If you woke up at 11:15 am and went to sleep at 1:55 am. How many hours where you awake?
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Answer:
base = 5 m
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A = bh ( b is the base and h the height )
here h = 3b + 1 ( 1 m greater than 3 times the base ), hence
A = b(3b + 1) = 40
Multiply both sides by 2
b(3b + 1) = 80 ← distribute and rearrange
3b² + b - 80 = 0 ← in standard form
Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term
product = 3 × - 80 = - 240 and sum = 1
The factors are - 15 and + 16
Use these factors to split the b- term
3b² - 15b + 16b - 80 = 0 ( factor the first/second and third/fourth terms )
3b(b - 5) + 16(b - 5) = 0 ← factor out (b - 5)
(b - 5)(3b + 16) = 0
Equate each factor to zero and solve for b
b - 5 = 0 ⇒ b = 5
3b + 16 = 0 ⇒ b = -
However, b > 0 ⇒ b = 5
The base of the triangle is 5 m
Let be the measure of the angle in question. Its complement has measure
. We're told that this angle is congruent to 1/3 of its complement, so that
The x-coordinate of the point which divide the line segment is 3.
Given the coordinates in the figure are J(1,-10) and K(9,2) and the 1:3 is the ratio in which the line segment is divided.
When the ratio of the length of a point from both line segments is m:n, the Sectional Formula can be used to get the coordinate of a point that is outside the line.
To find the x-coordinate we will use the formula x=(m/(m+n))(x₂-x₁)+x₁.
Here, m:n=1:3 and x₁=1 from the point J(1,-10) and x₂=9 from the point K(9,2).
Now, we will substitute these values in the formula, we get
x=(1/(1+3))(9-1)+1
x=(1/4)(8)+(1)
x=8/4+1
x=3
Hence, the x-coordinate of the point that divides the directed line segment from k to j into a ratio of 1:3 is 3 units.
Learn about line segments from here brainly.com/question/10240790
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