The sum of 8 times a number and 10 is 34. Find the number.
2 answers:
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To solve this problem, we need to first find the dimensions of the side of the blue and purple squares.
We're given that the purple (smaller) square has a side length of x inches.
We are also given that the blue band has a width of 5 inches.
Since the blue band surrounds the purple square on both sides, the length of the blue square is x+2(5)=x+10 inches.
The net area of the band is therefore the difference of the area of the blue square and the purple square, namely take out the area of the purple square from the blue.
Therefore
Area of band
[recall 
or 20(x+5) if you wish.
We're given that the purple (smaller) square has a side length of x inches.
We are also given that the blue band has a width of 5 inches.
Since the blue band surrounds the purple square on both sides, the length of the blue square is x+2(5)=x+10 inches.
The net area of the band is therefore the difference of the area of the blue square and the purple square, namely take out the area of the purple square from the blue.
Therefore
Area of band
Find the length of the radius.
Find the length of the diameter.
d = 2r = 2 × 5√2 = 10√2
Point B must lie on a line AC, where C is a center of a circle.
Find equation of line AC.
A(–4, 6), C(3, 5)
The distance from B(x, y) to C(3, 5) is 5√2.
Solve system of equations.
Point B could have coordinates
But (–4, 6) are the coordinates of point A.
Therefore, point B has coordinates (10,4).
Find the length of the diameter.
d = 2r = 2 × 5√2 = 10√2
Point B must lie on a line AC, where C is a center of a circle.
Find equation of line AC.
A(–4, 6), C(3, 5)
The distance from B(x, y) to C(3, 5) is 5√2.
Solve system of equations.
Point B could have coordinates
But (–4, 6) are the coordinates of point A.
Therefore, point B has coordinates (10,4).