Answer:
Slope, Angle, & Distance:
Slope: 0.5625
The slope of the line connecting (15, 20) and (-1, 11) is 0.5625
Slope (m): 0.5625
Angle (θ): 29.3578°
Distance: 18.3576
Δx: 16
Δy: 9
Slope Intercept Form:
(y = mx + b)
y = 0.5625x + 11.5625
Step-by-step explanation:
Steps to Find Slope
Start with the slope formula
m=
(y2 - y1)
(x2 - x1)
Substitute point values in the formula
m=
(11 - 20)
(-1 - 15)
Simplify each side of the equation
m=
(11 - 20)
(-1 - 15)
=
-9
-16
Solve for slope (m)
m=0.5625
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Step-by-step explanation:
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Answer: 1/2
Step-by-step explanation: To find out what fraction is greater, notice that the fractions that we're comparing in this problem have different denominators.
When fractions have different denominators, they're called unlike fractions.
To compare unlike fractions, we must first get a common denominator. The common denominator of 2 and 12 will be the least common multiple of 2 and 12 which is 12.
To get a 12 in the denominator of 1/2, we multiply the numerator and the denominator by 6 which gives us 6/12.
Notice that 1/12 already has a 12 in the denominator so now we are comparing like fractions since both of them has a 12 in the denominator.
To compare like fractions, we simply look at the numerators. Since 6 is greater than 1, this means that 6/12 is greater than 1/12.
Therefore, 1/2 is greater than 1/12.
Length of segment of the hypotenuse adjacent to the shorter leg is 5 inches and the length of the altitude is 3 inches.
Step-by-step explanation:
Step 1: Let the triangle be ΔABC with right angle at B. The altitude drawn from B intersects the hypotenuse AC at D. So 2 new right angled triangles are formed, ΔADB and ΔCDB.
Step 2: According to a theorem in similarity of triangles, when an altitude is drawn from any angle to the hypotenuse of a right triangle, the 2 newly formed triangles are similar to each other as well as to the bigger right triangle. So ΔABC ~ ΔADB ~ ΔCDB.
Step 3: Identify the corresponding sides and form an equation based on proportion. Let the length of the altitude be x. Considering ΔABC and ΔADB, AB/DB = AC/AB
⇒ 6/x = 12/6
⇒ 6/x = 2
⇒ x = 3 inches
Step 4: To find length of the hypotenuse adjacent to the shorter leg (side AB of 6 inches), consider ΔADB.
⇒ 
⇒
⇒
⇒
⇒
⇒AD = 5 inches
