Maths
Solve 'x' in:
2x+3=9
How much is 3?
Explanation:
To solve for x, you need to isolate x on one side of the equation by performing the same operation on both sides. In this case, you can start by subtracting 3 from both sides:
2x + 3 - 3 = 9 - 3
Simplifying the left-hand side:
2x = 6
Finally, to isolate x, you can divide both sides by 2:
2x/2 = 6/2
x = 3
Therefore, the solution to the equation 2x + 3 = 9 is x = 3.
Name the process by which plants convert light energy into chemical energy
What is photosynthesis?
Explanation:
The process by which plants convert light energy into chemical energy is called photosynthesis. During photosynthesis, plants use pigments called chlorophyll to absorb light energy from the sun. This energy is then used to convert carbon dioxide and water into glucose (a type of sugar) and oxygen. The glucose produced during photosynthesis is used by the plant as an energy source for growth and other metabolic processes. The oxygen produced during photosynthesis is released into the atmosphere as a byproduct.
Name the largest planet in our solar system
What is Jupiter?
What has a head and a tail but no body?
First president of the US
Who was George Washington?
If 3x + 2y = 10 and 2x - y = 4, say the value of x + y
x+y=10/7
Explanation:
To solve this problem, we need to use algebra to eliminate one of the variables, either x or y. One way to do this is to solve for y in terms of x from the second equation and then substitute that expression for y into the first equation.
From the second equation, we have:
2x - y = 4
Adding y to both sides, we get:
2x = y + 4
Subtracting 4 from both sides, we get:
2x - 4 = y
Now we can substitute this expression for y into the first equation and solve for x:
3x + 2(2x - 4) = 10
3x + 4x - 8 = 10
7x = 18
x = 18/7
Now we can substitute this value of x into either equation to solve for y:
2(18/7) - y = 4
36/7 - y = 4
-y = 4 - 36/7
-y = 8/7
y = -8/7
Therefore, x + y = 18/7 - 8/7 = 10/7.
Identify the smallest unit of matter that determines the properties of an element?
Who was the leader of the Soviet Union during World War II?
Joseph Stalin
What starts with an E, ends with an E, but only contains one letter?
The answer to this riddle is "an envelope". The word "envelope" starts and ends with the letter "E", but only contains one letter inside.
Largest moon in our solar system
Which moon is Ganymede?
Find the general rule for the sequence:
3, 5, 9, 17, 33, 65
General rule:
a_n = 2a_{n-1} - 1
where a_1 = 3.
Explanation:
General rule: Each term in the sequence is obtained by doubling the previous term and then subtracting 1. In other words, the nth term of the sequence is given by the formula:
a_n = 2a_{n-1} - 1
where a_1 = 3.
For example, to obtain the fourth term of the sequence, we take the previous term (9) and double it to get 18, and then subtract 1 to get 17. Therefore, the fourth term of the sequence is 17. Similarly, to obtain the fifth term, we take the previous term (17), double it to get 34, and then subtract 1 to get 33. And so on.
What is the molecular structure of a benzene molecule?
The molecular structure of a benzene molecule is a planar hexagonal ring consisting of six carbon atoms and six hydrogen atoms. Each carbon atom is bonded to two other carbon atoms and one hydrogen atom, with alternating double and single bonds. This arrangement of alternating double and single bonds is known as "resonance," which gives benzene its unique stability and reactivity. The chemical formula for benzene is C6H6.
Name the treaty that ended WW1
What is the treaty of versailles?
What can you hold in your left hand but not in your right?
Your right elbow
Find the general rule for: 2, 5, 10, 17, 26, 37, 50
The general rule for the sequence "2, 5, 10, 17, 26, 37, 50" is that each term is the sum of its position and the square of its position minus 1, i.e.,
nth term = n + (n^2 - 1)
For example, the first term is 2 because it is the sum of 1 and (1^2 - 1). The second term is 5 because it is the sum of 2 and (2^2 - 1), and so on.
Solve for x, y, and z:
2x + 3y + 4z = 20
x - y + 2z = 5
3x + 2y - z = 7
x = -2.54 y = 4.824 z = 0.912
Explanation:
To solve for x, y, and z in this system of equations, we can use a method such as substitution or elimination. Here's one possible way to solve it using elimination:
First, we'll eliminate z from the first two equations by multiplying the second equation by 2 and subtracting it from the first equation:
2x + 3y + 4z = 20
2x - 2y + 4z = 10
------------------
y - 2z = 5
Next, we'll eliminate z from the first and third equations by multiplying the third equation by 4 and subtracting it from the first equation:
2x + 3y + 4z = 20
12x + 8y - 4z = 28
------------------
14x + 11y = 48
Now we have two equations with two variables (y and x) that we can solve using substitution or elimination. Let's use substitution to solve for y first. Solving the second equation for y, we get:
y = 5 + x - 2z
Substituting this expression for y into the third equation, we get:
14x + 11(5 + x - 2z) = 48
Expanding and simplifying this equation, we get:
25x - 22z = 3
Now we can use the first equation (y - 2z = 5) to solve for y in terms of z:
y = 2z + 5
Substituting this expression for y into the equation 25x - 22z = 3, we get:
25x - 22(z) = 3
25x - 22(y - 5)/2 = 3 (substitute 2z + 5 for y)
25x - 11y + 110 = 3 (multiply both sides by 2 and distribute)
25x - 11(2z + 5) + 110 = 3 (substitute 2z + 5 for y)
25x - 22z = -72
Now we have two equations with two variables (x and z) that we can solve using substitution or elimination. Solving the first equation (y - 2z = 5) for y, we get:
y = 2z + 5
Substituting this expression for y into the first equation (2x + 3y + 4z = 20), we get:
2x + 3(2z + 5) + 4z = 20
2x + 10z + 15 = 20
2x + 10z = 5
x + 5z = 2.5
Now we can solve for x in terms of z by substituting x = 2.5 - 5z into the equation 25x - 22z = -72:
25(2.5 - 5z) - 22z = -72
62.5 - 147.5z = -72
147.5z = 134.5
z = 0.912
Finally, we can substitute z = 0.912 into the equation x + 5z = 2.5 to solve for x:
x + 5(0.912) = 2.5
x = -2.54
Therefore, the solution to the system of equations is:
x = -2.54
y = 4.824
z = 0.912
Difference between Einstein's special and general theory of relativity.
Einstein's special theory of relativity, published in 1905, deals with the laws of physics in non-accelerating frames of reference and introduces the concept of space and time being intertwined in a four-dimensional continuum known as spacetime. The theory is based on the idea that the speed of light is a constant and is independent of the motion of the observer.
Einstein's general theory of relativity, published in 1915, expands on the special theory by introducing the concept of gravity. According to the general theory, gravity is not a force but rather a curvature of spacetime caused by the presence of mass or energy. The theory explains the behavior of objects in the presence of strong gravitational fields, such as those found around black holes or during the early moments of the universe.
In summary, while the special theory of relativity deals with the laws of physics in inertial frames of reference and the constancy of the speed of light, the general theory of relativity incorporates gravity and describes the curvature of spacetime caused by the presence of mass or energy.