Answer:
A) 5 notebooks, 10 pencils
Step-by-step explanation:
n = notebook
p = pencil
1.97n + 1.16p = 21.45
A)✅
1.97(5) + 1.16(10) = 21.45
9.85 + 11.6 = 21.45
21.45 = 21.45
B) ❌
1.97(3) + 1.16(12) = 21.45
5.91 + 13.92 = 21.45
19.83 = 21.45
Answer:
hi if you want to solve fore x and y there must be 2 equations .
Step-by-step explanation:
so that you could solve them simultaneously
-7x + 2y = 4
here 2y - 4 = 7x
( 2y -4)/7 = x
Given that sequence 1.77, 1.92,2.07 is arithmetic sequence.
Using that we have to find 31st term.
To find that we can use nth term formula of arithmetic sequence which is given by:
![t_n=a_1+(n-1)d](https://tex.z-dn.net/?f=t_n%3Da_1%2B%28n-1%29d)
where n is the number of term so n=31
t_n indicates nth term
a_1 is the first term so a_1=1.77
r is the common difference which is given by difference of consecutive terms
then r=1.92-1.77=0.15
Now plug these values into above formula
![t_n=a_1+(n-1)d](https://tex.z-dn.net/?f=t_n%3Da_1%2B%28n-1%29d)
![t_{31}=1.77+(31-1)*0.15](https://tex.z-dn.net/?f=t_%7B31%7D%3D1.77%2B%2831-1%29%2A0.15)
![t_{31}=1.77+(30)*0.15](https://tex.z-dn.net/?f=t_%7B31%7D%3D1.77%2B%2830%29%2A0.15)
![t_{31}=1.77+4.5](https://tex.z-dn.net/?f=t_%7B31%7D%3D1.77%2B4.5)
![t_{31}=6.27](https://tex.z-dn.net/?f=t_%7B31%7D%3D6.27)
Hence final answer is 6.27.
Answer: FIrst option, Fourth option and Fifth option.
Step-by-step explanation:
First it is important to know the definition of "Dilation".
A Dilation is defined as a transformation in which the Image (which is the figure obtained after the transformation) and the Pre-Image (this is the original figure, before the transformations) have the same shape, but their sizes are different.
If the length of CD is dilated with a scale factor of "n" and it is centered at the origin, the length C'D' will be:
![C'D'=nCD=(n)(12\ units)](https://tex.z-dn.net/?f=C%27D%27%3DnCD%3D%28n%29%2812%5C%20units%29)
Therefore, knowing this, you can determine that:
1. If
, you get:
![C'D'=(\frac{3}{2})(12\ units)=18\ units](https://tex.z-dn.net/?f=C%27D%27%3D%28%5Cfrac%7B3%7D%7B2%7D%29%2812%5C%20units%29%3D18%5C%20units)
2. If
, then the length of C'D' is:
![C'D'=(4)(12\ units)=48\ units](https://tex.z-dn.net/?f=C%27D%27%3D%284%29%2812%5C%20units%29%3D48%5C%20units)
3. If
, then:
![C'D'=(8)(12\ units)=96\ units](https://tex.z-dn.net/?f=C%27D%27%3D%288%29%2812%5C%20units%29%3D96%5C%20units)
4. If
, then, you get that the lenght of C'D' is:
![C'D'=(2)(12\ units)=24\ units](https://tex.z-dn.net/?f=C%27D%27%3D%282%29%2812%5C%20units%29%3D24%5C%20units)
5. If
, the length of C'D' is the following:
![C'D'=(\frac{3}{4})(12\ units)=9\ units](https://tex.z-dn.net/?f=C%27D%27%3D%28%5Cfrac%7B3%7D%7B4%7D%29%2812%5C%20units%29%3D9%5C%20units)