🧮 algebra

1. **State the problem:** We need to find the size of a beetle in a photo that is enlarged to 785% of its actual size. The actual size of the beetle is 14 millimeters.

1. The problem is to convert the decimal number $0.036$ into a fraction and a percent. 2. To convert a decimal to a fraction, write the decimal as $\frac{\text{decimal number witho

1. The problem asks to write the decimal 0.036 as a percent. 2. Recall the formula to convert a decimal to a percent:

1. **State the problem:** Convert 338% to a fraction and a decimal. 2. **Recall the formula:** Percent means per hundred, so

1. The problem asks to label each point on a vertical number line using rational numbers. 2. The number line has marks at 2 and 3, which are integers and also rational numbers sinc

1. The problem asks to use rational numbers to label points on a number line. 2. Rational numbers are numbers that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ ar

1. **State the problem:** Simplify the expression $e^2 + e^1$. 2. **Recall the exponential notation:** $e^n$ means $e$ raised to the power of $n$.

1. **Problem a:** Write $\sqrt{3} \times \sqrt{6}$ in the form $b\sqrt{2}$ where $b$ is an integer. 2. Use the property of square roots: $\sqrt{a} \times \sqrt{b} = \sqrt{a \times

1. **State the problem:** Simplify the square roots $\sqrt{12}$, $\sqrt{27}$, and $\sqrt{50}$.\n\n2. **Formula and rules:** To simplify a square root, find the largest perfect squa

1. El problema pide traducir enunciados a lenguaje algebraico. 2. a) "El triple de la suma de dos números" se traduce como $3(x+y)$ donde $x$ y $y$ son los dos números.

1. **State the problem:** Find the range of the function $$h(x) = \frac{640}{x^2} + 0.5$$ for $$4 \leq x \leq 14$$.

1. The problem is to simplify or understand the expression $a^2 + b^2$. 2. This expression represents the sum of the squares of two variables $a$ and $b$.

1. **State the problem:** Roger had 250 more cakes than Fiona. Nicole had $\frac{2}{5}$ as many cakes as Roger. Together, they had 482 cakes. We need to find how many cakes Fiona h

1. The problem is to evaluate the expression $78:78:1x9:9x52:52x183:1-79$. 2. First, interpret the colons ":" as division and "x" as multiplication. So the expression becomes:

1. We start with the problem: Calculate the value of $-7^2$. 2. Important rule: Exponentiation has higher precedence than negation, so $-7^2$ means $-(7^2)$, not $(-7)^2$.

1. **State the problem:** Evaluate the function $f(x) = 3|x - 5| + \frac{3}{\sqrt{x}}$ at $x=5$ and $x=0$. 2. **Recall the function and domain:** The function involves an absolute

1. **State the problem:** We know that $y$ is inversely proportional to the square of $x$, which means $y \propto \frac{1}{x^2}$. Given $y=4$ when $x=10$, we want to find: a) $y$ w

1. **Stel het probleem vast:** We hebben de hoogte van een steen die verticaal omhoog wordt geschoten vanaf een toren, gegeven door de formule $$h(t) = -5t^2 + 20t + 65$$ waarbij $

1. **State the problem:** Calculate the value of $10^{2.37}$. 2. **Formula used:** The expression is an exponential function where the base is 10 and the exponent is 2.37.

1. **State the problem:** Solve for $x$ in the equation $\log_{10}(x) = 0.508754358631946$. 2. **Recall the definition of logarithm:** $\log_a(b) = c$ means $a^c = b$. Here, $a=10$

1. **Problem 1: Profit from assembling bicycles** Given: $$P = -x^2 + 50x - 300$$ where $P$ is profit and $x$ is number of bicycles.