Answer:
2 distinct real number zeros
Step-by-step explanation:
The discriminant b^2 - 4ac
= (-17)^2 - 4*4*3
= 241
So it has 2 distinct roots.
Let the sides of the polygon (which is a triangle, by the way) be x, y and z. The sum of x, y and z is the perimeter of the original poly, and this equals 18 cm.
Letting f be the scale factor, f(18 cm) = 12 cm. Then f=2/3.
The dilation reduces the size of the polygon by a factor of 1/3, producing a similar polygon which is 2/3 the size of the original one.
In each case we have 3 side lengths but no angles. We can use Heron's formula to obtain the area in each case. Look up Heron's formula. In one version of this formula, p is half the actual perimeter, meaning that p is 18 cm / 2 for the first triangle and 12 cm / 2 for the second.
The area of the first triangle would be
A18 = sqrt( 9(9-x)(9-y)(9-z) )
whereas
A12 = sqrt( 6(6-x*a)(6-y*a)(6-z*a) ), where a represents the dilation factor 2/3.
Then the ratio of the areas of the 2 triangles is
sqrt( 6(6-x*a)(6-y*a)(6-z*a) )
---------------------------------------
sqrt( 9(9-x)(9-y)(9-z) )
Answer:
The area of the deck after she doubles the length and width will be of 384 square feet.
Step-by-step explanation:
Area of a rectangle:
The area of a rectangle of length l and width w is given by:

Doubling length and width:
If we double the length and the width, the dimensions are 2l and 2w. Thus, the area will be of:

That is, if both dimensions are doubled, the area is multiplied by 4.
What will the area of the deck be after she doubles the length and width?
Was 96. Then, both dimensions were doubled, and the area has to be multiplied by 4.
96*4 = 384
The area of the deck after she doubles the length and width will be of 384 square feet.
Answer:

Step-by-step explanation:
Given
Shape: Rectangle
Division = 4 parts
Required
How much is one part of the division
Represent the rectangle with R and the parts with P
When a rectangle (R) is divided into 4 parts (P); the relationship between R and P is:


<em>This implies that the one part of the division is ¼ of the divided rectangle</em>