How do you solve for x in the equation 3x + 4 = 19?To solve for x, first subtract 4 from both sides of the equation: 3x + 4 – 4 = 19 – 4, which simplifies to 3x = 15. Next, divide both sides by 3: 3x/3 = 15/3, resulting in x = 5.
Homework
PopAi provides you with resources such as science, math, humanities, etc.
How do you derive the sine and cosine t-values given an angle on the unit circle, and how are these values used to solve right triangle problems?
How do you derive the sine and cosine t-values given an angle on the unit circle, and how are these values used to solve right triangle problems?To derive sine and cosine t-values given an angle θ on the unit circle, identify the coordinates (x, y) where the terminal side of the angle intersects the circle. Here, x = cos(θ) and y = sin(θ). These values can solve right triangle problems by using the definitions of sine and cosine: sin(θ) = opposite/hypotenuse and cos(θ) = adjacent/hypotenuse.
What is the greatest common factor (GCF) of 28 and 42?
What is the greatest common factor (GCF) of 28 and 42?The greatest common factor (GCF) of 28 and 42 is 14. This is determined by finding the largest integer that divides both numbers without leaving a remainder. In this case, 14 is the highest number that can evenly divide both 28 and 42.
How did the implementation and impact of the Marshall Plan contribute to the early stages of the Cold War and European recovery post-World War II?
How did the implementation and impact of the Marshall Plan contribute to the early stages of the Cold War and European recovery post-World War II?The Marshall Plan, initiated in 1948, provided over $12 billion in economic aid to Western European countries, facilitating rapid recovery and political stability. It countered Soviet influence, deepening Cold War divisions by promoting capitalist economies and democratic governments, thus strengthening Western alliances against the Eastern Bloc.
How does Herman Melville’s ‘Moby-Dick’ reflect the themes of existentialism and hubris against the backdrop of American Romanticism?
How does Herman Melville’s ‘Moby-Dick’ reflect the themes of existentialism and hubris against the backdrop of American Romanticism?Herman Melville’s ‘Moby-Dick’ reflects existentialism through its exploration of human insignificance in an indifferent universe, epitomized by the vast, uncaring ocean. The theme of hubris is embodied in Captain Ahab’s obsessive quest for the white whale, representing mankind’s overreaching ambition. These themes align with American Romanticism’s focus on individual experience, nature’s power, and the sublime.
What were the main causes of the Industrial Revolution in Europe, and how did it affect the lives of people during the 19th century?
What were the main causes of the Industrial Revolution in Europe, and how did it affect the lives of people during the 19th century?The Industrial Revolution in Europe was driven by technological innovations, availability of natural resources, economic changes, and political stability. It led to urbanization, improved transportation, and increased production. However, it also resulted in harsh working conditions, child labor, and environmental degradation, profoundly altering people’s lives.
Who painted the famous artwork ‘Starry Night’?
Who painted the famous artwork ‘Starry Night’?The famous artwork ‘Starry Night’ was painted by Vincent van Gogh. Completed in 1889, it depicts a dreamy interpretation of the artist’s asylum room’s sweeping view of Saint-Rémy-de-Provence at night, although it was painted from memory during the day.
What were the main causes and consequences of the Industrial Revolution?
What were the main causes and consequences of the Industrial Revolution?The Industrial Revolution was driven by innovations in technology, agricultural improvements, and access to natural resources. It led to urbanization, economic growth, and improved living standards but also resulted in labor exploitation, environmental degradation, and social upheavals.
How do I solve a proportion where one of the terms is unknown, like in the equation 3/4 = x/8?
How do I solve a proportion where one of the terms is unknown, like in the equation 3/4 = x/8?To solve the proportion 3/4 = x/8, cross-multiply to get 3 * 8 = 4 * x. This simplifies to 24 = 4x. Divide both sides by 4 to isolate x, resulting in x = 6. Therefore, x equals 6.
How do you interpret the p-value in a hypothesis test?
How do you interpret the p-value in a hypothesis test?The p-value in a hypothesis test quantifies the probability of obtaining results at least as extreme as those observed, assuming the null hypothesis is true. A low p-value indicates strong evidence against the null hypothesis, suggesting it may be false. Common thresholds are 0.05 or 0.01.
Start Using PopAi Today
More AI Tools
Suggested Content
More >
Prove that sin(π/6) using the unit circle
Answer 1 To prove that $ \sin(\frac{\pi}{6}) $ using the unit circle, we start by locating the angle $ \frac{\pi}{6} $ on the unit circle.The angle $ \frac{\pi}{6} $ corresponds to 30 degrees.Using the unit circle, we see that the coordinates for...
Determine the values of cos(θ) and sin(θ) using the unit circle when 0 ≤ θ ≤ 2π and θ is a solution to the equation tan(θ) = √3
Answer 1 The equation $\tan(\theta) = \sqrt{3}$ implies that: $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} = \sqrt{3}$ This happens at $\theta = \frac{\pi}{3}$ and $\theta = \frac{4\pi}{3}$ within the interval txt1 txt1 txt1 ≤ \theta ≤ 2\pi$. At...
Find the value of angle θ where cos(θ) = -1/2 on the unit circle
Answer 1 The cosine function represents the x-coordinate on the unit circle. Thus, finding $ \cos(\theta) = -\frac{1}{2} $ involves finding the angles where the x-coordinate is -1/2. On the unit circle, this occurs at:$ \theta = \frac{2\pi}{3} +...
Find the angle in radians and degrees for the point (-1/2, -√3/2) on the unit circle
Answer 1 We need to find the angle corresponding to the point $ \left(-\frac{1}{2}, -\frac{\sqrt{3}}{2}\right) $ on the unit circle. This point lies in the third quadrant where both sine and cosine are negative. The reference angle is given by: $...
Find the value of arcsin(1/2) in radians using the unit circle
Answer 1 To find the value of $ \arcsin(\frac{1}{2}) $, consider the unit circle and the definition of arcsin. The arcsin function outputs the angle whose sine is the given value within the range $ -\frac{\pi}{2} $ to $ \frac{\pi}{2} $. For $...
Find the value of cosine at $\theta = \frac{3\pi}{4}$
Answer 1 The unit circle helps us locate the angle $\theta = \frac{3\pi}{4}$ which lies in the second quadrant. The reference angle for $\theta = \frac{3\pi}{4}$ is: $\pi - \frac{3\pi}{4} = \frac{\pi}{4}$ In the second quadrant, the cosine of an...