I'm assuming D is the center of the circle. See the new figure.
Angle BDC = 106 degrees, that's the definition of arc measure.
Triangle BDC is isosceles (two radii make congruent sides) so the two remaining angles in BDC are equal, DBC=DCB=(180-106)/2=37 degrees.
Angle BAC = 106/2 = 53 degrees, subtending the arc of 106 degrees.
Angle CAD = 53/2 = 26.5 degrees because AD is a bisector, the shared hypotenuse of congruent right triangles AED and AFD.
AFD is also congruent to CFD, so angle DCA is also 26.5 degrees
Angle ACB is the sum of DCA and DCB, ACB = 26.5 + 37 = 63.5 degrees
The angle subtends the arc we seek, whose measure must be double:
10x - 23 = 2(63.5) = 127 degrees
10x = 150
x = 15
Answer: 15
Terri can swim 3 laps in 2.5 minutes. To find how long it takes to swim 20 laps, you can make a proportion.
Put the amount of laps on the top and the time(minutes) at the bottom.
Cross multiply:
Divide by 3:
It would take Terri 
OR 
minutes to run 20 laps.
The price of a staff ticket and the price of a student ticket is $8 and $14
Given:
Day 1:
Number of staff tickets sold = 3
Number of students tickets sold = 1
Total revenue day 1 = $38
Day 2:
<em>Number of staff tickets sold</em> = 3
<em>Number of students tickets sold</em> = 2
<em>Total revenue day</em> 2 = $52
let
<em>cost of staff tickets</em> = x
<em>cost of students tickets</em> = y
The equation:
<em>3x + y = 38 (1)</em>
<em>3x + y = 38 (1)3x + 2y = 52 (2)</em>
subtract (1) from (2)
2y - y = 52 - 38
y = 14
substitute y = 14 into (1)
3x + y = 38 (1)
3x + 14 = 38
3x = 38 - 14
3x = 24
x = 24/3
x = 8
Therefore,
cost of staff tickets = x
= $8
cost of students tickets = y
= $14
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Answer:
Answer Placeholder (I'm going to solve it and answer when I'm done)
Step-by-step explanation:
Answer:
1. (0, 1)
Step-by-step explanation:
Put x = 0 then work out the values of y:0
y = 3^0 = 1 y-intercept is (0,1)
y = 0,25^x , y = 0.25^0 = 1
All the others are done in same way
