Answer:
Answer options
A. Two cities that are 7.5 cm apart on the map are actually 50 km apart.
D. Two cities that are actually 66 km apart are 9.9 cm apart on the map.
Step-by-step explanation:
Step 1
Indicate the scale as shown;
3 cm : 20 km, meaning 3 cm on the map represents 20 km on the ground
A). what does 7.5 cm represent on the ground
Distance on ground=(7.5×20)/3=50 km
B). what does 4 cm represent on the ground
Distance on ground=(4×20)/3=26.67 km
C). what does 45 km on ground represent on the map
Distance on map=(45×3)/20=6.75 cm
D). what does 66 km on ground represent on the map
Distance on the map=(66×3)/20=9.9 cm
Answer:
Step-by-step explanation:
The entered points belong to an increasing, linear function.
Equation: y = 1x + 4.
Answer:
![q^{-30}](https://tex.z-dn.net/?f=q%5E%7B-30%7D)
Step-by-step explanation:
Given the expression:
![((p^2) (q ^5)) ^{-4} X ((p ^{-4}) (q^5)) ^{-2}](https://tex.z-dn.net/?f=%28%28p%5E2%29%20%28q%20%5E5%29%29%20%5E%7B-4%7D%20X%20%28%28p%20%5E%7B-4%7D%29%20%28q%5E5%29%29%20%5E%7B-2%7D)
First, we open the outer brackets
![=(p^{2X-4}) (q ^{5X-4})X (p ^{-4X-2}) (q^{5X-2})\\\\=(p^{-8}) (q ^{-20})X (p ^{8}) (q^{-10})\\\\$Next, we can collect like terms\\\\=p^{-8}Xp ^{8}Xq ^{-20}Xq ^{-10}\\\\$Applying addition law of indices\\\\=p^{-8+8}Xq^{-20+(-10)}\\\\=p^0 X q^{-30}\\\\=1 X q^{-30}\\\\=q^{-30}](https://tex.z-dn.net/?f=%3D%28p%5E%7B2X-4%7D%29%20%28q%20%5E%7B5X-4%7D%29X%20%28p%20%5E%7B-4X-2%7D%29%20%28q%5E%7B5X-2%7D%29%5C%5C%5C%5C%3D%28p%5E%7B-8%7D%29%20%28q%20%5E%7B-20%7D%29X%20%28p%20%5E%7B8%7D%29%20%28q%5E%7B-10%7D%29%5C%5C%5C%5C%24Next%2C%20we%20can%20collect%20like%20terms%5C%5C%5C%5C%3Dp%5E%7B-8%7DXp%20%5E%7B8%7DXq%20%5E%7B-20%7DXq%20%5E%7B-10%7D%5C%5C%5C%5C%24Applying%20addition%20law%20of%20indices%5C%5C%5C%5C%3Dp%5E%7B-8%2B8%7DXq%5E%7B-20%2B%28-10%29%7D%5C%5C%5C%5C%3Dp%5E0%20X%20q%5E%7B-30%7D%5C%5C%5C%5C%3D1%20X%20q%5E%7B-30%7D%5C%5C%5C%5C%3Dq%5E%7B-30%7D)
Therefore:
![((p^2) (q ^5)) ^{-4} X ((p ^{-4}) (q^5)) ^{-2}=q^{-30](https://tex.z-dn.net/?f=%28%28p%5E2%29%20%28q%20%5E5%29%29%20%5E%7B-4%7D%20X%20%28%28p%20%5E%7B-4%7D%29%20%28q%5E5%29%29%20%5E%7B-2%7D%3Dq%5E%7B-30)
All numbers except for the square root of 50