Determine the value of a and b so that x^4 6x^3 +7x^2+ax+b is a perfect square
1 answer:
You might be interested in
All of these can be solved by separating complex figur into simpler one.
Needed formulas are:
Area of rectangle A=a*b
Area of triangle A=a*h/2
Area of paralelogram A= a*h
QUESTION 1.
When we connect points F and S we get a rectangle and a triangle.
Dimensions of sides of a rectangle are a=9 and b=2.
A=9*2=18
For a triangle we need to take one side and it's height. Let's take side FS because it's easiest to find the height.
a=9
h=6
A=9*6/2=27
Tot+al area of a figure:
A=18+27=45
QUESTION 2.
We connect point (1,1) with (1,-2) and (-6,1). This way we get a rectangle and three triangles.
Rectangle:
a=3
b=4
A=3*4=12
Top right triangle:
a=4
h=3
A=4*3/2=6
Top left triangle:
a=7
h=2
A=7*2/2=7
Bottom left triangle:
a=7
h=3
A=7*3/2=10.5
Total area of a figure:
A=12+6+7+10.5=35.5
QUESTION 3.
We connect points (-4,2) and (-1,3). This way we get a paralelogram and a rectangle.
Paralelogram:
a=6
h=1
A=6*1=6
Rectangle:
a=distance between (-4,2) and (-1,3) =
b = distance between (-4,2) and (-2,-4) =
A=a*b=
Paralelogram:
a=6
h=1
A=6*1=6
Total area of a figure:
A=
+ 6
QUESTION 4.
We coonect missing side of a triangle. That side has a length of: 6in-3in=3in. Vertical side of triangle is: 13in-7in=6in
Area:
a=3
h=6
A=3*6/2=9
Rectangle:
a=7in
b=6in
A=7*6=42
Total area of a figure:
A=9+42=51
Needed formulas are:
Area of rectangle A=a*b
Area of triangle A=a*h/2
Area of paralelogram A= a*h
QUESTION 1.
When we connect points F and S we get a rectangle and a triangle.
Dimensions of sides of a rectangle are a=9 and b=2.
A=9*2=18
For a triangle we need to take one side and it's height. Let's take side FS because it's easiest to find the height.
a=9
h=6
A=9*6/2=27
Tot+al area of a figure:
A=18+27=45
QUESTION 2.
We connect point (1,1) with (1,-2) and (-6,1). This way we get a rectangle and three triangles.
Rectangle:
a=3
b=4
A=3*4=12
Top right triangle:
a=4
h=3
A=4*3/2=6
Top left triangle:
a=7
h=2
A=7*2/2=7
Bottom left triangle:
a=7
h=3
A=7*3/2=10.5
Total area of a figure:
A=12+6+7+10.5=35.5
QUESTION 3.
We connect points (-4,2) and (-1,3). This way we get a paralelogram and a rectangle.
Paralelogram:
a=6
h=1
A=6*1=6
Rectangle:
a=distance between (-4,2) and (-1,3) =
b = distance between (-4,2) and (-2,-4) =
A=a*b=
Paralelogram:
a=6
h=1
A=6*1=6
Total area of a figure:
A=
QUESTION 4.
We coonect missing side of a triangle. That side has a length of: 6in-3in=3in. Vertical side of triangle is: 13in-7in=6in
Area:
a=3
h=6
A=3*6/2=9
Rectangle:
a=7in
b=6in
A=7*6=42
Total area of a figure:
A=9+42=51