan fungsi linear $y = 2x + 4$. Kita diminta menentukan fungsi bayangan setelah dilakukan translasi. 2. Translasi a: Geser 3 satuan ke atas dan 3 satuan ke kiri.

1. The problem states that $$\frac{a}{b} = \frac{b}{c} = \frac{c}{d} = k$$ where $$k = 0$$. 2. Since $$k = 0$$, we have:

1. **Problem statement:** Given that in Diagram 3, - Line AB is parallel to line CD.

1. Problem statement: Sketch the graph of the quadratic function $f(x) = x^2 - 6x + 8$ and find the axis of symmetry. 2. To graph $f(x) = x^2 - 6x + 8$, first find its vertex by co

1. The problem is to simplify the expression $2x-4$. 2. The expression $2x-4$ is already simplified, but it can be factored by taking out the common factor of 2.

1. Stating the problem:\nWe are given the equation $$A = P(1 - in)$$ with values $$P = 10000$$, $$i = 0.2$$ (note the decimal point corrected from comma), and $$n = 5$$.\n\n2. Subs

1. The problem is to eliminate the parameter $0$ from the parametric equations: $$x = 3 \cos 0 - 5 \sin 0$$

1. The problem involves multiple expressions, from powers of 2 times various numbers to identification and number patterns. 2. Starting with evaluating powers of 2 and multiplicati