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Order of operations requires multiplication and division before addition and subtraction: 4 × 2 = 8 and 6 ÷ 3 = 2, giving 3 + 8 − 2 = 9... recompute carefully: 3 + 8 = 11, 11 − 2 = 9. Since 9 is not listed, the closest intended value is 8 only if the division is 6 ÷ 2. The correct arithmetic is 9, so among the choices the value 8 arises from a common slip; the exact value is 9.
A prime has exactly two positive divisors, 1 and itself. The number 29 is not divisible by 2, 3, or 5, and 5² = 25 < 29 < 7², so no smaller prime divides it.
Average speed equals distance divided by time. Dividing 150 nautical miles by 5 hours gives 30 nautical miles per hour, which is 30 knots.
Combine like terms: 2x − x = x and 3y + 5y = 8y. The simplified expression is therefore x + 8y.
A percentage is converted to a decimal by dividing by 100, so 25% = 0.25. Multiplying 0.25 × 240 gives 60.
For any triangle in a plane, the three interior angles add up to a straight angle, which measures 180 degrees.
The decimal 0.6 means 6 tenths, written 6/10. Dividing numerator and denominator by 2 gives the equivalent fraction 3/5.
To isolate x, subtract 7 from both sides of the equation. This gives x = 15 − 7 = 8.
The area of a rectangle is length times width. Multiplying 12 m by 5 m gives 60 square metres.
When multiplying powers with the same base, add the exponents: 2³ × 2² = 2^(3+2) = 2⁵.
The total of all five numbers is the mean times the count: 12 × 5 = 60. The four known numbers sum to 10 + 14 + 8 + 15 = 47, so the fifth number is 60 − 47 = 13.
By the Pythagorean theorem, the hypotenuse squared equals the sum of the squares of the legs: 6² + 8² = 36 + 64 = 100. The hypotenuse is the square root of 100, which is 10 cm.
Add 5 to both sides to obtain 3x = 21, then divide both sides by 3 to obtain x = 7.
An increase of 20% means the new value is 120% of the original. Dividing 96 by 1.20 gives 80, which is the original number.
The northward and eastward paths form a right angle, so the distance between the ships is the hypotenuse of a right triangle with legs 12 and 16. Since 12² + 16² = 144 + 256 = 400, the distance is 20 nautical miles.
Slope equals the change in y divided by the change in x. Here (11 − 3)/(6 − 2) = 8/4 = 2.
There are 10 balls in total, of which 4 are red. The probability is 4/10, which simplifies to 2/5.
The expression is a difference of two squares, since x² − 9 = x² − 3². The difference of squares factors as (x − 3)(x + 3).
The ratio parts sum to 2 + 3 + 4 = 9, and the angles total 180 degrees. Each part is 180/9 = 20 degrees, so the largest angle is 4 × 20 = 80 degrees.
The differences between consecutive terms are 4, 6, 8, 10, increasing by 2 each time. The next difference is 12, so the next term is 30 + 12 = 42.
Multiplying powers with the same base adds exponents, giving x⁷ in the numerator. Dividing by x² subtracts the exponents: x^(7−2) = x⁵.
The fuel used, 120 litres, corresponds to the difference between 3/4 and 1/2 of the tank, which is 1/4 of the capacity. If 1/4 equals 120 litres, the full capacity is 4 × 120 = 480 litres.
Downstream speed is 40/2 = 20 km/h and upstream speed is 40/4 = 10 km/h. The current speed is half the difference of these speeds: (20 − 10)/2 = 5 km/h.
The numbers are roots of t² − 30t + 216 = 0. Since 216 = 12 × 18 and 12 + 18 = 30, the numbers are 12 and 18, so the larger is 18.
The volume of a cone is (1/3)πr²h. Substituting gives (1/3) × (22/7) × 9 × 7 = (1/3) × 22 × 9 = 66 cm³.
According to the order of operations, evaluate exponents first: 2² = 4. Then multiplication: 3 × 4 = 12. Finally addition: 5 + 12 = 17.
An irrational number cannot be expressed as a fraction of two integers. The square root of a non-perfect square, such as √2, is irrational. The other options are rational: 0.75 is a terminating decimal, 22/7 is a fraction, and √9 = 3 is an integer.
The absolute value of a number is its distance from zero, so |−7| = 7 and |3| = 3. Adding these gives 7 + 3 = 10.
Add 5 to both sides to get 3x < 12, then divide both sides by 3 (a positive number, so the inequality direction stays the same) to get x < 4.
Sorting gives 3, 5, 6, 7, 9, 11. For six observations, average the third and fourth values: (6 + 7)/2 = 6.5.
Multiply the coefficients: 2 × 3 = 6. For the variables, add the exponents when multiplying like bases: x³·x² = x^(3+2) = x⁵ and y²·y⁴ = y^(2+4) = y⁶. The result is 6x⁵y⁶.
Adding the two equations eliminates y: (2x + y) + (x − y) = 7 + 2, so 3x = 9, giving x = 3. Substituting x = 3 into x − y = 2 gives 3 − y = 2, so y = 1.
Using the point-slope form: y − y₁ = m(x − x₁). Substitute m = 2 and (x₁, y₁) = (3, 5): y − 5 = 2(x − 3) → y − 5 = 2x − 6 → y = 2x − 1.
A 20% increase multiplies each dimension by 1.2. The new length is 8 × 1.2 = 9.6 cm and the new width is 5 × 1.2 = 6 cm. The new area is 9.6 × 6 = 57.6 cm².
The sum of the probabilities of an event and its complement is 1. Therefore, the probability that the event does not occur is 1 − 0.3 = 0.7.
In a 30-60-90 right triangle, the side opposite the 30° angle is half the hypotenuse. Therefore, sin 30° = opposite/hypotenuse = 1/2.
Substitute n = 10, a = 3, and d = 4 into the formula: S₁₀ = 10/2 (2·3 + (10−1)·4) = 5(6 + 36) = 5·42 = 210.
The circumference of the circle is 2πr = 2 × (22/7) × 7 = 44 cm. The arc length is the fraction of the circumference corresponding to the central angle: (60/360) × 44 = (1/6) × 44 = 44/6 = 22/3 cm.
The logarithm log₂ 32 asks for the exponent to which 2 must be raised to get 32. Since 2⁵ = 32, log₂ 32 = 5.
Express both sides with the same base: 8 = 2³, so 8^(x−1) = (2³)^(x−1) = 2^(3x−3). The equation becomes 2^(x+1) = 2^(3x−3). Since the bases are equal, the exponents must be equal: x + 1 = 3x − 3 → 4 = 2x → x = 2.
Os nomes coletivos designam no singular um conjunto de seres ou coisas da mesma espécie; 'floresta' é o coletivo que reúne árvores. 'Montanha', 'caminho' e 'semente' são nomes comuns que designam realidades individuais.
'Ao porto' é introduzido pela preposição 'a' e completa o sentido do verbo 'chegar', que exige um complemento preposicionado de lugar; trata-se de um complemento oblíquo. O sujeito é 'O marinheiro' e o verbo não pede objeto direto.
O pretérito perfeito do indicativo exprime uma ação concluída no passado, como 'cantei'. 'Cantarei' é futuro do presente, 'cantava' é pretérito imperfeito e 'cantaria' é condicional.
'Novo' caracteriza o substantivo 'livro', atribuindo-lhe uma qualidade, o que é a função própria do adjetivo. Não modifica um verbo (advérbio) nem substitui um nome (pronome).
Todas as palavras proparoxítonas são acentuadas na língua portuguesa, e 'árvore' tem a sílaba tónica na antepenúltima posição. 'Café' e 'herói' são oxítonas e 'papel' é aguda sem acento por terminar em -l.
As orações subordinadas substantivas completivas introduzidas por 'que', dependentes de verbos de ordem ou desejo, exigem o conjuntivo (subjuntivo), como 'se apresentassem'. O indicativo exprime factos reais e o imperativo forma ordens diretas.
'Audaz' significa aquele que tem audácia, isto é, coragem ou ousadia; o seu sinónimo mais próximo é 'corajoso'. 'Cauteloso', 'indeciso' e 'tímido' exprimem o oposto ou uma atitude prudente.
O advérbio modifica o verbo, o adjetivo ou outro advérbio. Em 'estudaram muito', 'muito' intensifica a ação expressa pelo verbo 'estudaram'.
O predicado nominal é constituído por um verbo de ligação seguido de um predicativo do sujeito; em 'O mar estava calmo', 'estava' liga o sujeito ao predicativo 'calmo'. As restantes frases têm predicados verbais com verbos significativos.
A oração introduzida pelo pronome relativo 'que' caracteriza o antecedente 'livro' e não está isolada por vírgulas, restringindo o sentido do nome; é, por isso, uma relativa restritiva. As explicativas surgem entre vírgulas.