Solve for x in the linear equation: 5(2x - 3) - 4(x + 2) = 7.
Matematicas
Question · Easy
Factor it
Short
What is the solution to the system of linear equations: 3x + 2y = 16 x - y = 2?
Factor the quadratic expression: x² - 5x - 24.
What are the roots of the quadratic equation: 3x² - 10x + 3 = 0?
Question · Medium
Simplify the expression: (2a³b²)⁴ / (4a⁶b⁵).
The houseplant does both
Simplify the rational algebraic expression for all values where it is defined: (x² - 9) / (x² - 2x - 15).
Solve the linear inequality for real x: 3x - 5 <= 5x + 7.
What is the equation of the line passing through the points P(2, -1) and Q(4, 5) in slope-intercept form?
What is the distance between the points A(-3, 2) and B(5, -4) in the Cartesian plane?
Which of the following lines is perpendicular to the line with equation 3x - 4y + 8 = 0?
What is the center and radius of the circle defined by the equation x² + y² - 6x + 8y + 9 = 0?
Question · Hard
What are the coordinates of the vertex of the parabola defined by y = -3x² + 12x - 5?
In a right triangle, the side opposite to angle theta has length 6 cm and the hypotenuse has length 10 cm. What is the value of cos(theta)?
If sin(x) = 5/13 and x is an acute angle, what is the value of tan(x)?
What is the domain of the real-valued function f(x) = sqrt(2x - 8) / (x - 6)?
Given f(x) = 2x² - 3 and g(x) = x + 4, what is the composition (f o g)(x)?
Evaluate the limit: lim (x -> 3) [ (x² - 2x - 3) / (x² - 9) ].
What is the derivative of f(x) = 4x³ - 5x² + 7x - 9 with respect to x?
Evaluate the definite integral: ∫ from 1 to 3 of (3x² - 4x) dx.
In an arithmetic progression, the 1st term is a₁ = 3 and the common difference is d = 4. What is the sum of the first 15 terms (S₁₅)?
A car accelerates uniformly along a straight road from an initial velocity of 10 m/s to 30 m/s over a distance of 100 meters. What is the acceleration of the car?
Fisica
An object is dropped from rest from the top of a building and hits the ground after 4.0 seconds. Assuming g = 9.8 m/s² and negligible air resistance, what is the height of the building?
According to Newton's Third Law of Motion, when a swimmer pushes against the water with her hands backwards, what force moves her forward?
According to Newton's Law of Universal Gravitation, if the distance between two masses is doubled while both masses remain constant, the gravitational force between them is:
A worker pulls a sled across horizontal ground by applying a constant force of 50 N at an angle of 60 degrees above the horizontal. How much work is done by this force over a displacement of 8.0 meters? (cos 60° = 0.5)
A roller coaster car of mass 500 kg starts from rest at the top of a hill of height h = 20 m. Neglecting friction and taking g = 10 m/s², what is the speed of the car at the bottom of the hill?
What is the hydrostatic pressure exerted by water at a depth of 5.0 meters in a freshwater reservoir? (Density of water = 1,000 kg/m³, g = 9.8 m/s²)
How much heat is required to raise the temperature of 500 g of liquid water from 20 °C to 80 °C? (Specific heat of water c = 1 cal/(g·°C))
Two resistors of 6 ohms and 12 ohms are connected in parallel across a 24 V DC power source. What is the total current supplied by the source?
A sound wave travels through air at 340 m/s and has a wavelength of 0.85 m. What is its frequency?
An atom of an isotope of carbon has a mass number (A) of 14 and an atomic number (Z) of 6. How many neutrons does this atom contain?
Quimica
What is the ground-state electron configuration of a neutral potassium atom (atomic number Z = 19)?
Which of the following elements has the greatest electronegativity according to periodic trends?
Balance the chemical equation for the combustion of propane: C₃H₈ + a O₂ -> b CO₂ + c H₂O. What are the stoichiometric coefficients a, b, and c?
What is the molar mass of nitric acid, HNO₃? (Atomic masses: H = 1.0 g/mol, N = 14.0 g/mol, O = 16.0 g/mol)
According to the reaction 2H₂ + O₂ -> 2H₂O, how many grams of water (H₂O, molar mass = 18 g/mol) are produced from the complete reaction of 4.0 grams of hydrogen gas (H₂, molar mass = 2.0 g/mol) with excess oxygen?
What is the molarity (M) of a solution prepared by dissolving 40.0 g of sodium hydroxide (NaOH, molar mass = 40.0 g/mol) in enough water to make 500 mL of solution?
What is the pH of an aqueous hydrochloric acid (HCl) solution with a hydronium ion concentration [H₃O⁺] = 1.0 x 10⁻³ M?
Which functional group characterizes carboxylic acids in organic chemistry?
Which of the following cellular features is found in eukaryotic cells but is entirely absent in prokaryotic cells?
Biologia
When red blood cells (erythrocytes) are placed in a hypotonic solution (such as distilled water), what physical process occurs?
What is the primary function of the light-independent reactions (Calvin cycle) of photosynthesis?
If a template DNA strand has the sequence 3'-TAC GGA CTT-5', what is the complementary messenger RNA (mRNA) sequence transcribed from it?
During which phase of meiosis does crossing over (genetic recombination between homologous chromosomes) occur?
In tomato plants, red fruit (R) is dominant over yellow fruit (r). If two heterozygous plants (Rr x Rr) are crossed, what fraction of the offspring is expected to be homozygous for this gene?
Which statement best describes the mechanism of natural selection proposed by Charles Darwin?
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