🧮 algebra

1. The problem asks to write the polynomial function $$f(x) = 2x + x^3 + 3x^5 + 4$$ in standard form. Standard form means writing the terms from the highest degree to the lowest de

1. Simplify each expression step-by-step: i. Simplify \(2\sqrt{8} + \sqrt{18} - \frac{6}{\sqrt{2}}\):

1. **State the problem:** Arniel received a 15% discount on a T-shirt priced at 895. We need to find: - How much Arniel paid for the T-shirt.

1. **Arniel's T-shirt discount problem** 1. The original price of the T-shirt is ₱895 and the discount given is 15%.

1. Simplify each expression as requested: (a) Simplify $\sqrt[3]{252 x^{5}}$.

1. Stated problem: Solve the system of linear equations and analyze the graph of the two lines: $$6x - 7y = 40$$

1. Stating the problem: We need to find the markup price and the selling price per box of mango bars given the original price and the markup percentage. 2. Given data:

1. **State the problem:** Thirdy paid 15291.50 after a 15% discount on a cellphone. We need to find the original price and the amount of discount. 2. **Define variables:** Let the

1. The problem asks to express the logarithmic equation \(\log(\frac{1}{8}) = -1\) in its equivalent exponential form. 2. Recall that \(\log_b(a) = c\) is equivalent to \(b^c = a\)

1. Understanding the problem: You provided the numbers 5, 3, 15 and the number 9, and you ask for an explanation "in quantitative" form, which is likely a question about the quanti

1. The problem asks to express the equation $\frac{\log \frac{1}{8}}{\log 8} = -1$ as an equivalent exponent. 2. Recall that $\log a = b$ means $10^b = a$ if the log is base 10 (co

1. (a) The problem states two conditions for an arithmetic progression (AP): the sum of the first 6 terms $S_6 = 72$ and the 8th term $a_8 = 16$. (i) Recall the formula for the $n^

1. **Problem statement:** (i) Find the common difference $a$ given $a_{11}=7$, $a_{22}=54$, and the sum of the first 6 terms of an arithmetic progression (AP) is 72 where the 8th t

1. The user asked to see the shape of a function, without specifying any particular function. 2. I will provide a simple example of a quadratic function $y = x^2$, which is a class

1. Solve the following exponential equations: i. Solve $3^{3-x} = 27^{x-1}$.

1. Simplify the expression $$\frac{4 - \frac{9}{x^2}}{2 - \frac{3}{x}}$$

1. Énoncé du problème : on cherche à calculer la valeur de l'expression $3x + 7$ pour $x$ allant de 1 à 50. 2. Dans un tableur, on commence par écrire le titre "valeur de x" dans l

1. Let's analyze the given sets of points and try to identify if they represent functions. 2. Recall that in a function, each input (x-value) must correspond to exactly one output

1. **Problem Statement:** Given that $\tan \theta = \frac{a^2 + ab + b^2}{ab}$, show that $\tan \theta > 3$. 2. **Rewrite the expression:** Start with the given expression:

1. The problem involves analyzing the function $$f(x) = \frac{a}{x+r} + t$$ with given information about its symmetry axis $$h(x) = -x + 3$$, points $$C=(0,3)$$ on the axis, and po

1. State the problem: Thirdy bought a cellphone for 15291.50 after a 15% discount. We need to find the original price and the discount amount. 2. Let the original price be $P$.