Answer:
Unit rates are expressed as a quantity of 1, such as 3 feet per second or 6 miles per hour, they are called unit rates.
In the given table shows the number of pictures taken and how much time it took.
For first camera;
Number of pictures (unit rate) per second = 
pictures.
For second Camera:
Number of picture per second = 
pictures.
For third Camera:
Number of picture per second = 
pictures.
The camera that takes picture the fastest is, Second Camera.
(a)
As per the given statement: At Davidson's Bike rentals, it costs $29 to rent a bike for 8 hour.
⇒ unit rate per dollar = 
hours
Therefore, 0.227 hours (nearest to hundredths) of bike use does a customer get per dollar.
(b)
Jessica bought 18 pounds of sugar for $10.
unit rate per dollar = 
therefore, 1.8 pounds of sugar did she get per dollar.
Answer:
-6 gets canceled out because it gets squared. When you square a number, you multiply it by itself. Any negative number times a negative number results in a positive number. So instead of -36 its just 36
Answer:
Step-by-step explanation:
Any point on a given parabola is equidistant from focus and directrix.
Given:
Focus of the parabola is at 
.
Directrix of the parabola is 
.
Let 
be any point on the parabola. Then, from the definition of a parabola,
Distance of from focus = Distance of from directrix.
Therefore,
Squaring both sides, we get
![(x-2)^{2}+(y-8)^{2}=(y-10)^{2}\\(x-2)^{2}=(y-10)^{2}-(y-8)^{2}\\(x-2)^{2}=(y-10+y-8)(y-10-(y-8))...............[\because a^{2}-b^{2}=(a+b)(a-b)]\\(x-2)^{2}=(2y-18)(y-10-y+8)\\(x-2)^{2}=2(y-9)(-2)\\(x-2)^{2}=-4(y-9)\\y-9=-\frac{1}{4}(x-2)^{2}\\y=-\frac{1}{4}(x-2)^{2}+9](https://tex.z-dn.net/?f=%28x-2%29%5E%7B2%7D%2B%28y-8%29%5E%7B2%7D%3D%28y-10%29%5E%7B2%7D%5C%5C%28x-2%29%5E%7B2%7D%3D%28y-10%29%5E%7B2%7D-%28y-8%29%5E%7B2%7D%5C%5C%28x-2%29%5E%7B2%7D%3D%28y-10%2By-8%29%28y-10-%28y-8%29%29...............%5B%5Cbecause%20a%5E%7B2%7D-b%5E%7B2%7D%3D%28a%2Bb%29%28a-b%29%5D%5C%5C%28x-2%29%5E%7B2%7D%3D%282y-18%29%28y-10-y%2B8%29%5C%5C%28x-2%29%5E%7B2%7D%3D2%28y-9%29%28-2%29%5C%5C%28x-2%29%5E%7B2%7D%3D-4%28y-9%29%5C%5Cy-9%3D-%5Cfrac%7B1%7D%7B4%7D%28x-2%29%5E%7B2%7D%5C%5Cy%3D-%5Cfrac%7B1%7D%7B4%7D%28x-2%29%5E%7B2%7D%2B9)
Hence, the equation of the parabola is .
Answer: each guest gets 4.19 cm²
Step-by-step explanation:
The cake is a circle. The area which he cuts for himself is a sector with a central angle of 120 degrees. The formula for determining the area of a sector is expressed as
Area of sector = θ/360 × πr²
Where
θ represents the central angle
π is a constant whose value is 3.14
r represents the radius of the circle.
From the diagram,
r = 4cm
Therefore, area of the cake that he cut for himself is
120/360 × 3.14 × 4²
= 16.75 cm²
The total area of the cake is
3.14 × 4² = 50.24 cm²
Therefore, the rest of the cake is
50.24 - 16.75 = 33.49 cm²
The amount that each guest gets would be
33.49/8 = 4.19 cm²
