Answer:
6!=720
3! • 2!=12
Step-by-step explanation:
We must recall that the factorial of a number n (positive or zero) is the product of all the integers from n down to 1
n!= n(n-1)(n-2)...1
Let's evaluate the given expressions
6!=6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1=720
Similarly
3!\cdot 2!=(3\cdot 2\cdot 1)\cdot (2\cdot 1)=6\cdot 2=12
Finally
\displaystyle \frac{6!}{3!}=\frac{6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{3\cdot 2\cdot 1}
\displaystyle \frac{6!}{3!}= \frac{720}{6}=120
Answer:
the arrow pointing to the left
Step-by-step explanation:
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) )
The equation for Tom: y=30+1x
The equation for Nita: y=18+5x
This is the answer
Hope it helps :)
If you are finding the area of a circle, then use A=pi x radius^2
A= 3.14 x 5^2(since 5 is half of 10)
A= 3.14 x 25
A=78.50 cm^2
