The rise and span for a roof are shown. the pitch of a roof is the ratio of the rise to the half-span. if the rise is 8 feet and the span is 30 feet, what is the pitch in simplest form?

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

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true