Nagaraj has a party-length sandwich that is 55 inches long and is to be cut into three pieces. The middle piece will be 4 inches longer than the shortest piece, and the shortest piece will be 9 inches shorter than the longest piece. How long will the pieces be?
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Answer:
S = 14 inches
M = 18 inches
L = 23 inches
Step-by-step explanation:
Let's being by defining our variables:
Shortest piece = S
Middle piece = M
Longest piece = L
So now we need to write down what formulas we're given:
"Nagaraj has a party-length sandwich that is 55 inches long and is to be cut into three pieces"
so we can start by knowing the S + M + L = 55
"The middle piece will be 4 inches longer than the shortest piece"
This means that M - 4 = S
"the shortest piece will be 9 inches shorter than the longest piece"
Finally, this means that S + 9 = L
What we need to do now is turn all of these things into the form of one letter. We can see that S is in all three of these equations, so lets solve everything in terms of S.
M = S + 4
L = S + 9
Now we can plug in both of those things into our first equation to get:
S + S + 4 + S + 9 = 55
and now we solve :)
3S = 42
S = 14
So now given this we can use this to solve the other three lengths
M = 14 + 4 = 18
L = 14 + 9 = 23
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The smallest unit is the ounce. We need to know the number of ounces there are in 1 gallon, 1 quart, and 1 pint
1 gallon = 128 ounces
1 quart = 32 ounces
1 pint = 16 ounces
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79 oz * 1gal/128 oz = 79 gal/128 = 0.617 gallon
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Here's the best way to solve ⇒
2/3 = x/48
Cross multiply them. ⇔ 2*48 = 3x
96 = 3x
x = 32
the missing value is 32
Because it is a proportion
2 × 48 = 3 × ?
96 = 3 × ?
Divide by 3 on both sides to isolate the unknown number
3 and 3 cancels out
32 = ?
The unknown number is 32
Answers
Let x be the rate of speed of slower cyclist
and x+10 = rate of speed of faster cyclist
Distance = Speed * Time
5x + 5(x+10) = 200
5x + 5x + 50 = 200
10x = 200-50
10x = 150
x = 15
Rate of speed of slower cyclist: 15 mph
Rate of speed of faster cyclist = 15+10 => 25 mph
Final answer:
In this problem, the speed of the faster cyclist is 25 mi/h and the speed of the slower cyclist is 15 mi/h. We determine this by setting up and solving an algebraic equation considering the total distance and time they traveled.
Explanation:
This problem is a typical example of relativerate and distance problems in algebra. First, define the speed of the faster cyclist as x m/h. Then, the speed of the slower cyclist is x-10 m/h. They travel towards each other, so their rates add up. That's why the equation becomes x+(x-10) = 200/5. We get this equation because the total distance they traveled is 200 miles (meeting in the middle), and they traveled for 5 hours.
Solving the equation x+(x-10) = 40 gives 2x-10 = 40, then 2x = 50, and finally x = 25. So, the faster cyclist is moving at 25 mi/h, and the slower cyclist is moving at 15 mi/h (25-10).
Learn more about Relative Rates here:
#SPJ2
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Answer: prism.
Step-by-step explanation:
Suppose you cut the objects horizontally.
The cylinder already has a circular base, so when you cut it you will have two cylinders, both with a circular base.
The sphere when cut in a horizontal line, will lead to two halves with a circular base of the same surface.
A cone already has a circular base, so when you cut it horizontally, you will end with a smaller cone (the top part that you cut) and the bottom part, that already had a circular base.
The prism has not circular sections, so it is kinda impossible to get a circular section when you cut a prism, then the correct option is a prism, this is because this is the only shape that has some faces confirmed by parallelograms.
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hope it helps