Solve the linear equation for x: 5(2x - 3) - 3(x + 2) = 14.
Matematica Amex
Question · Easy
Flip it: the negative swing
Short
What are the roots of the quadratic equation x² - 7x + 12 = 0?
In an artillery observation post, the angle of elevation to an enemy observation tower 1,000 meters away across flat terrain is 30°. What is the height of the tower above the observation post? (tan(30°) = 1/√3 ≈ 0.577)
What is the common difference d of the arithmetic progression whose first term is a₁ = 7 and 10th term is a₁₀ = 52?
Evaluate the value of x in log₂(3x + 1) = 4.
Cruise the loop: a log is an exponent
Two reconnaissance squads depart from base camp. Squad 1 marches vector u = (6, 8) km and Squad 2 marches vector v = (-6, -8) km. What is the vector connecting Squad 1 to Squad 2 (v - u)?
What is the remainder when the polynomial P(x) = 2x³ - 5x² + 3x - 7 is divided by (x - 2)?
Question · Medium
An infantry company commander needs to select a 3-soldier scout team from a squad of 10 available soldiers. In how many different ways can this team be selected?
What is the midpoint of the tactical defense sector between checkpoint A(-3, 8) and checkpoint B(7, 2)?
If sin(θ) = 3/5 and θ is an acute angle, what is the value of tan(θ)?
Solve the system of linear equations: x + 2y = 8 and 3x - y = 3. What is the value of the product x · y?
What is the slope of a military road passing through points A(1, 3) and B(5, 11)?
What is the sum of all interior angles of a regular hexagon representing a fortified perimeter?
A supply warehouse in Huambo receives ammunition crates whose count doubles every day: 5, 10, 20, 40, ... How many crates are received on the 7th day?
What is the inverse function f⁻¹(x) of the linear function f(x) = 3x - 6?
What is the magnitude of the 3D displacement vector d = (2, -3, 6) km?
Solve the inequality: 3x - 4 ≥ 5x + 8.
If log₁₀(x) = 3 and log₁₀(y) = 2, what is the value of log₁₀(x² / y)?
In a triangle, angle A = 45°, angle B = 60°, and side a opposite to angle A is 10 meters. Using the Law of Sines, what is the length of side b opposite to angle B?
Question · Hard
What is the area of a circle with a diameter of 14 meters? (Use π ≈ 22/7)
Simplify the algebraic expression: (2x²y³)² / (4x³y⁴).
What is the 8th term of the arithmetic sequence: -4, -1, 2, 5, 8, ...?
What is the value of cos(120°)?
Two vectors A = (3, k) and B = (4, -6) are orthogonal (perpendicular). What is the value of k?
A tactical fuel convoy travels 180 km at an average speed of 60 km/h and returns along the same route at 90 km/h. What is the average speed for the entire round trip?
What is the value of the discriminant Δ for the quadratic equation 3x² - 5x + 2 = 0?
What is the distance between the parallel lines 3x + 4y - 5 = 0 and 3x + 4y + 15 = 0?
Find the sum of the first 20 terms of the series 2 + 4 + 6 + 8 + ... + 40.
If 2^(2x - 1) = 1/8, what is the value of x?
What is the volume of a right circular cone representing a sand obstacle barrier with base radius r = 3 meters and vertical height h = 4 meters? (Use V = (1/3)πr²h)
In the sentence 'O oficial superior comunicou a decisão aos capitães', what is the syntactic function of 'aos capitães'?
Lingua Portuguesa Amex
Which of the following sentences exhibits correct verbal agreement (concordância verbal)?
Which of the following words is classified as a proparoxytone (palavra proparoxítona)?
In the sentence 'Quando o toque de corneta soou, a guarda formou no pátio', what type of subordinate clause is introduced by 'Quando'?
What is the antonym of the military term 'Hostil' (hostile)?
Which of the following sentences correctly applies standard Portuguese nominal regimen (regência nominal)?
In the phrase 'Os generais e os coronéis chegaram cansados após a manobra', what is the syntactic function of 'cansados'?
Which of the following words contains a diphthong (ditongo decrescente)?
In the sentence 'A pátria confia em ti', what is the morphological classification of 'em ti'?
Which of the following compound nouns forms its plural by altering only the second element?
What is the voice of the verb in: 'O plano de operações foi aprovado pelo Comandante do Exército'?
Which of the following sentences contains an error in the use of the crasis accent (acento grave / crase)?
What is the classification of the coordinate conjunction in: 'O pelotão avançou com cautela, porém não encontrou resistência'?
In the text 'A bravura dos militares garantiu a integridade territorial', what is the core nucleus of the subject?
Which of the following verbal forms is in the Pretérito Mais-Que-Perfeito Simples do Indicativo?
Which of the following sentences correctly demonstrates pronominal placement (mesóclise)?
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