23/4 miles is as much as 5 3/4 miles. We can also write it as a decimal, because 5 3/4 = 5,75 miles.
If Ammar hikes 5,75 miles in 1 1/4 hour, then we need to find out what distance does he hike in 1/4 hour (15 minutes). To do that we can just divide 5,75 by 5 (because dividing 1 1/4 by 5 will give us 1/4 we're looking for).
5,75 / 5 = 1,15
It means that in one hour Ammar hikes 5,75 - 1,15 = 4,6 miles.
We can also write it as a fraction:
4,6 = 4 6/10 = 4 3/5 = 23/5 miles
Just pick whichever form you like :)
Answer:
.
Step-by-step explanation:
We are given a geometric sequence { -16, 4, -1, .... }
i.e.
,
,
, ...
We will first find the common ratio 'r'.
Now, ![r=\frac{a_{n}}{a_{n-1}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_%7Bn%7D%7D%7Ba_%7Bn-1%7D%7D)
i.e. ![r=\frac{a_{2}}{a_{1}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_%7B2%7D%7D%7Ba_%7B1%7D%7D)
i.e. ![r=\frac{4}{-16}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%7D%7B-16%7D)
i.e. ![r=\frac{1}{-4}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B1%7D%7B-4%7D)
Similarly, i.e. ![r=\frac{a_{3}}{a_{2}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_%7B3%7D%7D%7Ba_%7B2%7D%7D)
i.e. ![r=\frac{-1}{4}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B-1%7D%7B4%7D)
So, we get that the common ratio is
.
Now, the recursive formula for the geometric sequence is given by,
![a_{n} =r \times a_{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3Dr%20%5Ctimes%20a_%7Bn-1%7D)
i.e. ![a_{n} =\frac{-1}{4} \times a_{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%5Cfrac%7B-1%7D%7B4%7D%20%5Ctimes%20a_%7Bn-1%7D)
i.e.
.
Hence, the recursive formula for this sequence is
.
Answer:
Circle B has an area of 200.96 in².
Step-by-step explanation:
π = 3.14
radius of circle A = diameter of circle A/2
= 16 in/ 2 = 8 in.
Area = πr² = (3.14)(8²)
= (3.14)(64)
= 200.96 in²
Answer:
x=26
Step-by-step explanation:
We can use the Pythagorean theorem for this answer.
Pythagorean Theorem: a^2 +b^2 = c^2
We can see that both triangles are right triangles. We should first find the hypotonus of the bottom triangle.
So, we plug in the values.
6^2 +8^2 = c^2
36 +64 = c^2
c^2= 100
c= square root of 100
c=10
The hypotonus for the bottom triangle is equivalent to the base of the top triangle. Therefore, we can use the Pythagorean Theorem again.
10^2 +24^2= c^2
100+576+c^2
c^2 = 676
c= square root of 676
c= 26
The answer to the problem is 26.
Anthony has a square-shaped, wooden board. To build a door, he uses the board and cuts 3 feet off of its width. The new area of the wooden board is given by the expression below, where x represents the length in feet.
x(x-3)
Which statement best describes the term (x - 3)?