Answer and Step-by-step explanation: Area of a right triangle, (as any other triangle), is calculated as: 
Area of a rectangle is calculated as: 
Area of a right trapezoid is: 
, where:
a is short base
b is long base
h is height
1) Expressing areas in terms of x:
Area of triangle S1:
Area of rectangle S2:
Area of trapezoid S3:
2) a) 
Which is the same as S = (2x-3)(5x-9)
b) For the areas to be the same:
Using Bhaskara to solve the second degree equation:
= 1.8
= 1.5
For the areas of AFGC and ADEB to be equal, x has to be 1.5 or 1.8.
c) <u>Expand</u> <u>a</u> <u>polynomial</u> (or equation) is to multiply all the terms, remiving the parenthesis. <u>Reduce</u> <u>a</u> <u>polynomial</u> (or equation) is to combine terms alike,e.g.:
(expand)
(reduce)
d) For area of AFCG to be bigger than area of ADEB by 27:
Solving:
2.82
= 0.48
According to the enunciation, x cannot be less than 1.5, then, the value of x so that area AFGC exceeds the area ADEB by 27 is 2.82
A system equations that can be used to determine after how many months the boys will owe the same amount is
60 x = $ 1000
20 y = $ 600
In mathematics, a system of equations, also known as a system of simultaneous or systems of equations, is a finite system of equations for which we have sought common solutions. A system of equations can be classified in a similar way to simple equations. A system of equations finds application in our everyday life in modeling problems where unknown values can be represented in the form of variables.
In algebra, a system of equations contains two or more equations and looks for common solutions to the equations. "A system of linear equations is a set of equations that are satisfied by the same set of variables."
We need to find a system equations that can be used to determine after how many months the boys will owe the same amount
Let lan take x months to pay $ 1000 to his parents
In 1 month Ian pays $60
In x months Ian pays =
60 x= $ 1000
Let Ken take y months to pay $ 600 to his parents
In 1 month Ian pays $20
In y months Ian pays =
20 y= $ 600
Hence 60 x= $ 1000 and 20 y= $ 600 are the system of equations
<u>Learn more about system of equations here</u>:
brainly.com/question/28053213
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Answer:
9
Step-by-step explanation:
sum of roots = α + β
= -b/a
= -3/1 …………………. [b = 3, a = 1]
= -3
- (α + β)² = ( -3 )² = -3 × -3 = 9
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It is 72 1/10. This is because 72 is a whole number and point one would be tenths.
