Find the area of a right triangle whose hypotenuse measures 9cm and has a base measuring 3cm.
If your remember the side lengths of some of the common right triangles you can easily ascertain the length of the other leg is going to be 4cm. However, if this is not known, Pythagorean Theorem can be used to find the length of the other leg. Pythagorean's Theorem states that if we add the square of one leg to the square of the other leg, it will equal the square of the hypotenuse. More simply put: a^2 + b^2 = c^2 Where a is a leg, b is a leg, and c is the hypotenuse. If you plug in the length of the leg and hypotenuse given in the question you will get: 3^2 + b^2 = 5^2 Then, you need to simplify and solve for b (the length of the other leg (or height of the triangle) 9 + b^2 = 25 Subtract 16 from both sides to get: b^2 = 16 Then take the square root to get b = 4. Then to find the area of the triange we use the formua Area = 1/2bh That is 1/2(base)(height) Where the the legs of a right triangle represent the base and height of the triangle. Plug in the length of the legs into the area formula to get: A= 1/2(3)(4) A=1/2(12) A= 6cm^2
Solve the following equation if x=2, y= -1 and z= 3 2z/x - 10(3y - (-2) + y
First you need to substitute the number for each variable into the equation. In the follow step, I have plugged the number 2 in for every "x," the number -1 in for every "y," and the number 3 in for every "z." 2(3)/2 - 10(3(-1) + 2) + (-1) Then I used the order of operations, known as PEMDAS, to solve P: Parenthesis E: Exponents M: Multiplication D: Division A: Addition S: Subtraction So first, you need to solve what is inside the parenthesis as follows: 2(3)/2 - 10(-3 + 2) - 1 2(3)/2 - 10(-1) - 1 The next step is to work through the Multiplication and Division. (These two operations are interchangeable in the order of operations) 6/2 - (-10) -1 3 - (-10 ) - 1 3 - (-10) - 1 is the same this as saying 3 -1(-10) - 1. So when we multiply -1 by -10 we get +10 as follows: 3 + 10 - 1 The final step is to add and subtract. These two steps are also interchangeable in the order of operations. T The final answer is: 12
What is the significance of the Battle of Yorktown to the Revolutionary War?
The Battle of Yorktown is known as the battle that ended the Revolutionary War. While the war persisted in other regions and at sea, this battle was the last battle that was fought in the American Colonies. In this decisive battle, General George Washington and French General Comte de Rochambeau led 17,000 forces in a final attach of British General Lord Corwallis' 9000 troops. This battle led to British surrender 3 days laters and peace negotiations from Britain shortly after.