Answers:
y = 50
angle AOB = 100
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Explanation:
Angle x is an inscribed angle that subtends or cuts off minor arc AB. This is the shortest distance from A to B along the circle's edge.
Angle y is also an inscribed angle that cuts off the same minor arc AB. Therefore, it is the same measure as angle x. We can drag point D anywhere you want, and angle y will still be an inscribed angle and still be the same measure as x.
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Point O is the center of the circle. This is because "circle O" is named by its center point.
Angle AOB is considered a central angle as its vertex point is the center of the circle.
Because AOB cuts off minor arc AB, and it's a central angle, it must be twice that of the inscribed angle that cuts off the same arc.
This is the inscribed angle theorem.
Using this theorem, we can say the following
central angle = 2*(inscribed angle)
angle AOB = 2*(angle x)
angle AOB = 2*50
angle AOB = 100 degrees
What is the initial fee to rent the cabin?
$50, this is the y-intercept
What is the cost per night?
$75, this is the slope
Write an equation to represent the situation.
y = 75x + 50
Answer:
6th week with $32
Step-by-step explanation:
Since both plan on adding or spending money weekly at a constant rate, this is a linear situation. Both Tommy's and Joey's money can be modeled with a line on a graph and linear equations.
Tommy's starting amount is $8 and this is the y-intercept so b=8. His rate of change is adding $4 per week. This is a slope of 4. His equation is y=4x+8.
Joey's starting amount is $44 and this is the y-intercept so b=44. His rate of change is subtracting $2 a week for each app he buys. This is a slope of -2. His equation is y=-2x+44.
To find when they have the same amount means when the amounts are equal. Solve 4x+8=-2x+44.
4x+8=-2x+44
6x+8=44
6x=36
x=6 weeks
To find how much money there is in 6 weeks, plug x=6 into one of the equations.
4(6)+8 = 24+8 = 32
