🧮 algebra

1. The problem is to express the decimal number 1.375 as a fraction. 2. Recall that a decimal can be converted to a fraction by writing it over a power of 10. Since 1.375 has three

1. The problem is to solve or manipulate an algebraic expression without simplifying it. 2. When asked not to simplify, we keep the expression in its original or expanded form with

1. The problem is to understand why simplification in math is important. 2. Simplification means making an expression easier to work with by reducing it to its simplest form.

1. The problem is to simplify the expression $\frac{\sqrt{12} \cdot \sqrt{2}}{\sqrt{24}}$ and compare it to the given options. 2. Recall the property of square roots: $\sqrt{a} \cd

1. **Stating the problem:** We are given the equation $$\frac{1}{a} + \frac{1}{b} = \frac{1}{13}$$ and need to find the value of $$a + b$$. 2. **Rewrite the equation:** Combine the

1. Ipagpalagay natin na ang problema ay tungkol sa pag-solve ng isang algebraic equation o expression. 2. Una, tukuyin ang problema nang malinaw. Halimbawa, "Solve for x: $$2x + 3

1. The problem is to find the value of the function $hgf(x)$ at $x=3$. 2. The function is given as:

1. The problem asks which ratios from the list are equivalent. 2. Two ratios $a:b$ and $c:d$ are equivalent if their cross products are equal, i.e., $a \times d = b \times c$.

1. **State the problem:** Aubrey needs to type a 5-page article in 18 minutes. She types at a constant rate of 0.25 pages per minute. We need to determine if she can finish typing

1. **State the problem:** Aubrey needs to type a five-page article and has 18 minutes before the deadline. She types at a constant rate of 0.25 pages per minute. We need to determi

1. The problem is to solve the equation $ye^{-3x} - 3x = y^2$ for $y$ in terms of $x$. 2. This is a nonlinear equation involving both $y$ and $x$. We want to isolate $y$ if possibl

1. The problem is to solve the equation $$ye^{-3x} - 3x = y^2$$ for $y$ in terms of $x$. 2. This is a nonlinear equation involving both $y$ and $x$. We want to isolate $y$ if possi

1. **State the problem:** Solve the quadratic equation $10147x^2 - 624.5x - 1 = 0$ for $x$. 2. **Formula used:** The quadratic formula is used to solve equations of the form $ax^2

1. **State the problem:** Solve the quadratic equation $10147x^2 - 624.5x - 1 = 0$ for $x$. 2. **Formula used:** The quadratic formula is given by

1. **State the problem:** Solve the equation $$\frac{3x + 1}{5} + \frac{x - 2}{2} = \frac{47}{10}$$. 2. **Find a common denominator:** The denominators are 5, 2, and 10. The least

1. **State the problem:** Simplify the expression $10147x^2 - 624.5x - 1$ or analyze it as a quadratic expression. 2. **Recall the quadratic form:** A quadratic expression is gener

1. The problem asks us to fully factorise the expression $20 + x - x^2$. 2. First, rewrite the expression in standard quadratic form: $$20 + x - x^2 = -x^2 + x + 20$$

1. The problem is to fully factorise the quadratic expression $20 + x - x^2$. 2. First, rewrite the expression in standard quadratic form:

1. **State the problem:** We need to factor the function $$f(x) = -27x^5 - 18x^4 - 3x^3$$ to find all its x-intercepts. 2. **Recall the rule for x-intercepts:** The x-intercepts oc

1. **State the problem:** We are given the quadratic expression $$2x^2 - 6x - 20$$ and asked to fill in the gaps in the expression $$2x^2 - 6x - 20 = [ ] (x^2 - [ ] x - [ ])$$.

1. **State the problem:** We need to find all x-intercepts of the function $$f(x) = -4x^4 + 2x^3 + 12x^2$$. The x-intercepts occur where $$f(x) = 0$$. 2. **Set the function equal t