There is 1 boy for every 3 girls in a class. If there are 60 students in the class, how many are boys?
1 answer:
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The area of polygon MNOPQR = Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units.
In the given polygon MNOPQR, side MN is parallel to side RQ and the side MR is parallel to side PQ
We will draw a perpendicular line from point O on the side RQ, which will intersect RQ at point S. So, we can now divide the whole polygon into two different rectangles MNSR and OPQS with the areas as A₁ and A₂ respectively.
In rectangle MNSR, length(MN) = 5 units and width (MR) = 3 units
According to the formula for Area of rectangle,
A₁ = (length)×(width)
A₁ = (5 units)×(3 units)
A₁ = 15 square units
Now in rectangle MNSR, side MN= side RS and side MR = side NS,
so RS= 5 units and NS= 3 units
That means, SQ= RQ- RS = 7-5 = 2 units
and OS= NS - NO = 3- 2 = 1 unit
In rectangle OPQS, we have length(SQ) = 2 units and width(OS) = 1 unit
So, A₂ = (length)×(width)
A₂ = (2 units)×(1 unit)
A₂ = 2 square units
So, the area of polygon MNOPQR = (Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units)
Answer:
f(x) = -2x + 7, when x > 1
f(x) = 4x + 1 when x ≤ 1
Step-by-step explanation:
The right side graph passe through points (1,5) and (2,3).
Hence, the equation of the line
⇒ (y - 5) = 2(1 - x)
⇒ y - 5 = 2 - 2x
⇒ y = -2x +7.......... (1)
Now, the left side graph passes through points (1,5) and (0,1)
Therefore, the equation of the graph will be
⇒ y - 5 = 4(x - 1)
⇒ y = 4x + 1 ........ (2)
Hence, the equation (1) gives the function in the right side of the given graph which does not include the point (1,5) and extends to the right from this point.
Therefore, f(x) = -2x + 7, when x > 1 (Answer)
Again, equation (2) gives the function in the left side of the given graph which includes the point (1,5) and extends to the left from this point.
Therefore, f(x) = 4x + 1 when x ≤ 1 (Answer)