MATHEMATICS HIGH SCHOOL

Solve the following three variable system. 2x + 3y + 4z = 9
-x + 2y - z = 0
-2x + 4y + z = 3

Answers

Answer 1
Answer: 1)\ \ \ 2x + 3y + 4z = 9\n2)\ \ \ -x + 2y - z = 0\n3)\ \ \ -2x + 4y + z = 3\n===================================\n3)\ \ \ -2x + 4y + z = 3\ \ \ \Rightarrow\ \ \ z=2x-4y+3\n\n1)\ \ \ 2x + 3y + 4z = 9\ \ \ \Rightarrow\ \ \ 2x + 3y + 4(2x-4y+3) = 9\n2x+3y+8x-16y+12=9\n10x-13y=-3\n\n2)\ \ \ -x + 2y - z = 0\ \ \ \Rightarrow\ \ \ -x+2y-(2x-4y+3)=0\n-x+2y-2x+4y-3=0\n-3x+6y=3\ /:(-3)\nx-2y=-1\ \ \ \Rightarrow\ \ \ x=2y-1\n\n

1)\ \ \ 10x-13y=-3 \ \ \ \Rightarrow\ \ \ 10(2y-1)-13y=-3\n20y-10-13y=-3\n7y=7\ /:7\ \ \ \Rightarrow\ \ \ y=1\n\n2)\ \ \ x=2y-1\ \ \ \Rightarrow\ \ \ x=2\cdot2-1=1\n\n3)\ \ \ z=2x-4y+3\ \ \ \Rightarrow\ \ \ z=2\cdot1-4\cdot1+3=2-4+3=1\n\nAns.\ x=y=z=1

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The sum of three consecutive odd numbers is 75 what is the smallest of three numbers?? Please help

Answers

The smallest number would be 23.

     Let "n" represent the smallest odd number.
So the consecutive odd integers would be:
n
n+2
n+4 

Adding these 3 will give you 75.
Here's a breakdown: 

n + n+2 + n+4 = 75  
3n + 6 = 75
3n = 75 - 6
3n = 69 
n = 69/3
n = 23 

So here's how to find the consecutive numbers:
n = 23 < --- (smallest number)
n+2 = 23+2 = 25
n+4 = 23+4 = 27 

So, the three consecutive odd numbers are 23, 25, 27.

23+25+27 = 75

A rectangular field with an area of 5000m^2 is enclosed by 300m of fencing. Find the dimensions of the field? How?

Answers

area of field=xy=5000
perimeter of field=2(x+y)300
x+y=150
x=150-y
y(150-y)=5000
y^2-150y+5000=0
solve it
u get y= 50 or 100
then  x=100 or 50
therefore the dimensions are 100m and 50m 

Which of the following expressions is the conjugate of a complex number with −5 as the real part and 4i as the imaginary part? 5 + 4i / 5 − 4i / −5 − 4i/ −5 + 4i

Answers

The mathematical expression of the given complex number above is -5 + 4i. The conjugate of this complex number is that which has an opposite operation. The given is an addition operation. That is -5 - 4i. Therefore, the answer is the third among the choices. 

4 hours and 25 minutes before 2:05am​

Answers

4 hours and 25 minutes before 2:95 am would be 9:40pm

Answer:10:20 pm

Step-by-step explanation:

Time is seperated into 2 sets of 12 hours, am and pm; and 24 hours with each being 60 minutes. AM is morning and PM is afternoon.

The question is what time is 4 hours and 25 minutes before 2:05 in the afternoon. This means you subtract.

 205 - 425= -220

Then, because it is negative, you change it from am to pm and subtract   220 from 1200=

1200-220=980

9:80 is has too high a number in the minutes section (the second part) so you see how many sets of 60 are in 80. There is one set of 60 meaning there is one hour added to the hour side (the left side):

9+1: 80-60

10:20

10:20 pm is the final answer.

Hope this helped;)

Eight to the power of 2 plus three to the power of 2

Answers

Answer:  73

Step-by-step explanation:

8² = 64    3² = 9    64 +9 = 73

8 to the power of 2 means 8 × 8 that is 64

3 to the power of 2 means 3 × 3 that is 9

567 ÷ 12 with working out

Answers

Answer:

Step-by-step explanation:

567 ÷ 12

= 47.25

Answer:

47.25

Step-by-step explanation:
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