Answer:
m(arc CD) = 112°
Step-by-step explanation:
Use the property of intersecting chords and angles between these chords,
m∠CED =
m∠CED + m∠AED = 180°
80° + m∠CED = 180°
m∠CED = 100°
Now substitute the measure of angle CED and arc AB in the expression,
100° =
200° = 88° + m(arc CD)
m(arc CD) = 112°
Answer:
91
Step-by-step explanation:
Let
x = first number
x+1 = second number
x+2 = third number
x+3 = fourth number
Total = 182
x + x + 1 + x + 2 + x + 3 = 182
4x + 6 = 182
Subtract 6 from both sides
4x + 6 - 6 = 182 - 6
4x = 176
Divide both sides by 4
x = 176 / 4
= 44
x = 44
x = 44
x+1 = 44 + 1 = 45
x+2 = 44 + 2 = 46
x+3 = 44 + 3 = 47
Sum of the two middle numbers = 45 + 46
= 91
Answer:12.59
Step-by-step explanation:
enter image source here
From the diagram you can see that we have constructed a right triangle, with height A and base 15.
Length of shadow = 15 feet.
Height of flagpole = A.
We know the angle of elevation is
40
∘
. Using this angle and the tangent ratio, we can find A.
tan
(
40
∘
)
=
opposite
adjacent
=
A
15
∴
tan
(
40
∘
)
=
A
15
Rearranging:
A
=
15
tan
(
40
∘
)
By calculator:
A
=
12.59
feet. ( 2 d.p.)
To convert 2.77777777777 to a fraction:
Assume x = 2.7777777777......equation 1
Now, notice that the repeating digit is 7
multiply both sides of the equation by 10:
10x = 27.7777777777.......equation 2
Subtract equation 1 from equation 2 as follows:
10x - x = 27.7777777777 - 2.7777777777
9x = 25
Therefore x = 25/9
Based on this, 2.7 repeated can be written as a fraction = 25/9
Answer:
(3 1/2, 7 1/4)
Step-by-step explanation:
A 1:3 ratio means we want 4 equal parts (1+3 = 4)
Find the distance of the segment and divide by 4
(x2+x1)/4, (y2+y1)/4
(8-2)/4 , (5-8)/4
6/4, -3/4
Since the first part is of ratio 1, we multiply by 1
Now add this to the starting point
(2 + 6/4, 8+ -3/4)
Getting a common denominator of 4
2*4/4 = 8/4
8 *4/4 = -3/4
(8/4 + 6/4, 32/4 -3/4)
(14/4, 29/4)
Now change back to a mixed number
(3 2/4 , 7 1/4)
(3 1/2, 7 1/4)