Answer:
x=8
Step-by-step explanation:
6x+42=90
6x=48
x=8
Answer: a and d
Step-by-step explanation:
First of all, we need to make a analysis of each letters:
a. factoring 32 = 2.2.2.2.2 = ![2^{5}](https://tex.z-dn.net/?f=2%5E%7B5%7D)
![2^{5}^{3} = 2^{15}](https://tex.z-dn.net/?f=2%5E%7B5%7D%5E%7B3%7D%20%3D%202%5E%7B15%7D)
then,
16 = ![2^{4}](https://tex.z-dn.net/?f=2%5E%7B4%7D)
but ![2^{4}^{4} =2^{16}](https://tex.z-dn.net/?f=2%5E%7B4%7D%5E%7B4%7D%20%3D2%5E%7B16%7D)
in conclusion that, this inequality is correct
b. 27 = ![3^{3}](https://tex.z-dn.net/?f=3%5E%7B3%7D)
this first situation is equal to ![3^{9}](https://tex.z-dn.net/?f=3%5E%7B9%7D)
the second situation is:
81 = ![3^{4}](https://tex.z-dn.net/?f=3%5E%7B4%7D)
and ![3^{4}^{4} = 3^{16}](https://tex.z-dn.net/?f=3%5E%7B4%7D%5E%7B4%7D%20%3D%203%5E%7B16%7D)
it's a mistake.
c. factoring 9: ![9 = 3^{3}](https://tex.z-dn.net/?f=9%20%3D%203%5E%7B3%7D)
< ![3^{5}](https://tex.z-dn.net/?f=3%5E%7B5%7D)
it's wrong.
d. factoring 8 = ![2^{3}](https://tex.z-dn.net/?f=2%5E%7B3%7D)
factoring 32 = ![2^{5}](https://tex.z-dn.net/?f=2%5E%7B5%7D)
> ![2^{10}](https://tex.z-dn.net/?f=2%5E%7B10%7D)
This is true.
Finally.. our correct answers is a and d.
The given is that A B C D <span>x 4 = D C B A
</span><span>
Possible values of A are 1 or 2. It can't be 1 since the </span><span> </span><span>final result A is in unit place and 1 is not possible when we multiply any number by 4
</span><span>
2 B C D x </span><span>4 = </span><span>D C B 2</span>
It is clear above, that D = 8
2 B C 8 x <span>4 = </span><span>8 C B 2</span>
Possible values of B should be 1 or 2
We try B=1
2 1 C 8 x <span>4 = </span><span>8 C 1 2
</span>To find for C, you can use the equation:
(2000+100+10C+8) x 4 = 8000+100C+10+240C = 432-12 = 420
Therefore,
C = 7
So, the number is 2178.
Answer: The average velocity of the object over the time interval [3,6] is 20.
Step-by-step explanation:
Since we have given that
s(3) = 156
s(6) = 216
We need to find the average velocity over the time interval [3,6].
So, average velocity becomes
![\dfrac{s(t_1)-s(t_0)}{t_1-t_0}\\\\=\dfrac{s(6)-s(3)}{6-3}\\\\=\dfrac{216-156}{3}\\\\=\dfrac{60}{3}\\\\=20](https://tex.z-dn.net/?f=%5Cdfrac%7Bs%28t_1%29-s%28t_0%29%7D%7Bt_1-t_0%7D%5C%5C%5C%5C%3D%5Cdfrac%7Bs%286%29-s%283%29%7D%7B6-3%7D%5C%5C%5C%5C%3D%5Cdfrac%7B216-156%7D%7B3%7D%5C%5C%5C%5C%3D%5Cdfrac%7B60%7D%7B3%7D%5C%5C%5C%5C%3D20)
Hence, the average velocity of the object over the time interval [3,6] is 20.
Answer:
x = 10
Step-by-step explanation:
Since both equations give y in terms of x, equate the right sides
3x - 28 = - 2x + 22 ( add 2x to both sides )
5x - 28 = 22 ( add 28 to both sides )
5x = 50 ( divide both sides by 5 )
x = 10