Pythagorean Theorem
What is the Pythagorean Theorem?
The Pythagorean Theorem is a fundamental principle in geometry that states in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
What is the Power of a power rule in exponents?
The power of a power rule is that if a power is being raised to another power, multiply the exponents and leave the base the same. -The power of rule for exponents: (am)n=am*n
How do you measure volume?
To measure the volume, you multiply length times width times height, for example 3x1x2, which it equals six. So the volume of the fish tank is 6 cubic feet.
What is scientific notation?
Scientific notation is a way to write numbers that are too large or too small to be written in decimal form. It's also known as scientific form, or as well standard form.
Simplify the expression (3(2x+4)-5x)?
Distribute the 3: (6x+12-5x). Combine like terms:/(x+12).
How do you calculate the length of the hypotenuse using the Pythagorean theorem?
To find the length of the hypotenuse (c) in a right triangle with sides of length a and b, you use the formula: c= a2 + b2 = c2
How do you simplify a product of powers with the same base?
How are area and volume similar and different?
Area and Volume of an object both are dependent on the dimension of a particular Shape or figure. While Area is the amount of space the object, figure occupies in a two dimensional space, Volume is the capacity of a Shape or figure in three dimensional space.
What are the parts of scientific notation?
Scientific notation has three parts: the coefficient, the base, and the exponent. The coefficient is a number between 1 and 10, the base is always 10, and the exponent can be any integer, including zero.
Which number is the closest approximation to π/4?
0.785 is approximately closet to 3.14/4.
Can the Pythagorean Theorem be used in non-right angled triangles?
No, the Pythagorean Theorem is specifically applicable to right-angled triangles.
What is the Quotient of Powers Rule?
The quotient of powers rule is when dividing two numbers with the same base (a), then we subtract their exponents to simplify the expression. This rule applies only if both bases are equal and positive.
How can you find the volume of cubes and rectangular prisms?
Firstly, the volume of a prism is the area of the base times the height, V = B h.
Secondly, the volume of a rectangular prism is the length times width times height, V = l w h .
Thirdly, the volume of a cube is the length of one side cubed, V = s 3 .
How do you write a number in scientific notation?
To write a number in scientific notation, multiply a number between 1 and 10 by a power of 10. For example, 650,000,000 written in scientific notation is 6.5 x 10^8.
Solve for y in the equation (2y-7=13)?
Add 7 to both sides: (2y=20). Divide by 2: (y=10).
How can the Pythagorean Theorem be applied in real-life situation?
The Pythagorean theorem is the two-dimensional navigation to find the shortest distance. Used to survey the steepness of the slopes of mountains or hills. To calculate the length of staircase required to reach a window.
How do you simplify a power of a product?
To find a power of a product, find the power of each factor and then multiply. In general, ( a b ) m = a m ⋅ b m . a m ⋅ b m = ( a b ) m .
How do you convert volume between units of measure?
You can convert volume between units of measures using the appropriate conversion factor or formula based on the specific context and unit types involved.
How do you convert scientific notation to standard form?
To convert a number from scientific notation to standard form, move the decimal point left if the exponent of 10 is negative, or right if it's positive.
Convert 0.2 ?
0.2 when converted into a fraction is 1/5.
How do you look for the hypotenuse?
To look for the hypotenuse you can use the Pythagorean theorem to find the hypotenuse of an isosceles right triangle if you know the length of each leg.
What happens when you raise any non-zero number to the power of zero?
Any non-zero number raised to the zero power will be equal to one, and that any number raised to the first power will be equal to itself.
The volume formula for cone is
V=3.142h/3 (fraction)
r=Radius
h=Height
How can you use scientific notation on a scientific calculator?
On a Scientific calculator, you can usually find scientific notation in the "SCI" display mode. To enter a number in scientific notation, you can:
What is the decimal expansion of 5/6?
The decimal expansion of 5.6 is 0.833.