🧮 algebra

1. Montrons que l'équation $$x^8 + 8x^3 + x - 3 = 0$$ admet au moins une racine réelle entre 0 et 1. Calculons $$f(0) = 0 + 0 + 0 - 3 = -3$$ et $$f(1) = 1 + 8 + 1 - 3 = 7$$.

1. The problem asks to compute the values of several complex numbers and express each either in standard form or simplified fraction form. (a) Given: $-18i$

1. The problem states that 1400g of flour is used to make a batch of shortbread biscuits. We need to find out how many grams of butter is used for this batch. 2. Typically, shortbr

1. The problem states that the masses of flour, butter, and sugar in shortbread biscuits are in the ratio 4 : 3 : 2 respectively. 2. To find the fraction of the shortbread biscuit

1. State the problem: Simplify or analyze the equation $$x^{2} y^{2} + 3y = 4x$$ or express it in a more useful form. 2. The equation is $$x^{2} y^{2} + 3y = 4x$$.

1. The provided expression is `4%@^5`, which contains symbols `%` and `@` that are not standard mathematical operators. 2. To solve or simplify any expression, we need a valid math

1. We are given the equation to solve: $$3 - 2(x - 9) = 0$$. 2. Begin by distributing the \(-2\) across the parentheses: $$3 - 2\cdot x + 2 \cdot 9 = 3 - 2x + 18$$.

1. Statement of the problem: We will solve a test problem involving fractions, area, and ratios suitable for Year 8 IGCSE level. 2. Problem example: If the ratio of the lengths of

1. The problem is to solve the equation at a grade 10 level. 2. Since no specific equation is provided, I will demonstrate solving a simple quadratic equation: $x^2 - 5x + 6 = 0$.

1. **State the problem:** Solve the equation $7x - 5 = 2x + 3$ for $x$. 2. **Isolate variables and constants:** Subtract $2x$ from both sides to get all $x$ terms on one side:

1. The problem involves analyzing the expression inside a triangle for question 1a with terms 40 and 5x. 2. Assuming the triangle represents an inequality or an expression involvin

1. Let's start with the problem: Simplify $\sqrt{20}$.\n\n2. The square root of a number asks: what number multiplied by itself gives 20?\n\n3. We try to factor 20 into its prime c

1. We are given the polynomial equation $P(D) = D^2 + 2D + 6 = 0$ and asked to find its roots (zeros). 2. The roots can be found using the quadratic formula:

1. Stating the problem: The net amount after a 2% deduction is 339, and we need to find the original gross amount before the deduction. 2. Let the gross amount be $x$.

1. The problem refers to "Ugo C Ugo 25th edition test 8 math" but does not specify a particular question. 2. Please provide the specific math problem from Ugo C Ugo 25th edition te

1. **State the problem:** Find two integers $x$ and $y$ such that $x - y = 4$ and their squares differ by 72, i.e., $x^2 - y^2 = 72$. 2. **Use the difference of squares formula:**

1. The problem is to solve a math question involving numbers from 1 to 50. 2. Since the question is not clearly specified, let's consider the typical problem: finding the sum from

1. **Problem statement:** Kent receives successive discounts of 3% and 7% on a purchase of $850. (a) Calculate the price Kent pays.

1. Let's identify the expressions based on the diagram. 2. The top two purple boxes are $5d + 2f$ and $3d + 4f$.

1. **State the problem:** We need to find expressions for $A$, $B$, and $C$ in the addition of algebraic expressions involving $d$ and $f$. Given the expressions: $$5d + 2f + 3d +

1. Problem statement: Find the missing terms A, B, and C in the expressions involving sums of terms with the variable $p$. 2. Given expressions: