Answer:
The ratio of the area of ABCD to the area of EFGH is 9:1.
Step-by-step explanation:
Let us assume that the shapes are rectangles and they are similar. If the two shapes are similar then their sides are in the same proportion. Therefore the ratio of the sides are in the same proportion.
![\frac{AB}{BC}=\frac{EF}{FG}\\ \\\frac{18}{24}=\frac{6}{x}\\\\18x=24*6\\ \\x=\frac{24*6}{18}=8](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7BBC%7D%3D%5Cfrac%7BEF%7D%7BFG%7D%5C%5C%20%20%5C%5C%5Cfrac%7B18%7D%7B24%7D%3D%5Cfrac%7B6%7D%7Bx%7D%5C%5C%5C%5C18x%3D24%2A6%5C%5C%20%20%5C%5Cx%3D%5Cfrac%7B24%2A6%7D%7B18%7D%3D8)
The area of ABCD = AB × BC = 18 × 24 = 432
The area of EFGH = EF × FG = 6 × 8 = 48
The ratio of the area of ABCD to the area of EFGH = Area of ABCD / Area of EFGH = 432 / 48 = 9/1 = 9 : 1
C
SSS can be used because ln is congruent to ln by reflexive property.
The answer is 9
36/4=9
63/7=9
108/12=9
315/35=9
Answer:
m < 5=27°
Step-by-step explanation:
we know that
When a transversal passes through two lines, the angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles.
In this problem
The transversal is the diagonal BD
The two lines are AB and CD
m < 5 and m < 2 are alternate interior angles
we have that
The two lines are parallel
AB || CD
therefore
m < 5= m < 2
we have that
m < 2=27°
so
m < 5=27°
Answer:
The function which represents this sequence will be:
![a_n=-15n+110](https://tex.z-dn.net/?f=a_n%3D-15n%2B110)
Hence, option (A) is true.
Step-by-step explanation:
Given the sequence
![95, 80, 65, 50, ...](https://tex.z-dn.net/?f=95%2C%2080%2C%2065%2C%2050%2C%20...)
An arithmetic sequence has a constant difference 'd' and is defined by
![a_n=a_1+\left(n-1\right)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%5Cleft%28n-1%5Cright%29d)
computing the differences of all the adjacent terms
![80-95=-15,\:\quad \:65-80=-15,\:\quad \:50-65=-15](https://tex.z-dn.net/?f=80-95%3D-15%2C%5C%3A%5Cquad%20%5C%3A65-80%3D-15%2C%5C%3A%5Cquad%20%5C%3A50-65%3D-15)
As the difference is the same, so
![d = -15](https://tex.z-dn.net/?f=d%20%3D%20-15)
as
![a_1=95](https://tex.z-dn.net/?f=a_1%3D95)
Thus, substituting
,
in the nth term of an arithmetic sequence
![a_n=a_1+\left(n-1\right)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%5Cleft%28n-1%5Cright%29d)
![a_n=-15\left(n-1\right)+95](https://tex.z-dn.net/?f=a_n%3D-15%5Cleft%28n-1%5Cright%29%2B95)
![a_n=-15n+110](https://tex.z-dn.net/?f=a_n%3D-15n%2B110)
Therefore, the function which represents this sequence will be:
![a_n=-15n+110](https://tex.z-dn.net/?f=a_n%3D-15n%2B110)
Hence, option (A) is true.