MATHEMATICS HIGH SCHOOL

Solve the following system of equations for all three variables.5x−2y+z = 8
−9x+2y+2z = 5
−9x−2y−5z = 4

Answers

Answer 1
Answer:   5x - 2y + 1z = 8 ⇒   5x - 2y + 1z = 8
-9x + 2y + 2z = 5 ⇒ -9x + 2y + 2z = 5
-9x -  2y -  5z = 4             -4x + 3z = 13

 5x -  2y + 1z = 8
-9x + 2y + 2z = 5 ⇒ -9x + 2y + 2z = 5
-9z -  2y -  5z = 4 ⇒ -9x -  2y -  5z = 4
                                        -18x - 3z = 9

     -4x + 3z = 13
    -18x - 3z =   9
           -22x = 22
            -22    -22
                x = -1
    -18x - 3z = 9
-18(-1) - 3z = 9
       18 - 3z = 9
     - 18       - 18
             -3z = -9
              -3     -3
                z = 3

    5x - 2y + z = 8
5(-1) - 2y + 3 = 8
     -5 - 2y + 3 = 8
     -2y - 5 + 3 = 8
           -2y - 2 = 8
                + 2 + 2
                -2y = 10
                 -2     -2
                   y = -5
          (x, y, z) = (-1, -5, 3)

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Round 32.697 to the nearest hundredths

Answers

32.697 is rounded to (32.7)because the hundreths place is 7 when the number is 5 and up you round up you round the tenths place up to 7

Plz help!!! I will give brainliest!!! No links!! Also plz explain how you got ur answer!Lainee brought a book to read on the way to California. Once we go to the hotel, she had read 5/6 of it. What fraction of the book does she have left to read?

Answers

1/6th left because she divided her book into 6ths and she red 5/6 and 5-6 is 1 so that means she still has 1/6 of the book to read

Answer:

1/6

Step-by-step explanation:

Because because there are six books in total and she only red 5 in the way

there are 720 children in our school. 5/8 of them have dark hair. How many children have blonde or red hair?

Answers

Assuming that the red and blonde hair are considered the 3/8ths of the school with light hair, 270 children in the school have red or blonde hair.

At what interest rate (to the nearest hundredth of a percent) compounded annually will money in savings double in five years?

Answers

For a single payment with compound interest, the equation to use is F=P(1+i)^n where F is the value after n periods, P is the present value, and i is the interest rate.

If we want the final value F to double in 5 years, F is then equal to P then n=5. The equation is now:

2P=P(1+i)^5
2=(1+i)^5
i=14.87% per year

Reese read twice as many pages Saturday than she read Sunday. If she read a total of 78 pages over the weekend, how many pages did Reese read Sunday?

Answers

Given:

Reese read twice as many pages Saturday than she read Sunday.

She read a total of 78 pages over the weekend.

To find:

The number of pages she read on Sunday.

Solution:

Let x be the number of pages she read on Sunday.

Reese read twice as many pages Saturday than she read Sunday. So, the number of pager she read on Saturday is 2x.

Total number of page she read over the weekend is:

Total=x+2x

Total=3x

She read a total of 78 pages over the weekend.

3x=78

x=(78)/(3)

x=26

Therefore, Reese read 26 pages on Sunday.

Write an equation that is perpendicular to the line y = 2x + 13?

Answers

An equation can't be perpendicular to a line, but the graph of the equation can.

When that happens, we recall that the slopes of perpendicular lines are negative reciprocals.

One line is the graph of [ y = 2x + 13 ].  The slope of the line is 2 .
So the slope of a line perpendicular to it must be -1/2 .

The equation of a line perpendicular to it is:    y = (-1/2 x) plus (any number).

The y-intercept of the perpendicular line doesn't matter.  Only its slope does.
k:\ y=m_1x+b_1\ \ \ and\ \ \ l:\ y=m_2x+b_2\n\nk\perp l\ \ \ \Leftrightarrow\ \ \ m_1\cdot m_2=-1\n------------------------\n\nk:\ y=2x+13\ \ \ \ and\ \ \ \ l:\ y=m_2x+b_2\n\n2\cdot m_2=-1\ \ \ \Leftrightarrow\ \ \ m_2=- (1)/(2) \n\nl:\ y=- (1)/(2) x+b_2\ \ \ and\ \ \ b_2\ \in\ R\n\nfor\ example:\n\ny=- (1)/(2) x,\ \ \ y=- (1)/(2) x+5 (1)/(7) ,\ \ \ y=- (1)/(2)x - √(13)\ ,\ ...
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