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serious [3.7K]
3 years ago
14

Solve the simultaneous equations. You must show all your working to find x and y. 1/2x -3y = 9 5x y + y = 28

Mathematics
2 answers:
dedylja [7]3 years ago
7 0

Answer:

\huge\boxed{x = 6 , y = -2}

Step-by-step explanation:

\sf \frac{1}{2} x - 3y = 9-----------(1)\\5x + y = 28 ----------(2)

Taking equation (1)

\sf \frac{1}{2} x -3 y=9

Multiplying both sides by 2

\sf x-6y = 18

Adding 6y to both sides

\sf x = 18+6y

Putting this in (2)

5(18+6y) + y = 28

5(18+6y) + y = 28

90 + 30y+y = 28

31y+90-28 = 0

31 y + 62 = 0

31y = -62

Dividing both sides by 31

y = -2

Now,

x = 18 + 6y

x = 18+6(-2)

x = 18-12

x = 6

mamaluj [8]3 years ago
6 0
1/2x - 3y = 9 (1)
5x + y = 28 (2)

(1) x 2
x - 6y = 18

(2) x 6
30x + 6y = 168
—————

x - 6y = 18 (3)
30x + 6y = 168 (4)

(3) + (4)
31x = 186
x = 6

sub x into (2)
30 + y = 28
y = -2
—————

x = 6
y = -2
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Describe how multiplying the width by 14 affects the perimeter and the area of the figure.
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Answer:

Step-by-step explanation:

Area of rectangle=width times height

Perimeter of rectangle=width plus width plus height plus height

If you have a rectangle that is 10 units  wide and 5 units tall.  The area would be 10X5=50units squared and the perimeter would be 10+10+5+5=30 units.

If you multiply the width by 14, everything changes.  10X14 is 140 units.  So the width of the rectangle is now 140 units while the height is 5.  The area would now be 140X5=700 Units squared and the perimeter would be 140+140+5+5=290 units.  

Area of triangle= base time height divided by 2

Perimeter of triangle= side plus side plus side

If its a triangle, let's say a right triangle 10 units at the base and 5 units in height.  The area will be 25 Units squared. 10X5=50 divide by 2=25 units squared.  If you multiply the base by 14....140X5=700 divide by 2=350.

I didn't figure out the perimeter of the triangle, because I'm being too lazy to figure out the length of the third side.

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3 years ago
Help with one last math question <br> thank u
Vitek1552 [10]
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3 years ago
For whole numbers between 1 and 1001, inclusive, let m be the sum of odd numbers and n be the sum of even numbers. What is the v
Svetradugi [14.3K]

Answer:

m - n = 501

Step-by-step explanation:

Remark

The first thing you have to do is find the number of odd and even numbers. This is where you have to be careful because there is a danger of being out by one.

equation

l = a + (n - 1)*d

Solution even

l = 1000

a = 2

d = 2

1000 = 2 + (n - 1)*2

998/2 = (n - 1) * 2 / 2

499 =  n - 1

n = 500

Solution odd

l = 1001

a = 1

d = 2

1001 = 1 + (n - 1)*2

1000 =  (n - 1)*2

1000/2 =  (n - 1)2/2

500 =  n - 1

501 = n

Sum Even of even numbers from 1 to 1001

Givens

a = 2

n = 500

l = 1000

Equation

Sum = (a + l ) * n / 2

Solution

Sum = (2 + 1000)*500/2

Sum = 1002 * 250

Sum = 250500

Sum of Odd numbers from 1 to 1001

a = 1

l = 1001

n = 501

Equation

sum = (a + l)*n/2

sum = (1 + 1001) * 501

sum = (1002)*501 / 2

Sum =  251001

Answer

m - n = 251001 - 250500 = 501

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