The pitch or slope of a roof is defined as the ration of rise and half of the span. In equation we can write:
Half-Span equals the run. So we can define the Pitch as:
Rise = 8 feet
Run = Half of span = 15 feet
Using the values in the above formula, we get:
Therefore, the pitch (or slope) of the roof in simplest form is 8/15
Pitch is normally defined as the vertical rise of a roof for ever 12 feet increase in its horizontal run. The above fraction shows the vertical rise is 8/15 for each 1 feet increase in the horizontal run. So if we simply multiply the the above fraction by 12, we will get the pitch in standard units.
So,
Pitch = 8/15 x 12 = 6.4
Therefore, the pitch of the roof will be 6.4
its D) Division because you are going to divide both sides by 3 to get x by its self
segment D G with points D E F G on the segment in order from left to right
Prove: DE=FG
DG is a given line segment with points D E F G on the segment in order from left to right as shown in the given image.
1. DF = EG (Given)
2. As, DF=DE+EF
and EG=EF+FG
Also, DF=EG(Given)
Substituting the values of DF and EG in the given equation,
DE+EF = EF+FG (Substitution property of equality)
Subtracting EF from both the sides ,
DE=FG (Subtraction property of equality).
The answered table is attached.
What makes a NUMBER rational is the ability to have a perfect square root, cube root, or have these components: Perfect square/cube, whole number, repeating (pattern) decimal, termination decimal, and I think one more that I can't remember.
The properties of the rational exponents are given and a rational equation is of the form b = aˣ
What are the laws of exponents?
When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the rational exponent equation be A
Now , the properties of the exponent equations are
mᵃ×mᵇ = mᵃ⁺ᵇ
The powers of the exponents are added together
mᵃ / mᵇ = mᵃ⁻ᵇ
The powers of the exponents are subtracted together
( mᵃ )ᵇ = mᵃᵇ
The powers of the exponents are multiplied together
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
Any number raised to the power of 0 is 1
m⁻ᵃ = ( 1 / mᵃ )
Hence , the exponents are solved
Rational exponents have properties that help to simplify expressions and solve mathematical problems. These properties include the product rule, the quotient rule, and the power rule. Utilizing these rules, especially in scientific notation, helps provide concise computations for very large or small numbers.
The properties of rational exponents play a key role in simplifying expressions and solving mathematical problems. Here are three key properties:
These properties are crucial for solving problems. For example, scientific notation, which is used to represent very large or small numbers, employs these properties of exponents. In scientific notation, numbers are expressed as a product of a digit term and an exponential term. This method is useful for making computations convenient and precise.
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