What are the coordinates of three points that lie on both planes of 20x+15y+12z=60 and 10x+30y+12z=60

Answers

Answer 1

Answer: 20x + 15y + 12z = 60 ⇒ 20x + 15y + 12z = 60
10x + 30y + 12z = 60 ⇒ 20x + 60y + 24z = 120
      -45y - 12z = -60
-45y + 45y - 12z = -60 + 45y
   -12z = -60 + 45y
      -12    -12
      z = 5 - 45/12y
      20x + 15y + 12(5 - 45/12y) = 60
      20x + 15y + 12(5) - 12(45/12y) = 60
   20x + 15y + 60 - 45y = 60
   20x + 15y - 45y + 60 = 60
   20x - 30y + 60 = 60
   -60   -60
   20x - 30y = 0
      20x - 20x - 30y = 0 - 20x
       -30y = -20x
      -30 -30
      y = 2x/3
      20x + 15(2x/3) + 12(5 - 45/12y) = 60
      20x + 10x + 60 - 45y = 60
      30x - 45y + 60 = 60
      -60 -60
      30x - 45y = 0
      30x - 45y + 45y = 0 + 45y
   30x = 45y
      30 30
   x = 3/2y
      20(3/2y) + 15(2x/3) + 12(5 - 45/12y) = 60
   30y + 10x + 60 - 45y = 60
       10x + 30y - 45y + 60 = 60
   10x - 15y + 60 = 60
       -60 -60
   10x - 15y = 0
   10(3/2y) + 30(2x/3) + 12(5 - 45/12y) = 60
      15y + 20x + 60 - 45y = 60
      20x + 15y - 45y + 60 = 60
          20x - 30y + 60 = 60
      -60 -60
      20x - 30y = 0
   10x - 15y = 0 ⇒ 20x - 30y = 0
   20x - 30y = 0 ⇒ 20x - 30y = 0
      -60y = 0
   -60 -60
   y = 0
   10x - 15(0) = 0
   10x - 0 = 0
      +0 +0
      10x = 0
       10 10
      x = 0
      20x + 15y + 12z = 60
      20(0) + 15(0) + 12z = 60
      0 + 0 + 12z = 60
      0 + 12z = 60
      12z = 60
   12    12
      z = 5
       (x, y, z) = (0, 0, 5)

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A nut mixture of almonds and cashew nuts at a small fair is $1.00 per pound of almonds and $3.55 per pound of cashew nuts. Over the entire day, 65 pounds of the nut mixture were sold for $189.95. If p is the number almonds and n is the number of cashew nuts, then the system of equations that models this scenario is: p+n=65 p+3.55n=189.95 Determine the correct description and amount of pounds for almonds and cashew nuts that were sold

Answers

Answer:

p is 16 and N is 49.

Step-by-step explanation:

Answer:

p = 16

n = 49

Step-by-step explanation:

p + n = 65

p + 3.55n = 189.95

To solve this system of equations, you have to use substitution. This means that you have to set one equation equal to one of the variables. You then have to substitute that variable into the second equation.

Rearrange the first equation so that it equals p.

p + n = 65

p = 65 - n

Substitute the p-value into the second equation.

p + 3.55n = 189.95

(65 - n) + 3.55n = 189.95

Solve for n.

65 - n + 3.55n = 189.95

65 + 2.55n = 189.95

(65 + 2.55n) - 65 = 189.95 - 65

2.55n = 124.95

(2.55n)/2.55 = 124.95/2.55

n = 49

Use this n-value to solve for p. You can pick whichever equation you want to solve for p and get the same answer. I will use the first answer.

p + n = 65

p + 49 = 65

(p + 49) - 49 = 65 - 49

p = 16

There are 16 pounds of almonds and 49 pounds of cashews.

Simplify with steps 9 to 3/2 power

Answers

$9^(3/2)$
9= $3^(2)$
= $3^(2)$ ^3/2
=27

Staci is attending a music festival. The ticket to the festival costs $87.96. Staci plans to purchase $30.00 t-shirts from the event for close friends. She is taking $200.00 to the festival. What is the maximum number of t-shirts Staci can purchase?

Answers

since stacy is bringing $200, and the initial cost is $87.96 you would have to subtract $200-87.96 which equals $112.04 this is the money left that stacy could buy shirts with, to figure out how many she needs you would have to do $112.04÷$30.00 this equals a decimal of 3.734666666666667 which would have to round down to 3 because stacy cant make it 4 shirts because she doesn't have enough money. So stacy can purchase a maximum of 3 shirts.
hope this helped:))

A function is _____ a relation.

A) always
B) sometimes
C) never

Answers

I believe that; A function is {A) sometimes} a relation.

A function is created to represent the balance on a credit card each month. What restrictions would be made to the range?A)The range would only include integers.
B)The range would only include positive integers.
C)The range would only include negative integers.
D)The range would include all real numbers.

Please, support your answer with an example.

Answers

Answer:

D)The range would include all real numbers.

Step-by-step explanation:

Range is all real number because function represent the balance on credit card each month. It may be cross over limit or lower limit.

If we purchase any goods using credit card balance will deduct from credit card and mark as negative number.

If we pay bill of credit card bill, this amount shows as positive number because any amount add to credit card.

In a month we purchased ,

Month Debit Credit

12/9/2018 $58.65

15//9/2018 $42.23

23/9/2018 $21.49

28/9/2018 $180.23

Total - $122.33 +$180.23

Net Balance in credit card = Debit + Credit = $57.90

Thus, Balance on credit card would be any real number.

It could include all real numbers, really. If you have +$130 you could use them to pay for something. If you have -$27.5 you need to pay this sum to the bank, since you overused your credit.

an exclusive clothing boutiques doubles the price of the item that purchases for resale part 1 out of 2 what is the Boutiques markup percent?

Answers

9514 1404 393

Answer:

100%

Step-by-step explanation:

The markup of the item is the difference between the sale price and the cost:

2 - 1 = 1 . . . . markup of 1 on cost of 1

The percentage markup is the ratio of markup to cost, converted to a percentage:

markup/cost × 100% = 1/1 × 100% = 100%

The boutique's markup percentage is 100%.

The percent that you get from multiplying both of them ?

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