🧮 algebra

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.

1. **State the problem:** We are given a geometric progression (GP) where the sum to infinity is 16, and the sum of the first four terms is 15. We need to find the first four terms

1. The problem involves solving the equation $1 - \frac{1}{2} = 2a$ for $a$. 2. First, simplify the left side:

1. El problema ens diu que cada dècim val 20 i volem comprar un dècim per a cada nombre que acaba en 395. 2. Primer, hem d'entendre quants nombres acaben en 395 dins d'un interval

1. **State the problem:** Mdm Grace's shop sells plates and cups. The price ratio of a plate to a cup is 3:2, and the price difference is 3. In the first month, 4/7 of the items we

1. **State the problem:** Simplify the expression $$\frac{8y}{2 - 3y} - \frac{4}{-3y^2 + 2y} + \frac{3y + 2}{y}$$. 2. **Rewrite the expression and factor denominators:** Note that

1. **State the problem:** Solve for $y$ in the equation $$\ln(y - 3) = 2t + t^2.$$\n\n2. **Recall the formula and rules:** The natural logarithm function $\ln(x)$ is the inverse of

1. **Stating the problem:** Given points A(-2,1), B(2,3), and C(-1,-2), find: a) The equation of the line BC.

1. **State the problem:** Solve the quadratic equation $2x^2 + x - e^2 = 0$ for $x$. 2. **Recall the quadratic formula:** For an equation $ax^2 + bx + c = 0$, the solutions are giv