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mamaluj [8]
3 years ago
10

Solve the following system of equations.

Mathematics
1 answer:
natita [175]3 years ago
5 0

That's a 3x3 linear system.  Let's do Gaussian elimination

4 3 1 -10   A

1 -3 2 -8   B

11 -2 3 -38 C

0 15 -7 22 D=A-4B

0 31 -19 50 E=C-11B

0 1 -7/15 22/15  F=D/15

1 0 3/5 -18/5  G=B+3F

0 0 -68/15 68/15 H=E-31F  -19-31(-7/15), 50-31(22/15)

0 0 1 -1    I=-15/68 H

1 0 0 -3   J=G - 3/5 I

0 1  0 1  K=F+ 7/15 I

We read off from the last three lines the

Answer: x=-3, y=1, z=-1



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Despite booming new car sales with their cha-ching
Elena-2011 [213]

Answer to the 1st question: 8 years

Answer to the 2nd question: The year 2022

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

Further explanation:

x = number of years after 2008

y = average price of a new car

The prices are going up by $1250 per year on average. This is the slope because the slope is the rate of change. So m = 1250.

The y intercept is b = 30100 as this is the price in 2008.

This leads us to go from y = mx+b to y = 1250x+30100

Plug in x = 0 and you should get y = 30100.

Also, plugging x = 6 into the equation leads to y = 37600 to help confirm things.

-----------------

Next, we plug in y = 47600 and solve for x.

y = 1250x+30100

47600 = 1250x+30100

47600-30100 = 1250x

17500 = 1250x

1250x = 17500

x = 17500/1250

x = 14

This means 14 years after the year 2008 is when the average new car price will be $47,600.

2008+14 = 2022

2022-2014 = 8

Therefore, <u>8 years</u> after 2014 (aka the <u>the year 2022</u>) is when the new car average price will be $47,600.

6 0
2 years ago
Which statement about 5 multiplied by 1/8 must be true?
Kipish [7]

Answer:

The product is less than 1.

Step-by-step explanation:

Since 5\times \frac{1}{8} = \frac{5}{1}\times \frac{1}{8}=\frac{5}{8}

and \frac{5}{8}= 0.625

which is less than 1, therefore we can say that the product is less than 1.

3 0
3 years ago
What is the awnser to the equation r-4+6r=3+8r I'm trying to find what “r” is and if you can please solve the problem step by st
sattari [20]
Remember that you can do anything to an equation as long as you do it to both sides except divide by zero
so you can add like terms like this
you can add similar things like 1+3 and m+2m and m^2+2m^2 but not unlke things like 1+m or m+m^2

so m+2m=1m+2m=3m so

r-4+6r=3+8r
use commutative property to move numbers around (a+b=b+a)
group like terms
r+6r-4=3+8r
add like terms
1r+6r-4=3+8r
7r-4=3+8r
subtract 7r from both sides
7r-7r-4=3+8r-7r
0r-4=3+1r
-4=3+r
subtract 3 from both sides
-3-4=3-3+r
-7=0+r
-7=r

r=-7
7 0
3 years ago
In a classroom,there are 12 girls and 8 boys.What fraction of the students in class are girls?What percent of the class are girl
tekilochka [14]

Answer:

Step-by-step explanation:

Add the total number of students:

Boys: 8, + Girls: 12 = 20 students

\frac{12}{20} = \frac{6}{10} of the students are girls

6/10 also equates to 60%, which is the percent of girls in the class.

4 0
4 years ago
the directions are : find the constant of proportionality for the graph and write in the form y = kx.n​​
Lelechka [254]

here is the answer (A) y=1/5 x

5 0
3 years ago
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