Suppose the coordinate of P is 2, PQ = 8, and PR = 12. What are the possible coordinates of the midpoint of the given segment? T
1 answer:
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Answer:
Look to the attached graph
Step-by-step explanation:
* Lets revise how to graph the quadratic function
- Find the vertex of it
- Find the y-intercept
- Find the x-intercept
∵ f(x) = (x - 5)² + 1 ⇒ the completing square form
- The completing square form for any quadratic is
( x - h)² + k, where h and k are the coordinate of the vertex point
* Lets compare the two forms
∵ (x - h)² + k = (x - 5)² + 1
∴ h = 5 and k = 1
∴ The vertex of the parabola is (5 , 1)
- To find the x-intercept put f(x) = 0
∵ (x - 5)² + 1 = 0 ⇒ subtract 1 from both sides
∴ (x - 5)² = -1 ⇒ the square can not give -ve number
∴ The parabola does not intersect the x-axis
- To find the y-intercept put x = 0
∵ f(0) = (0 - 5)² + 1 = 25 + 1 = 26
∴ The parabola intersects the y-axis at point (0 , 26)
- The parabola is opened upward because the coefficient of x² is +ve
* Now lets graph it
- Look to the attached graph
Answer:
x = y
Step-by-step explanation:
Given x : y = 2 : 3
Express the ratios as a fraction, that is
=
( cross- multiply )
3x = 2y ( divide both sides by 3 )
x = y
Answer:
Part A)
Part B) option 1,option 4
Step-by-step explanation:
Part A) Derive the formula for the area of a sector
we know that
The area of circle is equal to
The area of circle subtends a central angle of 360 degrees
so
using proportion
Find out the area of a sector by a central angle of ∅ degrees
Part B) Verify each case
case 1) we have
radius = 5 cm
angle = 120°
area = 26.2 cm 2
Find the area of the sector and then compare with the value of the given area
assume
substitute the given values
so
The given value of area is correct
case 2) we have
radius = 4 cm
angle = 105°
area = 16.7 cm 2
Find the area of the sector and then compare with the value of the given area
assume
substitute the given values
so
The given value of area is not correct
case 3) we have
radius = 6 cm
angle = 85°
area = 23.7 cm 2
Find the area of the sector and then compare with the value of the given area
assume
substitute the given values
so
The given value of area is not correct
case 4) we have
radius = 7
angle = 75°
area = 32.1 cm 2
Find the area of the sector and then compare with the value of the given area
assume
substitute the given values
so
The given value of area is correct