What is the value of x in the given equation: 3x + 2 = 9 -4x
First, we will need to make x be on one side of the equation and isolate it to be the only thing on that side of the equation. To do this, we can first add 4x to both sides of the equation, because whatever is done to one side of the equation must be done to the other. 3x + 2 = 9 - 4x +4x =4x 7x + 2 = 9 Next, we need to subtract 2 from both sides to make the x be by itself. 7x + 2 = 9 -2 -2 7x = 7 Finally, to completely isolate and solve for x, we must divide by 7 on both sides. 7x = 7 7x/7 = 7/7 x = 1 x = 1 is the final answer
Without using the periodic table, determine the group, period, and block of an atom with the following electron configuration: [Ne]3s^2
The group of this atom can be determined by noticing s^2. The fact that this atom falls in the s block of the periodic table ( which is only the first two groups) and it has 2 electrons in that orbital as represented by the squared number, tells us that it is the group of alkaline earth metals. If it had been s^1, we would know it was the first group of alkali metals. The period of the atom is represented by the number following the noble gas in the noble gas configuration given. In this case that is period 3. The block of the atom is the last letter given in the electron configuration. In this case, the s block.
A car’s seat has been shot through the car’s window. The bullet hole is located four feet above the ground. The nearest building is 50 feet (or 600 inches) away along the horizon. The distance from the bullet hole in the seat to the window of the car where the bullet entered is 22.5 inches, and the distance from the bullet hole in the seat to the window along the horizon is 22.1 inches. Calculate the height the shooter was at when he fired the gun.
For this problem, you can draw a triangle to represent the path of the bullet (as the hypotenuse or side “c”), the height of the shooter as side “b”, and the horizon as side “a”. In order to solve for the height of the shooter (side b), we need to know the full lengths of sides “a” and “c”. We know the length of side “a” given in the problem: 600 inches. We also know that part of that length comes from the distance from seat to window along the horizon: 22.1 inches, and that the distance from seat to window along the path of the bullet (side b) is 22.5 inches. With these partial lengths, we can set up a proportion to solve for the remaining length of the path of the bullet, side b. This is done as follows: 22.5/22.1 = x/600 When you divide 22.5 by 22.1, and multiply that answer by 600, you get that x is 610.9 inches. x = 610.9 inches Now, you can calculate the length of c by adding the length of the distance from the bullet hole to the window to the length you just calculated, x. C = 610.9 + 22.5 C = 633.4 Next, you can solve for the height of the shooter, b, by using the Pythagorean theorem. a2 + b2 = c2 6002 + b2 = 633.42 b = 203 inches BUT DON’T FORGET! The bullet hole was 4 feet above the ground, which means you need to account for this by adding 4 feet to your value for b. Therefore, the height of the shooter is 203 + 4 = 207 inches or 17.25 feet.