To find the measure of angle OPQ, we have two equations...
y+5x-17=180 because angles OPN and OPQ are supplementary...
AND
x+17+2x-4+y=180 because the total degrees of a triangle must add up to 180.
The equations...
5x+y=197
3x+y=167
solce the system of equations...
x=15
y=122
Since we wanted to solve for y, 122 is the answer.
The measure of angle OPQ is 122.
Sorry this took forever. The website is hard to use because I'm used to using the app:)
Best of wishes!
Answer:
3603 boxes.
Step-by-step explanation:
Rectangular Prism is actually a cuboid.
Volume of cuboid = length * width * height.
It is given that length = 16.5 m, width = 18.2 m, and height = 12 m. Therefore:
Volume = 16.5 * 18.2 * 12 = 3603.6 cubic meters.
Volume is actually the capacity of the shape. If the box has the volume of 1 cubic meters, then the number of boxes that can fit in the rectangular prism will be:
Number of boxes to be fit = Volume of Large container/Volume of Small Container.
Number of boxes = 3603.6/1 = 3603 boxes.
Therefore, 3603 boxes will fit the rectangular prism and 0.6 cubic meters will be the spare space!!!
Answer:
5 7/24
Step-by-step explanation:
First, you need to make the denominators the same. When you multiply 6 with 4 you get 24, and if you multiply 8 with 3 you get 24. Then you have to multiply the numbers you multiplied with the denominators with the numerator. So, 5 x 4 is 20 and 3 x 1 is 3. Once you put all the numbers together it should look like this: 3 20/24 and 9 3/24. In order to find the answer, you have to subtract the numbers from each other. Which would look like this: 9 3/24 - 3 20/24. But as you can see you can't subtract 3 from 20. So you have to carry the 9. This means you have to subtract 9 from 1, and then you have 27 for the numerator, this then makes it possible to subtract from 20. So then the fractions subtracted from each other is 7 and the whole numbers subtracted from each other is 5 (because the 9 is now 8 since we subtracted one from it). Whole numbers subtracted from each other: 5. Fractions subtracted from each other: 7/24. Add it together you get 5 7/24.
Numerator - the number above the fraction, ex 3 in 3/4
Denominator - the number below the fraction, ex 4 in 3/4
Answer:
A) 
Step-by-step explanation:
Answer:
To make the cup 64.57 square inches of plastic were used.
Step-by-step explanation:
A cup has the format of a cylinder with a open top. The surface area of the cup is given by the area of it's base (a circle) and the area of it's walls, wich can be seen as rectangle where the width is the length of the circle at the base and the height is the height of the cylinder. So we have:
area of the base = pi*r^2 = 3.14*(1.75)^2 = 3.14*3.0625 = 9.616 square inches
area of the walls = 2*pi*r*h = 2*3.14*(1.75)*5 = 54.95 square inches
surface area of the cup = area of the base + area of the walls = 9.616 + 54.95
surface area of the cup = 64.57 square inches
To make the cup 64.57 square inches of plastic were used.
