Answer:
Step-by-step explanation:
Area = 1/2 b h
= 1/2 * 4 * 5
= 10 unit^2.
Answer:
13 3/4
-3 1/4
First subtract the fractions so, 3/4 - 1/4 is 2/4, or 1/2. (Like 3-1)
Then subtract the whole numbers, 13-3=10.
The answer is 10 1/2.
10 1/2 bags of popcorn were left uneaten.
Step-by-step explanation:
Answer: ![x=\frac{37}{9}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B37%7D%7B9%7D)
Step-by-step explanation:
By the negative exponent rule, you have that:
![(\frac{1}{a})^n=a^{-n}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7Ba%7D%29%5En%3Da%5E%7B-n%7D)
By the exponents properties, you know that:
![(m^n)^l=m^{(nl)}](https://tex.z-dn.net/?f=%28m%5En%29%5El%3Dm%5E%7B%28nl%29%7D)
![(m^n)(m^l)=m^{(n+l)}](https://tex.z-dn.net/?f=%28m%5En%29%28m%5El%29%3Dm%5E%7B%28n%2Bl%29%7D)
Rewrite 4, 8 and 32 as following:
4=2²
8=2³
32=2⁵
Rewrite the expression:
![(2^2)^{(x-7)}*(2^3)^{(2x-3)}=\frac{32}{2^{(x-9)}}](https://tex.z-dn.net/?f=%282%5E2%29%5E%7B%28x-7%29%7D%2A%282%5E3%29%5E%7B%282x-3%29%7D%3D%5Cfrac%7B32%7D%7B2%5E%7B%28x-9%29%7D%7D)
Keeping on mind the exponents properties, you have:
![(2)^{2(x-7)}*(2)^{3(2x-3)}=32(2^{-(x-9)}](https://tex.z-dn.net/?f=%282%29%5E%7B2%28x-7%29%7D%2A%282%29%5E%7B3%282x-3%29%7D%3D32%282%5E%7B-%28x-9%29%7D)
![(2)^{2(x-7)}*(2)^{3(2x-3)}=(2^5)(2^{-(x-9)})\\\\(2)^{(2x-14)}*(2)^{(6x-9)}=(2^5)(2^{(-x+9)})\\\\2^{((2x-14)+(6x-9))}=2^{(5+(-x+9))}](https://tex.z-dn.net/?f=%282%29%5E%7B2%28x-7%29%7D%2A%282%29%5E%7B3%282x-3%29%7D%3D%282%5E5%29%282%5E%7B-%28x-9%29%7D%29%5C%5C%5C%5C%282%29%5E%7B%282x-14%29%7D%2A%282%29%5E%7B%286x-9%29%7D%3D%282%5E5%29%282%5E%7B%28-x%2B9%29%7D%29%5C%5C%5C%5C2%5E%7B%28%282x-14%29%2B%286x-9%29%29%7D%3D2%5E%7B%285%2B%28-x%2B9%29%29%7D)
As the bases are equal, then:
![(2x-14)+(6x-9)=5+(-x+9)\\\\2x-14+6x-9=5-x+9\\\\8x-23=14-x\\9x=37](https://tex.z-dn.net/?f=%282x-14%29%2B%286x-9%29%3D5%2B%28-x%2B9%29%5C%5C%5C%5C2x-14%2B6x-9%3D5-x%2B9%5C%5C%5C%5C8x-23%3D14-x%5C%5C9x%3D37)
![x=\frac{37}{9}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B37%7D%7B9%7D)
Answer:
9.5 is the distance between the two points rounded to the nearest tenth.