Answer:
129
Step-by-step explanation:
If three lines CD, CE and CF extend from point C, then the following addition postulate is true;
<DCE + <ECF = <DCF
If the space between line C D and C E is 75 degrees, then <DCE = 75
If the space between lines C E and C F is 54, then <ECF = 54.
Substitute the given values into the expression above will give;
<DCF =<DCE + <ECF
<DCF = 75+54
<DCF = 129
Hence the measure of <DCF is 129°
Answer:
81 x y^5
Step-by-step explanation:
Simplify the following:
9×3×3 x y^4 y
3×3 = 9:
9×9 x y^4 y
9 x y^4×9 y = 9×9 x y^(4 + 1):
9×9 x y^(4 + 1)
4 + 1 = 5:
9×9 x y^5
9×9 = 81:
Answer: 81 x y^5
The volume of the composite figure is the third option 385.17 cubic centimeters.
Step-by-step explanation:
Step 1:
The composite figure consists of a cone and a half-sphere on top.
We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.
Step 2:
The volume of a cone is determined by multiplying 
with π, the square of the radius (r²) and height (h). Here we substitute π as 3.1415.
The radius is 4 cm and the height is 15 cm.
The volume of the cone :
cubic cm.
Step 3:
The area of a half-sphere is half of a full sphere.
The volume of a sphere is given by multiplying 
with π and the cube of the radius (r³).
Here the radius is 4 cm. We take π as 3.1415.
The volume of a full sphere 
cubic cm.
The volume of the half-sphere 
cubic cm.
Step 4:
The total volume = The volume of the cone + The volume of the half sphere,
The total volume 
cub cm. This is closest to the third option 385.17 cubic centimeters.
Answer:
option A. Multiply the unpaid balance by the monthly interest rate
Step-by-step explanation:
Finance charges are the monthly service fee charged by lender on the credit used by borrower if they wish to skip the payment of monthly bill and carry forward it to next month.
So, we can calculate finance charges as monthly interest accrued on the unpaid balance.
Finance charges = Unpaid balance x Monthly interest rate.
Hence, option A is correct, i.e. Multiply the unpaid balance by the monthly interest rate.
Answer:
The width of the scale model is 33 inches.
Step-by-step explanation:
This question is solved making a relation with the scale model.
In the scale, 3 inches are worth 11 real feet.
The actual width of the building is 121 feet, so we find it's scale by a rule of three.
3 inches - 11 feet
x inches - 121 feet
Simplifying by 3, both sides
The width of the scale model is 33 inches.
