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Montano1993 [528]
3 years ago
12

Which number goes in the box to make this a true number sentence? 7 × (3 + 9) = 21 +

Mathematics
2 answers:
Bumek [7]3 years ago
4 0
7(3 + 9) = 7(3) + 7(9) = 21 + 63
LekaFEV [45]3 years ago
4 0
The number that would go in the box is 63.   7X12=21+63
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A mountain has a peak of 7070 meters above sea level. A valley has a depth of 7460
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7,265 is the average of those two numbers, though i am not sure what the sign that is mentioned is
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2 years ago
If 1800ml of a juice drink is 15% grape juice, how much grape juice should be added to make a drink that is 20% grape juice?
Svetach [21]

Answer:

  112.5 mL

Step-by-step explanation:

Let x represent the amount of grape juice to add. Then the total amount of grape juice in the mix is ...

  0.15(1800) +x = 0.20(1800+x)

  270 +x = 360 + 0.2x . . . . . . eliminate parentheses

  0.8x = 90 . . . . . . . . . . . . . . . subtract 270+0.2x

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112 mL of grape juice should be added to make a mix that is 20% grape juice.

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3 years ago
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3 years ago
Read 2 more answers
A football is selling for $35 off the original price. The original price was $60. What is the sale price of the football?
Strike441 [17]
All you have to do it do 60 - 35 = 25 dollars because they want to know if the original price would be 60 dollars and they wanna know the anwser if you took away 35 dollars. so then you just subtract
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3 years ago
98 POINTS! PLEASE HELP! I been stuck on this assignment for over 2 weeks. My teacher gave me a simple explanation when I asked f
Colt1911 [192]

See the attached picture.

  • Create an equation for the volume of the box, find the zeroes, and sketch the graph of the function.

The resulting box has a volume

V(x)=x(8-x)(12-x)=x^3-20x^2+96x

because the volume of a box is the product of its width (12-x), length (8-x), and height (x).

  • find the zeroes

You know right away from the factored form of V(x) that the zeroes are x=0,8,12. (zero product property)

  • sketch the graph of the function

Easy to plot by hand. You know the zeroes, and you can check the sign of V(x) for any values of x between these zeros to get an idea of what the graph of V(x) looks like. See the second attached picture.

Here's what I mean by "check the sign" in case you don't follow. We know V(x)=0 when x=0 and x=8. So we pick some value of x between them, say x=1, and find that

V(1)=1(8-1)(12-1)=7\cdot11=77

which is positive, so V(x) will be positive for any other x between 0 and 8. Similarly we would find that V(x) for x between 8 and 12, and so on.

  • What is the size of the cutout he needs to make so that he can fit the most marbles in the box?

It's impossible to answer this without knowing the volume of each marble...

  • If Thomas wants a volume of 12 cubic inches, what size does the cutout need to be?

Thomas wants V(x)=12, so you solve

x^3-20x^2+96x=12

While this is possible to do by hand, the procedure is tedious (look up "solving the cubic equation"). With a calculator, you'd find three approximate solutions

x\approx0.1284

x\approx7.6398

x\approx12.2318

but you throw out the third solution because, realistically, the cutout length can't be greater than either of the sheet's dimensions.

  • What would be the dimensions of this box?

The box's dimensions are (x in) x (8-x in) x (12-x in).

If x\approx0.1284, then 8-x\approx7.8716 and 12-x\approx11.8716.

If x\approx7.6398, then 8-x\approx0.3602 and 12-x\approx4.3602.

8 0
3 years ago
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