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scoundrel [369]
3 years ago
10

X-y+4z=5 4x+z=2 x+5y+z=17

Mathematics
1 answer:
JulsSmile [24]3 years ago
6 0

Answer:x = 0, y = 3, z = 2

Step-by-step explanation:

The given system of equations is expressed as

x - y + 4z = 5 - - - - - - - - - - - - - -1

4x + z = 2

z = 2 - 4x- - - - - - - - - - - - - -2

x + 5y + z = 17- - - - - - - - - - - - - -3

From equation

Substituting equation 2 into equation 1 and equation 3, it becomes

x - y + 4(2 - 4x) = 5

x - y + 8 - 16x = 5

x - 16x - y = 5 - 8

- 15x - y = - 3 - - - - - - - - - - - - - -4

x + 5y + 2 - 4x = 17

x - 4x + 5y = 17 - 2

- 3x + 5y = 15- - - - - - - - - - - - - -5

We would eliminate y by multiplying equation 4 by 5 and equation 5 by 1. It becomes

- 1

- 75x - 5y = - 15

- 3x + 5y = 15

Adding both equations, it becomes

- 78x = 0

x = 0

Substituting x = 0 into equation 2, it becomes

z = 2 - 4 × 0

z = 2

Substituting x = 0 and z = 2 into equation 1, it becomes

0 - y + 4 × 2 = 5

- y + 8 = 5

y = 8 - 5

y = 3

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Step-by-step explanation:

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5 0
2 years ago
an angle measures 24° less than the measure if a supplementary angle . what is the measure of each angle​
vagabundo [1.1K]

Hey there!

If two angles are supplementary, that means that the measures of the two angles have a sum of 180.

If the two angles were of equal measure, they would both be 90 degrees.

The easiest way to get this would be to subtract 12 degrees from one 90 degree angle and add them to the other 90 degree angle so one angle has 24 more degrees then the other.

90 - 12 = 78

90 + 12 = 102

Let's check to make sure this works.

102 + 78 = 180 That checks out.

102 - 24 = 78 That also works.

So, the measures of the angles are 102 and 78.

Hope this helps!

4 0
3 years ago
14. Team 8A is selling snacks at the football game to raise money for a field trip. They are selling popcorn for $2.50 and pretz
Mamont248 [21]

Answer:

  • 40 popcorns and 90 pretzels sold.

============

Let the number of popcorns is x and pretzels is y.

Set up equations:

  • x + y = 130
  • 2.5x + 2y = 280

Solve by elimination, multiply the first equation by 2 and subtract from the second equation:

  • 2.5x + 2y - 2x - 2y = 280 - 2*130
  • 0.5x = 280 - 260
  • 0.5x = 20
  • x = 20/0.5
  • x = 40

Find y:

  • 40 + y = 130
  • y = 130 - 40
  • y = 90

5 0
1 year ago
Read 2 more answers
The perimeter of a playing field for a certain sport is 174 ft. The field is a rectangle, and the length is 45 ft longer than th
Leno4ka [110]

Answer:

21 ft by 66 ft

Step-by-step explanation:

From the question,

P = 2(L+W)............... Equation 1

Where P = Perimeter of the playing Field, L = Length of the playing Field, W = width of the playing Field.

If the Length of the Field is 45 ft longer than the width,

L = 45+W............ Equation 2

Substitute Equation 2 into equation 1

P = 2(45+W+W)

P = 90+4W............. Equation 3

Given: P = 174 ft.

Substitute into equation 3

174 = 90+4W

4W = 174-90

4W = 84

W = 84/4

W = 21 ft.

Substituting the value of W into equation 2

L = 45+21

L = 66 ft.

Hence the dimensions of the playing field is 21 ft by 66 ft

3 0
3 years ago
A man invests his savings in two accounts ,one paying6% and the other paying 10% simple interest per year. He puts twice as much
AnnyKZ [126]

Answer: he invested $46062.5 at 6% and $23031.25 at 10%

Step-by-step explanation:

Let x represent the amount which he invested in the account paying 6% interest.

Let y represent the amount which he invested in the account paying 10% interest.

He puts twice as much in the lower-yielding account because it is less risky.. This means that

x = 2y

The formula for determining simple interest is expressed as

I = PRT/100

Considering the account paying 6% interest,

P = $x

T = 1 year

R = 6℅

I = (x × 6 × 1)/100 = 0.06x

Considering the account paying 10% interest,

P = $y

T = 1 year

R = 10℅

I = (y × 10 × 1)/100 = 0.1y

His annual interest is $7370dollars. it means that

0.06x + 0.2y = 7370 - - - - - - - - - -1

Substituting x = 2y into equation 1, it becomes

0.06 × 2y + 0.2y = 7370

0.12y + 0.2y = 7370

0.32y = 7370

y = 7370/0.32

y = $23031.25

x = 2 × 23031.25

x = 46062.5

6 0
3 years ago
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