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Subtract 8 from both sides to obtain 4x = 24, then divide both sides by the coefficient 4 to obtain x = 6. Every operation performed on one side of an equation must be performed on the other side as well.
The symbol Fe is derived from the Latin name ferrum, and many element symbols come from Latin or Greek roots rather than the English name. Symbols are written with an initial capital letter followed by a lower-case letter when a second letter is present.
The word 'late' tells us when the action of arriving happened, so it modifies the verb 'arrived'. Adverbs are the class of words that modify verbs, adjectives or other adverbs.
Drawing a line through one vertex parallel to the opposite side shows that the three interior angles fit together to form a straight angle, which measures 180°. This sum is the same for every plane triangle regardless of its shape.
Mitochondria carry out aerobic respiration, oxidising pyruvate and releasing energy that is captured as ATP. Cells with high energy demands, such as muscle cells, contain large numbers of mitochondria.
One newton is the force that gives a mass of one kilogram an acceleration of one metre per second squared, so it is equivalent to kg·m/s². This follows directly from Newton's second law, F = ma.
'Child' is an irregular noun that forms its plural with the old English suffix -en, giving 'children'. Because the plural is already marked, no additional -s may be added.
pH is defined as the negative logarithm of the hydrogen ion concentration. At 25 °C pure water has [H⁺] = 1 × 10⁻⁷ mol/dm³, so its pH is 7, and such a solution is described as neutral.
By Pythagoras' theorem the square of the hypotenuse equals the sum of the squares of the other two sides: 6² + 8² = 36 + 64 = 100. Taking the square root gives a hypotenuse of 10 cm.
Newton's second law states that force equals mass multiplied by acceleration, F = ma. Substituting 5 kg and 3 m/s² gives 5 × 3 = 15 N.
The number of moles is found by dividing the mass of the sample by its molar mass: n = m/M = 44/44 = 1 mol. Molar mass is numerically equal to the relative molecular mass expressed in grams per mole.
Human body cells are diploid, containing 23 pairs of homologous chromosomes, which gives a total of 46. Gametes are haploid and contain only 23 chromosomes, one from each pair.
In the passive voice the object becomes the subject, the verb becomes a form of 'be' plus the past participle, and the original subject is placed after 'by'. The original verb is in the past simple, so the passive requires 'were marked'.
The median is the middle value once the data are arranged in order. With five values, the third value is the median, which here is 9.
The refractive index of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium: n = c/v. Substituting the values gives 3.0 × 10⁸ ÷ 2.0 × 10⁸ = 1.5.
Ohm's law states that current equals voltage divided by resistance, I = V/R. Substituting 12 V and 4 Ω gives 12 ÷ 4 = 3 A.
Hydrogen is assigned +1 and oxygen −2 in this compound, and the sum of oxidation numbers in a neutral molecule must be zero. Solving 2(+1) + x + 4(−2) = 0 gives x = +6 for sulphur.
'Since' is used with a specific point in time to mark the beginning of an action that continues up to the present. 'For' would be used with a length of time, such as 'for five years'.
In a 30°–60°–90° triangle the side opposite the 30° angle is half the hypotenuse, so sin 30° = 1/2. The same value follows from the standard trigonometric ratio table.
The pulmonary artery leaves the right ventricle and carries deoxygenated blood to the lungs, making it the one artery that carries deoxygenated blood. After gas exchange the pulmonary veins return oxygenated blood to the left atrium.
Factorising gives (x − 2)(x − 3) = 0, so x = 2 or x = 3. Equivalently, the roots must have a sum of 5 and a product of 6, which only 2 and 3 satisfy.
Power is the rate of doing work, P = W/t. Dividing 600 J by 4 s gives 150 W, where one watt equals one joule per second.
Hydrochloric acid is fully ionised, so [H⁺] equals the acid concentration, 1 × 10⁻² mol/dm³. Then pH = −log(1 × 10⁻²) = 2.
The cross Aa × Aa gives the genotypic ratio 1 AA : 2 Aa : 1 aa, so one quarter of the offspring are homozygous recessive. Only the aa genotype expresses the recessive phenotype when dominance is complete.
The group contains a subject and a finite verb, so it is a clause, but the subordinating conjunction 'although' makes it dependent. It functions like an adverb by expressing concession about the main clause, so it is an adverbial clause.
A preposition is a word placed before a noun or pronoun to show the relation of that noun to another word in the sentence. Here 'on' links 'the mat' to the verb 'sat', expressing place.
Express each number in prime factors: 12 = 2² × 3 and 18 = 2 × 3². The LCM takes the highest power of every prime, giving 2² × 3² = 36.
The kidney is made up of about a million microscopic filtering units called nephrons, each consisting of a glomerulus, Bowman's capsule and a tubule. Filtration of blood and formation of urine occur within these units.
Sound is a mechanical wave, so it travels faster in media whose particles are closely packed and strongly bonded. Solids such as steel have the highest elasticity and density combination, giving sound the greatest speed there.
Table salt is sodium chloride, formed by the ionic combination of one sodium ion (Na⁺) with one chloride ion (Cl⁻), giving the formula NaCl.
An antonym expresses the opposite meaning of a word. 'Generous' means willing to give freely, so its opposite is 'miserly', meaning reluctant to give or spend.
HTML is the acronym for HyperText Markup Language, the markup system used to structure content such as headings, paragraphs and links on the World Wide Web.
Mars appears reddish because its surface is rich in iron oxide (rust) dust. This distinctive colour is why it is commonly called the Red Planet.
To evaluate a function at a given input, substitute that value for x in the rule. Replacing x with 4 gives 2(4) + 3 = 8 + 3 = 11.
Even at constant speed the direction of motion changes continuously, so the velocity changes and an acceleration exists. This centripetal acceleration always points towards the centre of the circular path.
Zinc is above hydrogen in the reactivity series, so it displaces hydrogen from the acid: Zn + 2HCl → ZnCl₂ + H₂. The gas produced burns with a 'pop' sound, which is the standard test for hydrogen.
The cerebellum lies at the back of the brain beneath the cerebrum and coordinates muscular activity, posture and balance. Damage to it causes unsteady movement and loss of coordination.
When the reporting verb is in the past ('said'), the present tense of the reported clause shifts one step back, so 'am' becomes 'was'. The first-person pronoun also changes to match the speaker, giving 'he was tired'.
The area of a circle is given by A = πr². Substituting r = 7 cm and π = 22/7 gives A = (22/7) × 49 = 22 × 7 = 154 cm².
For any wave, speed equals frequency multiplied by wavelength (v = fλ). Thus v = 50 Hz × 2 m = 100 m/s.
Sodium hydroxide is a strong base, so [OH⁻] = 1 × 10⁻³ mol/dm³ and pOH = 3. Since pH + pOH = 14 at 25 °C, the pH is 14 − 3 = 11.
Vitamin A is needed to form rhodopsin, the light-sensitive pigment in the rod cells of the retina. Its deficiency impairs vision in dim light and leads to night blindness.
An adverb modifies a verb, an adjective or another adverb, often answering the question 'how?'. Here 'softly' tells how she spoke, so it modifies the verb 'spoke'.
The interior angles of an n-sided polygon add up to (n − 2) × 180°. For a hexagon n = 6, so the sum is 4 × 180° = 720°.
Each binary digit represents a power of 2, reading from right to left: 0×2⁰ + 1×2¹ + 0×2² + 1×2³ = 2 + 8 = 10.
With uniform acceleration the average velocity is (u + v)/2 = (20 + 5)/2 = 12.5 m/s. Distance = average velocity × time = 12.5 × 5 = 62.5 m.
By Le Chatelier's principle the system opposes an increase in pressure by shifting towards the side with fewer gas molecules. The left side has 4 moles of gas and the right side has 2, so the equilibrium shifts to the right.
When the two gene pairs assort independently and each shows complete dominance, each 3:1 monohybrid ratio multiplies independently. The combined outcome is 9:3:3:1 for the four phenotypic classes.
Since 8 = 2³, the power rule of logarithms gives log₁₀ 8 = 3 log₁₀ 2. Therefore log₁₀ 8 = 3 × 0.3010 = 0.9030.
Personification gives human qualities to non-human things. Whispering is a human action attributed here to the wind, which is therefore personified.