Problem 4
x = interior angle
y = exterior angle
x = 3y since "each interior angle...is three times the measure of each exterior angle"
The interior and exterior angles are supplementary, meaning,
x+y = 180
3y+y = 180
4y = 180
y = 180/4
y = 45
So we know that
n = 360/y
n = 360/45
n = 8
You are correct in saying that this is an octagon
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Problem 5
x = measure of missing angles
Find the sum of the interior angles
S = 180*(n-2)
S = 180*(5-2)
S = 540
The five interior angles add up to 540 degrees
Add up the five angles, set equal to 540, then solve for x
90+90+90+x+x = 540
2x+270 = 540
2x+270-270 = 540-270
2x = 270
2x/2 = 270/2
x = 135
So you have the correct answer of choice C) 135 degrees
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Problem 6
S = 180*(n-2)
S = 180*(6-2)
S = 180*4
S = 720
You have the correct answer. Nice work on all three correct answers.
Answer:
1. 1
1. 13π.
--
20
explain:
1. 1 because any any non-zero expression raised to the power of 0 equals 1
13π.
2. --. because to convert into radian measure multiply by. π
20. ----
180°
Answer:
l(l - 2) = 168
Step-by-step explanation:
Let w = width
Let l = length
Let A = area
w = l - 2
A = l * w
also, A = 168
equating the two values of A
l * w = 168
l * (l - 2) = 168
l^2 - 2l = 168
l(l - 2) = 168
Answer:
The equation that describes the amount of mass left after a time t of a radioactive isotope is the following:
where
is the mass of the sample at t = 0
is the half-life of the sample
For the element X in this problem,
We want to find the time t at which
So we need to re-arrange the equation making t the subject:
Step-by-step explanation:
Answer:
Take x = 10.2 in. or x = 10 in.
Step-by-step explanation:
Given :
Length = (2x+3) in.
Breadth = x in.
Also, the Area of Rectangle = 240 sq in.
We know that,
Area of Rectangle = length x breadth
240 = (2x+3) x
2x² + 3x = 240
2x² + 3x - 240 = 0
Solving 2x²+3x-240 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B²-4AC
x = ————————
2A
In our case, A = 2
B = 3
C = -240
Accordingly, B² - 4AC = 9 - (-1920) = 1929
Applying the quadratic formula :
-3 ± √ 1929
x = ——————
4
√ 1929 , rounded to 4 decimal digits, is 43.9204
So now we are looking at:
x = ( -3 ± 43.920 ) / 4
Two real solutions:
x =(-3+√1929)/4=10.230 ≈ 10
or
x =(-3-√1929)/4=-11.730
We'll take x = +ve value for calculation of length and breadth.
Therefore,
Length = [2(10.2) + 3 ]
L = 23.4 in.
Breadth = 10.2 in.
OR
Length = [2(10) + 3]
L = 23 in.
Breadth = 10 in.
