Applying the inscribed angle theorem, the measure of arc AB that doesn't go through point C is: 100 degrees.
<h3>What is the Inscribed Angle Theorem?</h3>
Based on the inscribed angle theorem, if ∅ is the inscribed angle measure, the measure of the central angle subtended by the same arc equals 2(∅).
m∠BAC = 40 degrees.
Central angle = 2(40) = 80 degrees [based on the inscribed angle theorem]
Corresponding arc BC = 80 degrees.
Arc AC through point B = 180 degrees [half circle]
Arc AB = 180 - arc BC = 180 - 80 = 100 degrees.
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By definition we have an integer number given by:
An integer is an element of the numeric set that contains the natural numbers {N} = {1,2,3,4, ...}, its opposite and zero.
On the number line we find the negative numbers to the left of the zero and to its right the positive numbers.
We have then, according to the definition, that the following are whole numbers:
-527, 1
Answer:
B = {x | x is an integer}
-527 ∈ B
1 ∈ B
option D
Answer:
Dimensions of printed area
w = 8.95 cm
h = 13.44 cm
A(max) = 120.28 cm²
Step-by-step explanation:
Lets call " x " and "y" dimensions of the poster area ( wide and height respectively) . Then
A(t) = 180 cm² = x*y y = 180/ x
And the dimensions of printed area is
A(p) = ( x - 2 ) * ( y - 3 ) then as y = 180/x we make A function of x only so
A(x) = ( x - 2 ) * ( 180/x - 3 ) ⇒ A(x) = 180 - 3x - 360/x +6
A(x) = - 3x - 360 /x + 186
Taking derivatives on both sides of the equation we get:
A´(x) = -3 + 360/ x²
A´(x) = 0 -3 + 360/ x² = 0 -3x² + 360 = 0
x² = 120 ⇒ x = √120 x = 10.95 cm
And y = 180 / 10.95 ⇒ y = 16.44 cm
Then x and y are the dimensions of the poster then according to problem statement
w of printed area is x - 2 = 10.95 - 2 = 8.95 cm
and h of printed area is y - 3 = 16.44 - 3 = 13.44 cm
And the largest printed area is w * h = ( 8.95)*(13.44)
A(max) = 120.28 cm²
Answer:
12:15 is NOT proportional to 3:4
Step-by-step explanation:
7.5:10 is proportional to 3:4 because 3×2.5=7.5, and 4×2.5=10.
39:52 is proportional to 3:4 because 3×13=39, and 4×13=52
45:60 is proportional to 3:4 because 3x15=45, and 4×15=60
12:15 is not proportional to 3:4 because while you can multiply 3x4=12, you can not multiply 4×4 to get 15, you get 16 instead.
