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katen-ka-za [31]
3 years ago
15

Sapphire and Abe are shelving books at a public library. Sapphire shelves 5 books at a time, where as Abe shelves 6 at a time. I

f they end up shelving the same number of books, what is the smallest number of books each could have shelved.
Mathematics
2 answers:
Crank3 years ago
7 0
The answer is 30 because 5×6=30 and 6×5=30.So the smallest number of books each could have shelved is 30 books...
iris [78.8K]3 years ago
6 0

Answer:

The smallest number of books each could have shelved = 30 books

Step-by-step explanation:

We have given that:

Sapphire shelves 5 books at a time and Abe shelves 6 books at a time.

If they end up shelving the same number of books, then we need to find  smallest number of books each could have shelved.

That means,  we need to find the smallest number that is the multiple of both 5 and 6.

Taking LCM of 5 and 6.

We get LCM of 5 and 6 is 30.

And 30 is the smallest number of books each could have shelved.




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Write the equation of the circle below to complete the square. Also determine the area of the circle.
diamong [38]

Answer: (x-7)^2+(y+2)^2=11^2 ; A=121\pi

Step-by-step explanation:

I have never done a problem like this, so this is my first time attempting it.

The standard form for the equation of a circle is:

(x-a)^2+(y-b)^2=r^2

Begin by grouping the 'x' terms and 'y' terms:

(x^2-14x)+(y^2+4y-68)=0

Complete the square for the second polynomial:

(\frac{b}{2} )^2=(\frac{4}{2} )^2=4

(x^2-14x)+(y^2+4y+4-4-68)=0

(x^2-14x)+(y^2+4y+4)-4-68=0

(x^2-14x)+(y^2+4y+4)-72=0

(x^2-14x)+(y+2)^2-72=0

Do the exact same process with the other polynomial:

(x^2-14x-72)+(y+2)^2=0

Complete the square:

(\frac{14}{2} )^2=49

(x^2-14x+49-49-72)+(y+2)^2=0

(x^2-14x+49)-49-72+(y+2)^2=0

(x^2-14x+49)-121+(y+2)^2=0

(x-7)^2-121+(y+2)^2=0

Bring the 121 to the other side to get:

(x-7)^2+(y+2)^2=121

(x-7)^2+(y+2)^2=11^2

The above expression is the equation of our circle in standard form. It is centered at the coordinates (7, -2) and has a radius of 11 units. The area of a circle if given by:

A=\pi r^2=121\pi

8 0
2 years ago
Please help whats the answer to this question ???
Nimfa-mama [501]

Answer:

C

Step-by-step explanation:

8 0
3 years ago
If u go to sleep at 9:30 p.m. and wake up at 6:30a.m. The next morning how long did u sleep
puteri [66]
Well first do this
12.00 - 9.30 = 2.30
2.30 + 6.30 = 9
You slept 9hrs
8 0
3 years ago
Read 2 more answers
Ms. Estrada plans to take 36 chocolate chip cookies to sell at a bake sale. She wants to bake enough to keep at least 24 cookies
Kruka [31]

Answer:

36-x≥24

Step-by-step explanation:

4 0
3 years ago
One third of a number reduced by 11 is equal to 4 more than the number
Alecsey [184]
1/3x -11 = 4+x is what we start with, then add 11 to both sides, then subtract x from both sides. Then when we divide both sides by -2/3, x will equal -22.5.
6 0
3 years ago
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